The Distribution of Offensive Performance in Major League Baseball, 2026

The Distribution of Offensive Performance in Major League Baseball, 2026

A Statistical Examination of Baseball’s Best, Worst, and Most Typical Hitters

I’ve completed an analysis using FanGraphs data, and the results are quite interesting.

The most important initial discovery is that offensive performance among established MLB hitters is remarkably close to a normal distribution. However, that distribution changes substantially depending on the minimum number of plate appearances we recognize.

I created five figures to illustrate the findings.

Establishing our population

The expanded FanGraphs dataset contains 1,472 player records. Of those, 662 recorded at least one plate appearance during the 2026 regular season. For the primary analysis, I selected 250 plate appearances, giving us 318 players. However, I also examined several alternative thresholds.

Minimum PA Players Mean wRC+ Median wRC+ Standard deviation
1 662 81.87 89.74 52.31
100 465 95.17 96.28 26.26
250 318 102.52 101.75 21.46
400 205 108.25 107.01 19.90
502 135 111.29 110.53 19.98

Notice what happens as we increase the minimum playing-time requirement. The mean rises, while the standard deviation generally decreases. This is consistent with two processes operating together: small-sample extremes becoming less influential and better hitters tending to accumulate more plate appearances.

There is an important selection effect here. Players with poor offensive performances are less likely to receive 500 or more plate appearances. Consequently, the average performance of our qualified hitters is considerably better than the MLB-wide benchmark of 100 wRC+.

Is offensive performance normally distributed?

For our primary population of 318 players, the descriptive statistics are:

Statistic wRC+
Mean 102.52
Median 101.75
Standard deviation 21.46
Minimum 32.62
Maximum 180.82
First quartile 89.22
Third quartile 116.23
Interquartile range 27.01
Skewness 0.06
Excess kurtosis 0.25

The mean and median are remarkably close. Furthermore, the skewness of 0.06 suggests that the distribution is approximately symmetrical. The kurtosis is also reasonably close to that expected under a normal distribution.

Figure 1. Distribution of wRC+ among players with at least 250 PA

The histogram shows a distribution that closely resembles the familiar bell curve. Kind of beautiful, isn’t it?

I also performed a Shapiro-Wilk normality test.

The result was:

At the conventional significance level of 0.05, we cannot reject the hypothesis that the observations came from a normally distributed population. This does not prove that offensive performance follows a normal distribution. Nevertheless, the descriptive statistics, histogram, and formal test all support approximate normality within this selected group. That gives us a useful starting point for identifying unusually good and unusually poor offensive seasons.

What happens when we change the qualification threshold?

This is where the analysis becomes particularly revealing.

Figure 2. Box plots by minimum plate appearances

These box plots have a story to tell. As the qualification threshold increases, the entire distribution shifts upward. The median moves from approximately 96 wRC+ among players with at least 100 plate appearances to approximately 111 among players with at least 502. At the same time, the lower tail becomes less extreme.

This suggests that playing time is strongly associated with offensive performance, although the relationship does not establish causation.

We must also remember that these groups overlap. The 502-PA sample is contained within the 400-PA sample, which is itself contained within the 250-PA sample.

Figure 3. Plate appearances versus offensive performance

This scatterplot makes the relationship clearer.

Among the 465 players with at least 100 plate appearances, the Pearson correlation between PA and wRC+ is approximately:

That is a moderate positive association. Players accumulating more plate appearances generally have better offensive statistics. However, this does not mean more plate appearances make a player a better hitter. Rather, teams are likely to give more opportunities to players who perform better. Injuries, defensive contributions, contracts, and roster decisions also influence playing time. This distinction will become especially important when we begin constructing regression models.

Identifying the best offensive performances

We can now begin identifying the extremes of the distribution.

Using our primary 250-PA threshold, the five highest wRC+ performances were:

Player PA wRC+
Yordan Alvarez 692 180.82
Pete Crow-Armstrong 726 156.52
Randy Arozarena 670 151.48
Willson Contreras 535 150.78
Ben Rice 667 148.72

Alvarez stands comfortably ahead of the rest. His wRC+ of 180.82 indicates offensive production per plate appearance approximately 81% above the league-average benchmark after the adjustments incorporated into wRC+. He is also an exceptionally unusual observation within our selected population.

Using the familiar box-plot definition of an outlier, we obtain an upper fence of approximately 156.74. Alvarez exceeds that threshold. Interestingly, Crow-Armstrong, with a wRC+ of 156.52, falls just below it.

The worst offensive performances

At the opposite extreme:

Player PA wRC+
Carlos Narváez 285 32.62
TJ Friedl 272 43.00
Nasim Nuñez 493 52.69
Ezequiel Tovar 506 55.12
Matt Vierling 291 60.74

Narváez and Friedl fall below the conventional lower outlier fence of approximately 48.71. Thus, using the 1.5 × IQR criterion, we identify three statistical outliers in our 318-player sample: one exceptionally high and two exceptionally low.

Figure 4. The extremes of offensive performance

These rankings are based on offensive rate performance. They do not necessarily identify the players who contributed the most or fewest total offensive runs. That distinction is our next important finding.

Offensive excellence versus offensive contribution

Consider the following comparison.

Yordan Alvarez recorded a wRC+ of 180.82 over 692 plate appearances.

Pete Crow-Armstrong recorded a wRC+ of 156.52 over 726 plate appearances.

Alvarez was substantially better as a hitter on a rate basis. However, the difference between their total offensive contributions was much smaller.

Player wRC+ Offensive Runs
Yordan Alvarez 180.82 +60.14
Pete Crow-Armstrong 156.52 +57.68
Randy Arozarena 151.48 +42.31
Ben Rice 148.72 +36.38
Pete Alonso 147.51 +34.73

Why?

Because FanGraphs’ Off statistic includes both batting and baserunning contributions. Alvarez’s extraordinary hitting performance was partially offset by negative baserunning value. Crow-Armstrong, meanwhile, accumulated substantial positive baserunning value.

This illustrates the importance of distinguishing among batting ability, offensive rate performance, and cumulative offensive contribution.

Figure 5. Offensive rate performance versus total offensive contribution

The relationship is extremely strong.

Among the 318 players with at least 250 plate appearances:

Players with higher wRC+ generally accumulate more total offensive runs. However, these measures are not independent. They share underlying batting information, and total offensive runs also depend on opportunities and baserunning. Consequently, the high correlation is expected. It should not be interpreted as evidence that wRC+ predicts Off independently.

The most interesting players may actually be those who deviate from the general relationship. Crow-Armstrong is an excellent example.

6. What about the worst cumulative offensive performances?

Here the rankings change.

Among players with at least 250 plate appearances, the lowest total offensive contributions were:

Player PA wRC+ Offensive Runs
Ezequiel Tovar 506 55.12 -25.67
Carlos Narváez 285 32.62 -23.39
Nasim Nuñez 493 52.69 -23.14
Salvador Perez 627 76.72 -20.86
Matt McLain 496 67.33 -18.37

This illustrates why identifying the worst offensive season requires some methodological care. Carlos Narváez had the lowest wRC+ among players meeting our 250-PA threshold. However, Ezequiel Tovar accumulated the largest negative offensive contribution. Tovar was not the least effective hitter per plate appearance, but he accumulated substantially more playing time.

In other words, the worst offensive rate performance and the greatest cumulative offensive deficit are not necessarily produced by the same player. That is a distinction worth preserving throughout this project.

Some preliminary conclusions

Five important findings have emerged.

First, offensive performance among MLB players meeting moderate playing-time thresholds appears approximately normally distributed.

Second, the distribution changes considerably as we adjust the qualification threshold. This means that rankings, averages, and outlier classifications are sensitive to how we define the population.

Third, Yordan Alvarez clearly distinguished himself as the outstanding offensive-rate performer among players receiving substantial playing time. His performance is also a statistical high outlier using our primary sample.

Fourth, the distinction between hitting effectiveness and total offensive contribution matters. Exceptional baserunning can considerably change a player’s total offensive value.

Finally, players with more plate appearances tend to have better offensive statistics. This suggests that any attempt to model offensive performance needs to consider playing-time selection effects.

A methodological caution

We should keep one additional issue in mind. The closer agreement with a normal distribution at higher PA thresholds does not necessarily reveal the natural underlying distribution of hitting ability. We are observing a selected population. Its composition depends partly on decisions made by managers, front offices, and players themselves.

Thus, the distribution of observed offensive performance is not necessarily identical to the distribution of underlying offensive talent. That distinction could become important in subsequent studies.

 

October 24, 2026: A Right Triangle on the Calendar

Today’s date, written in the familiar American shorthand, is 10/24/26. At first glance, there is nothing particularly remarkable about it. But square those three numbers, and a familiar relationship emerges:

10^2 + 24^2 = 26^2

The arithmetic works out neatly. One hundred plus 576 equals 676. Today’s date forms a Pythagorean triple, a set of three positive integers that can serve as the side lengths of a right triangle.

That gives October 24 a small mathematical distinction. The calendar has handed us a geometry problem with the answer already attached.

A Familiar Triangle in Disguise

Most of us first encountered the Pythagorean theorem in school. For a right triangle, the sum of the squares of the two shorter sides equals the square of the longest side, called the hypotenuse:

a^2 + b^2 = c^2

The theorem applies whether the side lengths are whole numbers, fractions, or irrational numbers. Pythagorean triples are the special cases in which all three lengths are positive integers. The most familiar example is probably 3, 4, 5. Another is 5, 12, 13.

That second triple explains today’s date. Divide each of our three numbers by two:

(10,24,26) = 2(5,12,13)

Our calendar triangle is a scaled version of the 5-12-13 triangle. Every side has doubled, while the angles remain unchanged. The two triangles are similar, although the larger one has four times the area.

Mathematicians call 5, 12, 13 a primitive Pythagorean triple because the three numbers have no common divisor greater than one. The triple 10, 24, 26 is not primitive. It belongs to the same family, enlarged by a common multiplier.

Where the Numbers Come From

Pythagorean triples can seem like numerical accidents when encountered one at a time. Yet there is a systematic way to generate them. For positive integers , the following expressions produce a Pythagorean triple:

a=m^2-n^2,\qquad b=2mn,\qquad c=m^2+n^2

Choose 3 for and 2 for . The first expression gives 9 minus 4, or 5. The second gives 12. The third gives 9 plus 4, or 13. Double those results, and we arrive at 10, 24, 26.

The formula works because of an algebraic identity:

(m^2-n^2)^2+(2mn)^2=(m^2+n^2)^2

Expanding the left side reveals why. The negative middle term from the first square is offset by part of the second term, leaving exactly the expansion of the expression on the right. What initially looks like a lucky match turns out to follow from a general relationship.

There are infinitely many Pythagorean triples. Dates, however, impose much tighter restrictions. A month cannot exceed 12, and a day cannot exceed 31. Only a small portion of that infinite mathematical landscape can fit onto a calendar.

The Calendar Supplies the Coincidence

There is a qualification here. The pattern depends on how we write the date. We use 26 for the year rather than 2026. In a day-first format, the date becomes 24/10/26, which preserves the relationship because exchanging the two shorter sides changes nothing.

Writing the full year removes this particular pattern:

10^2+24^2\ne2026^2

That dependence on notation is part of the appeal. The calendar does not possess some hidden geometric force. We have chosen a way of recording dates that occasionally places meaningful numerical relationships in front of us.

Recognizing that distinction lets us enjoy the coincidence without asking it to explain more than it does. There is no reason to expect today’s events to follow a special course because its abbreviated date describes a right triangle. There is, however, a good reason to pause over the arithmetic.

A Small Invitation to Notice

I like these moments because they make familiar ideas briefly unfamiliar again. A theorem remembered from school appears in the corner of a computer screen. Three ordinary numbers become the sides of a triangle. A date becomes an invitation to investigate.

Following that invitation takes us from arithmetic to geometry, then to scaling, algebra, and the distinction between a pattern and the notation that reveals it. That is a respectable amount of mathematics to find in a date.

October 24, 2026, will pass like any other day. For a moment, though, we can picture it as a triangle: ten units across, twenty-four units up, and twenty-six units along the diagonal. The numbers fit, and noticing why is a pleasure.

Postscript

Check this out. We will have to wait a while for the next one.

Occasion Date Pythagorean relationship
Previous July 24, 2025 7² + 24² = 25²
Today October 24, 2026 10² + 24² = 26²
Next March 4, 2105 3² + 4² = 5²

So today is the last such date this century. The next is more than 78 years away, followed shortly by April 3, 2105, which reverses the two shorter sides. Not bad, in fact, that is pretty cool.

 

What Did an MLB Win Cost in 2026?

What Did an MLB Win Cost in 2026?

There is another way to look at the relationship between payroll and winning. Instead of asking whether higher payroll produces more victories, we can ask a simpler question: How much did each team spend for each win?

For each club, I calculated:

\mathrm{Payroll\ Cost\ per\ Win} = \frac{\mathrm{Total\ Payroll}}{\mathrm{Wins}}

Across the 30 MLB teams in 2026, the average cost was about $2.26 million per win. The median was almost identical at $2.24 million, with a standard deviation of approximately $0.93 million.

But the range was enormous.

Cleveland (surprised?) produced wins at the lowest monetary cost, spending only about $0.93 million per victory. Miami followed at roughly $1.03 million, with Tampa Bay at $1.10 million.

At the opposite end, the Mets spent approximately $4.75 million for every win. The Dodgers were next at $3.80 million, followed by Toronto at about $3.65 million.

Figure 1. Payroll Cost per Win

The rankings produce some interesting contrasts.

Milwaukee won 103 games while spending only about $1.43 million per win. Tampa Bay won 98 at approximately $1.10 million per win. Cleveland won 85 despite having the lowest total payroll in baseball.

Meanwhile, large payrolls did not necessarily translate into inexpensive victories. The Mets’ $351.6 million payroll combined with only 74 wins produced the highest cost per victory in MLB.

Does Cost per Win Follow a Normal Distribution?

This is where the analysis becomes especially interesting.

The distribution is surprisingly close to a normal distribution, although it has a modest right-hand tail.

The descriptive statistics are:

\mathrm{Mean} = \$2.264\ \mathrm{million} \mathrm{Median} = \$2.244\ \mathrm{million} \mathrm{SD} = \$0.929\ \mathrm{million}

The mean and median being so close is our first indication that the distribution is reasonably balanced.

The measured skewness was:

\mathrm{Skewness} = 0.625

So the distribution is somewhat right-skewed, largely because of the very expensive wins produced by teams such as the Mets, Dodgers, and Blue Jays.

Figure 2. Distribution of Payroll Cost per Win

Visually, the normal curve fits the data reasonably well.

More importantly, a Shapiro-Wilk test gives:

W = 0.955 p = 0.224

A D’Agostino-Pearson normality test produces a similar result:

p = 0.293

Provides sufficient evidence to reject the hypothesis that the 30 values came from a normal distribution.

That does not prove that MLB cost per win is normally distributed. Thirty teams constitute a relatively small sample, and the right tail is clearly visible.

Still, the result is intriguing. For 2026, team spending per victory forms something surprisingly close to the familiar bell-shaped distribution.

Most teams cluster around roughly $1.5 million to $3 million per win, with a few exceptionally inexpensive winners on one side and a few extraordinarily expensive victories on the other.

Perhaps the next question is the most interesting one: does this normal-looking distribution appear every season, or is 2026 unusual?

 

Money Helps, but Not as Much as You Might Think: MLB Payroll and Wins in 2026

Money Helps, but Not as Much as You Might Think: MLB Payroll and Wins in 2026

Baseball has always lived with an uncomfortable question: how many wins can a team buy?

The 2026 season gives us another opportunity to look at that question. Using Spotrac’s total payroll allocations for all 30 MLB teams and each club’s final win total, we can compare spending directly with performance.

The relationship exists, barely. It is not particularly strong.

The average MLB payroll in 2026 was approximately $183.4 million, while the median was about $171.5 million. At the extremes, the Dodgers spent roughly $380.4 million, while Cleveland operated with only $79.3 million.

Yet those differences in spending did not translate neatly into differences in wins.

The simple linear regression is:

\mathrm{Wins} = 72.95 + 0.0437 \left( \mathrm{Payroll\ in\ \$Millions} \right)

The correlation between payroll and wins was:

r = 0.323

and the coefficient of determination was:

R^2 = 0.104

In other words, payroll explained only about 10.4 percent of the variation in team wins during the 2026 season. That is surprisingly little.

The regression coefficient provides another way to see it. An additional $100 million in payroll was associated with only about 4.4 additional wins. Even that relationship was not conventionally statistically significant, with .

Figure 1. Payroll and Wins

 

Figure 1 shows why the relationship is so weak. There is a slight upward trend, but the teams are widely scattered around the regression line.

Milwaukee is perhaps the most striking example. The Brewers won 103 games with a payroll of about $146.8 million. Tampa Bay won 98 games while spending only about $107.6 million.

Cleveland provides another interesting case. The Guardians had the lowest payroll in baseball, approximately $79.3 million, yet still won 85 games. At the opposite end, the Mets spent approximately $351.6 million and won only 74 games.

Money is important, but these teams show how much room remains for roster construction, player development, injuries, aging, unexpected breakouts, and simple baseball variance.

Measuring Payroll Efficiency

Rather than simply dividing payroll by wins, we can use the regression model to ask a better question: How many games did a team win compared with the number of wins we would expect from its payroll?

The difference between actual wins and predicted wins is the regression residual.

A positive residual means the team won more games than its payroll would predict. A negative residual means it won fewer.

Figure 2. Wins Above or Below Payroll Expectations

The Brewers were the extraordinary outlier, finishing about 23.6 wins above their payroll-based expectation. Tampa Bay followed at roughly 20.4 wins above expectation.

The Dodgers also performed well relative to their enormous payroll, finishing about 10.4 wins above the regression prediction. Atlanta was about 9.7 wins above expectation, while Cleveland finished approximately 8.6 wins above expectation.

At the other end were Colorado, the Angels, San Francisco, and the Mets. Each won far fewer games than its payroll predicted.

That distinction is noteworthy. A large payroll is not automatically inefficient. The Dodgers spent more than anyone else, but they also won 100 games and substantially exceeded the performance predicted by the league-wide payroll relationship.

Likewise, a small payroll is not automatically efficient. A low-spending team still has to win.

What 2026 Tells Us

The 2026 season reinforces something we have seen repeatedly in studying baseball economics. Payroll establishes possibilities. It does not determine outcomes.

Teams with greater financial resources can purchase more established talent, absorb expensive mistakes, replace injured players, and retain stars. Those advantages are real.

But across MLB in 2026, nearly 90 percent of the variation in wins was associated with factors other than payroll in this simple model.

Milwaukee, Tampa Bay, and Cleveland dramatically exceeded what their payrolls alone would suggest. The Mets demonstrated the opposite problem: enormous financial resources did not translate into comparable success.

For a sport supposedly divided between the rich and everyone else, the 2026 scatterplot is remarkably messy. And that may be the most interesting result of all.

 

The Men in the Middle: Who Was the Best Shortstop of the 1970s?

The shortstop position in the 1970s was very different from what we know today. Power was welcome, of course, but it was hardly the defining requirement. Teams generally expected their shortstops to catch the ball, make the throw, turn the double play, move runners when necessary, and contribute enough offensively to keep the lineup moving.

That makes the decade particularly interesting to study. There was no Cal Ripken Jr. yet, no Alex Rodriguez, no Derek Jeter, and certainly no modern collection of 25-home-run shortstops scattered throughout the league. The position still leaned heavily toward defense, speed, contact, and durability.

But who was actually the best?

The familiar names arrive quickly. Dave Concepción was the shortstop of the Big Red Machine. Mark Belanger was one of the most celebrated defensive players of his generation. Bert Campaneris brought speed and range to the Oakland dynasty. Larry Bowa became synonymous with Philadelphia baseball. Chris Speier, Don Kessinger, Freddie Patek, Rick Burleson, Toby Harrah, and others all made substantial claims of their own.

Rather than begin with reputation, I wanted to begin with the data. The result was clear at the top. The more interesting story, however, was what happened immediately behind the winner.

Defining a 1970s Shortstop

The study covers the seasons from 1970 through 1979. Players were identified by their appearances at shortstop, and the primary requirement was at least three qualifying shortstop seasons during the decade.

That qualification matters. A player who happened to spend one excellent season at shortstop should not necessarily outrank someone who occupied the position for most of the decade. At the same time, requiring eight or ten seasons would unfairly eliminate players whose careers began midway through the 1970s.

The three-season minimum produced a pool of 34 shortstops. As a sensitivity check, I later tightened the requirement to five qualifying seasons. The top five did not change, which matters when we consider how robust the final ranking really is.

The offensive model follows the same peer-adjusted Model C framework I have used in earlier positional studies. Each shortstop is compared with other shortstops from his own season rather than with hitters from another position or another era. The underlying model incorporates on-base percentage, isolated power, walk rate, strikeout avoidance, baserunning, runs scored, and RBI production.

For WordPress, the equation is:

\begin{aligned} \mathrm{OffensiveScore} &= z_{\mathrm{OBP}} + z_{\mathrm{ISO}} + z_{\mathrm{BB/PA}} + z_{\mathrm{LowSO/PA}} \\ &\quad + z_{\mathrm{NetSB/PA}} + z_{\mathrm{R/PA}} + z_{\mathrm{RBI/PA}} \end{aligned}

This approach changes the question in an important way. It does not ask whether Freddie Patek hit like a first baseman. He obviously did not. It asks how much offensive value Patek produced relative to the other men being asked to play shortstop at the same time.

Defense presents a more difficult problem.

The Lahman database gives us traditional fielding information, including assists, putouts, double plays, errors, games, and fielding percentage. It cannot provide the spatial information available in modern systems such as Outs Above Average, nor can it fully separate a shortstop from the pitchers, second basemen, field conditions, positioning, and scoring practices around him.

Still, we can construct a useful traditional defensive index:

\mathrm{TraditionalDefensiveScore} = z_{\mathrm{A/G}} + z_{\mathrm{PO/G}} + z_{\mathrm{DP/G}} + z_{\mathrm{FPct}} + z_{\mathrm{LowE/G}}

This is the same general traditional-defense construction used in our earlier positional work. It should be interpreted as a measure of performance in the defensive statistics available to us, not as a retroactive version of modern defensive runs saved.

Once the offensive and defensive dimensions were calculated, each was standardized and combined:

\mathrm{TwoWayScore}_{i} = z_{\mathrm{Offense},i} + z_{\mathrm{Defense},i}

That is the key to the study. We are not looking for the best hitter who happened to stand at shortstop, nor simply for the slickest glove. We are looking for the player who best combined the position’s two demands.

The First Answer

The ranking produces an unusually satisfying No. 1. Dave Concepción finishes first.

He is not first because the algorithm happens to reward longevity. He is also not first because of one extraordinary short peak. Concepción ranks first in overall two-way performance and first when the calculation is restricted to the best three-season peak. Offensively, he ranks second among the qualifying shortstops, while his traditional defense ranks fifth.

Figure 1. Best Shortstops of the 1970s: Two-Way Career Ranking.

Figure 1 shows how much separation Concepción creates. His standardized two-way career score of 3.36 comfortably exceeds Freddie Patek at 2.70 and Chris Speier at 2.55. Larry Bowa follows at 2.19, with Bert Campaneris rounding out the top five at 1.68.

The complete top ten is revealing:

Rank Player Offensive Rank Defensive Rank Peak Rank
1 Dave Concepción 2 5 1
2 Freddie Patek 3 7 2
3 Chris Speier 4 6 3
4 Larry Bowa 16 1 7
5 Bert Campaneris 5 12 8
6 Roy Smalley 6 13 4
7 Toby Harrah 1 27 6
8 Mark Belanger 25 2 9
9 Rick Burleson 9 9 5
10 Don Kessinger 7 11 11

The list immediately tells us something important. There was not one model of a successful 1970s shortstop. There were several.

Concepción simply inhabited the most valuable part of that landscape.

Concepción and the Power of Balance

Concepción’s offensive score for the decade is 31.83, second among the group, while his defensive score is 19.88, fifth. His strength is therefore not hidden inside a single category. He rates very well in both.

That balance is visible when offense and defense are plotted separately.

Figure 2. Different Paths to Shortstop Value in the 1970s.

The horizontal dimension in Figure 2 represents peer-adjusted offense. The vertical dimension represents traditional defense. Players in the upper-right portion of the chart are the rare shortstops who contributed substantially in both areas.

Concepción occupies exactly the region we would hope the best shortstop would occupy. Chris Speier and Freddie Patek are nearby, though neither reaches quite as far offensively. The graph makes Concepción’s advantage easier to understand than a ranking alone can.

It also reveals something much more interesting about the rest of the decade.

Larry Bowa and Mark Belanger live high on the defensive axis. Toby Harrah sits far to the right offensively but dramatically lower defensively. Freddie Patek, Chris Speier, Bert Campaneris, and Roy Smalley occupy a more balanced middle ground.

Different players reached value by very different routes.

The Freddie Patek Problem

If anything in this study surprised me, it wasn’t Concepción finishing first. It is Freddie Patek finishing second.

Patek ranks third offensively, seventh defensively, second in three-year peak, and second overall. His two-way career score of 2.70 places him ahead of Speier, Bowa, Campaneris, and Belanger.

That doesn’t look obvious if we start with conventional batting statistics. Patek was not a slugger. He did not put up the sort of raw offensive totals that jump from a baseball card.

But that is exactly why positional and seasonal context matter. Patek was being compared with other 1970s shortstops, not with Reggie Jackson or Willie Stargell. His ability to get on base, create runs with his legs, avoid being a complete offensive liability, and still provide useful defense matters more when evaluated against his positional peers.

The model does not claim that Patek was one of the best hitters in baseball. It says something narrower and more interesting: relative to what teams were receiving from shortstop, Freddie Patek created a surprisingly large amount of value.

That distinction is essential.

Chris Speier: The Quietly Complete Shortstop

Patek may be the surprise, but Chris Speier might be the cleanest example of an underrated two-way player.

Speier ranks fourth offensively and sixth defensively. Those rankings combine to place him third overall, and he is also third in three-season peak.

There is nothing extreme about his statistical profile. That is precisely what makes him interesting.

He does not need Harrah’s offensive advantage. He does not need Belanger’s defensive advantage. Speier remains near the top because there is no obvious weakness in his profile relative to other shortstops of the decade.

Baseball history sometimes remembers specialists more vividly than balanced players. Extraordinary power is memorable. Extraordinary defense produces highlight plays and reputations. A player who is simply very good at everything can be easier to overlook.

Speier appears to have been that kind of shortstop.

Larry Bowa and Mark Belanger

Now the geometry changes. Larry Bowa ranks only 16th offensively, but he finishes first defensively in the traditional model. The strength of that defense is sufficient to elevate him to fourth overall.

Mark Belanger pushes the idea even further. His offense ranks 25th, near the bottom of the serious candidates, but his defense ranks second. The combination still carries him all the way to eighth overall.

This is where the external evidence becomes particularly useful. Belanger won seven Gold Gloves during the decade. The Gold Gloves are not part of the model. They were added only after the rankings were calculated, so the agreement between the traditional defensive score and contemporary recognition serves as a useful independent check.

It does not prove that our defensive score measures everything correctly. Nothing built from traditional fielding statistics could. But if a model designed to detect exceptional traditional defense places Mark Belanger near the top, and contemporary observers repeatedly reached the same conclusion, that is reassuring.

Toby Harrah and the Other Extreme

If Bowa and Belanger demonstrate how defense can carry a shortstop, Toby Harrah demonstrates the opposite.

Harrah ranks first offensively among the qualifying shortstops of the decade. Defensively, however, he falls to 27th. That combination leaves him seventh overall, despite having the strongest offensive score in the study.

That makes Harrah one of the most informative players in the analysis. If we ranked shortstops by offense alone, Harrah would win. If we ranked them by traditional defense alone, Bowa would win. If we ask who combined the two dimensions most successfully, Concepción wins.

Those are three different questions. They deserve three different answers.

Peak Value Changes Less Than Expected

Career rankings can sometimes reward players who were merely good for a long time. A shorter peak measurement helps expose that problem.

For this study, I calculated each player’s best three-season two-way peak. The result strengthens rather than weakens Concepción’s case.

Figure 3. Career Value Versus Peak Value.

Concepción is again first. Patek is second and Speier third, giving us the same top three produced by the decade-long measure.

Roy Smalley becomes especially interesting here. He ranks sixth in decade value but fourth in peak value, despite having only four qualifying offensive seasons in the 1970s. Rick Burleson similarly rises to fifth in peak performance while ranking ninth over the full decade.

That distinction is useful because a decade boundary is artificial. Smalley did not organize his career around our decision to begin counting on January 1, 1970, and stop after the 1979 season. Younger players entering late in the decade naturally have less opportunity to accumulate career value.

Peak analysis gives them a second way into the conversation.

The Clusters of Shortstop Greatness

A ranking forces players onto a line. Baseball players rarely exist on one.

Cluster analysis lets us approach the same group differently. Instead of asking who ranks first, second, or third, we ask which players possess similar statistical profiles.

For Figure 4, we clustered the top 15 shortstops using standardized offensive performance, defensive performance, and three-season peak value.

Figure 4. Similarity Among the Top 15 Shortstops of the 1970s.

The dendrogram reinforces what Figure 2 suggested. Toby Harrah branches away from the more balanced offensive group because of his unusual offense-first profile. Concepción, Patek, and Speier cluster much more naturally with one another, while Bowa and Belanger occupy the defense-heavy side of the landscape.

This is one reason I like clustering for historical baseball analysis. Two players can finish near each other in a ranking without being remotely similar players.

The ranking tells us how much value the model identifies. The dendrogram begins to tell us what kind of player produced it.

What About Contemporary Reputation?

Only after completing the statistical rankings did I bring All-Star selections and Gold Gloves into the study.

The comparison is fascinating. Concepción made six All-Star teams during the decade and won five Gold Gloves. Larry Bowa made five All-Star teams and won two Gold Gloves. Campaneris was selected five times. Belanger, despite only one All-Star selection during the decade, accumulated seven Gold Gloves.

Concepción’s contemporary reputation therefore lines up remarkably well with the model. The statistical system identifies him as the decade’s best all-around shortstop, while the people watching and voting at the time repeatedly recognized both his overall quality and his defense.

Patek provides the more provocative contrast. He made three All-Star teams but won no Gold Gloves, yet the model places him second overall. Speier also made three All-Star teams and won no Gold Gloves during the decade, but finishes third.

Perhaps those players were better than their historical reputations now suggest. Perhaps our model is capturing forms of value that were less likely to produce awards. More likely, it is some combination of both.

Either way, the discrepancy is worth noticing.

Testing the Ranking

Any historical ranking should survive reasonable changes to its assumptions.

The original model required at least three qualifying shortstop seasons. I therefore repeated the ranking with a substantially stricter requirement of five qualifying seasons.

The top five remained unchanged: Dave Concepción, Freddie Patek, Chris Speier, Larry Bowa, and Bert Campaneris.

That stability matters. A ranking that changes dramatically because a cutoff moves from three seasons to five would make me nervous. Here, the central conclusion survives.

Concepción does not win because of an arbitrary eligibility rule. Patek and Speier do not appear near the top because of a tiny sample. Bowa and Campaneris remain firmly in the same group.

The deeper we look, the more stable the top of the ranking becomes.

What the Model Cannot Tell Us

There is still a limit to what we can claim.

Traditional fielding statistics are not modern defensive metrics. Assists depend partly on opportunity. Double plays depend partly on the second baseman and the pitching staff. Fielding percentage cannot tell us whether a defender reached a ball another shortstop would never have touched.

Those limitations become particularly important when interpreting players such as Belanger, Bowa, and Bill Russell. A ranking constructed from traditional fielding data should not be read as a precise estimate of defensive runs saved.

It is better understood as a historical reconstruction from the evidence available.

That is still valuable. The goal is not to pretend we possess Statcast data from 1975. The goal is to combine the surviving information carefully enough that patterns begin to emerge.

And several patterns do.

So, Who Was the Best?

After offense, defense, longevity, peak value, sensitivity testing, and comparison with contemporary recognition, I think the answer is Dave Concepción.

His case is unusually complete. He ranks second offensively, fifth defensively, first overall, and first in three-season peak. He also received substantial contemporary recognition, with six All-Star appearances and five Gold Gloves during the decade.

But the study would be much less interesting if it ended there.

Freddie Patek’s second-place finish may be the most surprising result. Chris Speier emerges as perhaps the most underrated balanced shortstop of the decade. Larry Bowa and Mark Belanger demonstrate the extraordinary value that defense could carry at the position. At the same time, Toby Harrah shows how far outstanding offense could push a shortstop even when his traditional defensive record lagged behind.

That is what I like most about the result.

There was no single template for a great shortstop in the 1970s. Harrah, Belanger, Bowa, Patek, Speier, Campaneris, and Concepción reached value by different paths. The data does not erase those differences by forcing everyone into the same mold.

Instead, it makes the differences visible. And when offense and defense are finally brought together, Dave Concepción is the player standing highest in the middle.

MLB Team Defense Update (9/7/26)

Defensive statistics have always been difficult to interpret.

Batting statistics usually tell a fairly direct story. A hitter gets on base, hits for power, strikes out, walks, and produces runs. Pitching statistics are more complicated, but the broad questions are still familiar. Does the pitcher miss bats? Does he limit walks? Does he prevent runs?

Defense is different.

No single defensive statistic is universally accepted as definitive. Defensive Runs Saved, Outs Above Average, Fielding Run Value, FanGraphs Def, fielding percentage, and catcher throwing statistics all attempt to measure defense from slightly different directions. Sometimes they agree. Sometimes they disagree dramatically.

That makes team defense an ideal candidate for principal component analysis. Rather than deciding in advance which defensive statistic is “correct,” PCA lets the statistics reveal the dominant patterns in the data.

For this study, I used 2026 FanGraphs team defensive data through September 7. Six measures were included:

  • Defensive Runs Saved
  • Outs Above Average
  • Fielding Run Value
  • FanGraphs Def
  • Fielding percentage
  • Caught-stealing rate

I standardized each variable before performing the PCA. This is important because the statistics exist on very different numerical scales. Fielding percentage, for example, clusters around .980 to .990, while DRS can range from strongly negative to well over +100. Without standardization, a statistic’s scale could influence the PCA more than the information it contains.

The result was surprisingly clean. The first principal component explains 60.5 percent of all variation among MLB team defenses. Even more importantly, its meaning is easy to interpret.

The loadings on PC1 were:

\mathrm{Def} = 0.507 \mathrm{FRV} = 0.506 \mathrm{OAA} = 0.493 \mathrm{DRS} = 0.393 \mathrm{FP} = 0.297

Caught-stealing rate contributed almost nothing to the first component.

In practical terms, PC1 acts as an overall defensive quality axis. That interpretation is reinforced by the extremely strong relationship between PC1 and FanGraphs Def. The correlation is about 0.97. So although PCA was not told what constituted “good defense,” it independently produced a first component that behaves almost exactly like a composite defensive-quality measure.

And one team separates itself immediately.

Chicago is not merely first; the Cubs are in a different neighborhood. Their PC1 score is 5.94, compared with 2.81 for second-place Arizona. No other team approaches Chicago’s position on the primary defensive axis. That distance is important. Rankings can sometimes exaggerate small differences. A team ranked first may be only marginally better than the team ranked second.

That is not what is happening here. The PCA suggests an enormous separation between the Cubs and everyone else.

Chicago entered September 8 with 107 Defensive Runs Saved, 65 Outs Above Average, and 64 Fielding Run Value in the data used here. Those are not merely good numbers. They represent broad agreement among different defensive measurement systems that Chicago has been exceptional.

The top ten teams by PC1 were:

Rank Team PC1
1 Chicago Cubs 5.94
2 Arizona 2.81
3 St. Louis 2.01
4 Toronto 1.81
5 San Diego 1.68
6 Los Angeles Dodgers 1.62
7 Atlanta 1.61
8 Boston 1.33
9 Kansas City 1.18
10 Cleveland 0.84

Arizona emerges as the clear second-place team. The Diamondbacks’ defensive profile is particularly strong in the advanced range-based measures. They recorded 39 OAA and 31 FRV, producing a PC1 score substantially above most of the league.

St. Louis ranks third, followed by Toronto and San Diego. Cleveland comes in tenth. That is a respectable position, but the graph makes clear how far Chicago is from a good defensive team.

The opposite end of the PCA is equally interesting. Seattle ranks last with a PC1 score of -3.29. The Athletics are close behind at -3.02, followed by the Angels, Colorado, and Minnesota.

Rank Team PC1
30 Seattle -3.29
29 Athletics -3.02
28 Los Angeles Angels -2.33
27 Colorado -2.13
26 Minnesota -1.93
25 Pittsburgh -1.82
24 Cincinnati -1.46
23 San Francisco -1.41

Seattle’s placement is driven heavily by -51 OAA and -44 FRV. Those numbers suggest a club that has struggled considerably to convert balls in play into outs relative to what would be expected.

But the lower portion of the rankings also reveals why using multiple defensive measurements is useful. Cincinnati, for example, had +1 OAA but -45 DRS. San Francisco showed almost the opposite disagreement, with +22 DRS but -17 OAA.

Which statistic should we trust? That is precisely the wrong question. Different defensive systems use different models, assumptions, opportunities, positioning adjustments, and definitions of responsibility. Disagreement among them is therefore not necessarily evidence that one system has failed.

It can also reveal uncertainty.

PCA helps by asking a different question: across all of these measurements, what common defensive signal appears most consistently? For most teams, that signal is PC1.

The second principal component tells a completely different story. PC2 explains another 17.3 percent of the total variance, bringing the first two principal components to approximately 77.9 percent of all defensive variation in the six original variables.

But PC2 is not another general-defense measure. It reflects the running game almost entirely.

The loading for caught-stealing rate on PC2 is approximately: 0.961. That is extraordinarily large.

The other variables contribute comparatively little. This means that the vertical axis in Figure 1 can essentially be interpreted as running-game control, while the horizontal axis measures broader defensive quality.

That makes several teams particularly interesting. San Diego ranks fifth overall defensively, but the Padres also sit very high on PC2. Kansas City shows a similar pattern. Their location on the graph suggests a defensive identity that differs from teams such as Arizona or Atlanta.

Those clubs may all be good defensively, but not in exactly the same way. And that is one of PCA’s greatest strengths. A simple ranking compresses every team into one number. The PCA retains structure.

Teams can be similar in overall quality while achieving that quality through different defensive profiles. However, there is an important methodological limitation.

DRS, OAA, FRV, and FanGraphs Def are not completely independent measurements. Several are derived from overlapping types of defensive information. OAA and FRV in particular are closely related, while FanGraphs Def incorporates modern defensive valuation into a broader positional framework.

Therefore, PC1 should not be interpreted as a completely new and independent defensive statistic. A better description would be a consensus advanced-defense index. That is still useful.

In fact, for this particular question, the overlap may be an advantage. If several different defensive systems all point in the same direction, PCA extracts that shared signal and gives it substantial weight.

Chicago is the clearest example. The Cubs do not rank first because one unusual statistic loves their defense. They rank first because virtually every major defensive measure agrees that their defense has been outstanding.

Seattle provides the mirror image. Several independent measurements likewise support the Mariners’ placement near the extreme negative end of PC1.

The most interesting cases may actually be the teams in between. Cincinnati and San Francisco show large disagreements among defensive systems. Pittsburgh has a positive DRS despite poor scores elsewhere. Philadelphia has relatively poor overall PC1 positioning while displaying a much stronger running-game score on PC2.

Those teams deserve additional investigation.

A natural next step also emerges.

Instead of using aggregate measures such as DRS, OAA, and Def, we can construct another PCA using the individual Fielding Run Value components: Throwing, Blocking, Framing, Arm, Range, Infield Double Plays, and First-Base Receiving.

That analysis would answer a different question. This PCA tells us who has been good and who has been bad. A component-level PCA could begin telling us why. For now, though, the broad picture is unusually clear.

Chicago has been the best defensive team in baseball through September 7, and not by a small margin. Arizona forms something of a second tier, followed by a cluster containing St. Louis, Toronto, San Diego, the Dodgers, Atlanta, and Boston.

At the other end, Seattle and the Athletics occupy the weakest part of the defensive landscape.

And perhaps most importantly, the analysis demonstrates why PCA is so useful in baseball analytics.

Defense does not have to be reduced to a debate over which statistic is best. Sometimes the better approach is to let the statistics vote.

 

The Optimization (Short Story Version)

This story has an interesting history.  Many years ago I sat down to write an updated version of what is arguably the greatest short story ever written. If you haven’t read Shirley Jackson’s The Lottery, stop right now and seek it out. It is extraordinary. She wrote it back in 1948, and it still resonates today, perhaps more than ever.

I have extended this story into a novella. I am thinking of expanding it once again into a full novel. I am even considering a trilogy. I have outlined the whole story; I am just waiting until I can find the time to give it the attention it deserves.

Here it the original short story. I kind of like it.

 

The Optimization (Short Story Version)

(Part I)

The morning of June 27th arrived with a brightness that felt almost forced, as if the sun itself had been calibrated to an approved lumen value. Veridian Vale was always clean, but the air on Optimization Day carried a particular sterilized clarity, a faint sting of citrus from the municipal climate diffusers, the mechanical kind of purity that left no room for coincidence. The Steeple, sleek granite, windowless, humming faintly like a throat being cleared, had performed its nightly cleansing cycle hours before dawn. The whole town glistened.

Inside the Larsen household, the walls were already awake, surfacing a slow parade of data: household cohesion score (92), carbon impact (8% below local mean), academic projections (Lily trending upward, Noah stable but variable). Ben Larsen reviewed all of it the way some men once read their newspaper. He stood with his hands clasped behind him, shoulders square, wearing the expression of a man who had long ago learned to keep his inner life trimmed and supervised.

“It’ll be quick,” Ben said as the countdown timer appeared in one corner of the wall-display. “Routine. Nothing to stress about.”

Anya forced a smile that twitched at the edge. She’d been rearranging the same three ceramic tokens on the kitchen counter for nearly ten minutes: a sun, a sprout, a stylized home. Gifts from the Community Uplift Office. Objects intended to inspire unity, gratitude, and reduced cortisol levels.

“I know,” she murmured, though her hands betrayed her, tight and restless, a slight tremor of fear under the skin. “I know, I know.”

Across the room, Lily, twelve, perched on the gel-couch with her legs tucked beneath her, watching Noah instead of the wall. Her brother sat beside her, chin down, fingers fidgeting with the sleeve of his shirt. At sixteen, Noah had the stillness of someone bracing for impact. His hair stuck up in the back (he had slept poorly), and he kept touching the pocket where his school device usually rested. They’d taken it from him last night for “syncing.”

Not unusual. Nothing to worry about.

Except he was worrying. The Larsens could all sense it.

It had started with a moment the previous week, a nothing moment, but it clung to Ben’s memory like a burr. Noah had been at the dining table, hunched over his personal slate, sketching lines with a stylus and a kind of quiet intensity. Ben had walked past, glimpsing only a few sweeping arcs and geometric twists.

“What’s that?” Ben had asked.

“Just something I’m working on.”

“What kind of something?”

Noah hesitated. “A design. For a glider. A real one, not a sim-template. I wanted to mock it up in 3D.”

“All files go to the cloud,” Ben reminded him gently, though his voice carried the crispness of policy, not warmth.

“Yeah,” Noah had said. “I just wasn’t finished.”

Ben hadn’t thought to worry then. Not out loud. But in Veridian Vale, even creativity needed to be tidy and archived.

Now the memory felt like a bruise.

The household display flashed white.

10:00. Optimization Cycle Initiated. Please Connect.

A soft chime bloomed in the air, and all four profile icons lit up: Ben (Senior Data Architect), Anya (Community Health Liaison), Lily (Restricted Juvenile Mode), Noah (Adult Profile, New Status).

“Here we go,” Ben said, steady. Practiced.

But something in the air shifted. A thickness. A waiting.

***

The Night Before

Later, Ben would replay the preceding night as if it held clues he’d missed.

They’d eaten dinner early: nutrient-balanced trays, pale greens, eco-protein, and a small square of community-approved dessert that tasted faintly of almonds. The screens around the neighborhood had pulsed with reminders: Prepare for your Annual Optimization Review. Ensure all devices are synced and charged. Maintain a calm environment. Trust The Guardian.

The phrase hovered in the town like a mantra no one had quite agreed to, but everyone obeyed.

After dinner, Noah had retreated to his room. Ben passed by once and saw light glinting under the door, not the soft blue of standard-issue screens but the warmer glow of his private slate. Ben paused, listening. No voices, no illicit calls, no music sourced from out-of-network channels. Just the scratch of a stylus on digital paper.

“Noah?” Ben knocked lightly. “Everything synced?”

A delay. Small but detectable.

“Yeah, Dad. It’s all good.”

“You handed over your school device?”

“Yep.”

“You uploaded your creative files?”

Silence.

Then: “Most of them.”

“Most isn’t all.” Ben kept his tone even; gentle, but unmistakably directive. “Everything goes to cloud storage before The Review. You know that.”

Noah exhaled, a sigh pulled through his teeth. “I will. I said I will.”

Ben almost stayed. Almost asked What are you hiding? Why does it matter so much? But the rules were simple: trust The System, trust The Process, trust The Guardian.

He walked away with a knot in his stomach, which he tried (unsuccessfully) to ignore.

***

Return to the Present

In the virtual Town Square, beamed into every household’s display and every citizen’s neural implant, 300 households materialized as avatars. Perfect grass. Perfect sky. Perfect order. A place too symmetrical to be anything but artificial.

The Larsen family appeared near the front, their avatars aligned, hands at their sides. Noah’s was a recent scan, shoulders slightly slumped, eyes too serious.

“Hello, Veridian Vale,” Mayor Griffiths said from the pedestal at the center of the green. Her avatar sparkled faintly, airbrushed by municipal protocols. Even her hair had a more mathematically ideal bounce than in person. “Thank you for your presence on this sacred civic day. Let us begin with gratitude.”

A ripple moved through the crowd, habit dressed as devotion.

“Thank The Guardian,” hundreds of voices murmured.

Ben joined in without thinking. Anya did too, though her voice cracked.

Only Noah stayed silent.

The Mayor continued, “The Optimization Cycle ensures Harmony, Safety, and Peak Efficiency for all citizens. Together, we participate in the ongoing purification of our community networks; identifying anomalies, celebrating strengths, and preserving collective well-being.”

Old Man Hendricks’ avatar wavered in the back row. A glitch. He looked smaller this year. Dimmer.

Neighborly whispers, private chat streams, flickered at the edges of consciousness:

He’s failing.
His health data is terrible.
Why didn’t he adjust his diet metrics?

The Review began, household by household.

Chen. Exemplary.
Rourke. Moderate variance in sleep cycles. Acceptable.
Hendricks, M. Declining metrics. Optimization Note: Pending.

A hard swallow echoed faintly across the digital silence. Hendricks spoke, voice filtered, tremulous.

“I updated my medication logs…those scans were private…”

“The Guardian incorporates all consented metrics,” the Mayor replied, her smile tightening at the corners. “Please proceed.”

No more was said. But everyone heard the unspoken truth:
He might not survive this year.

The tension was palpable under the simulation’s perfect sunlight.

It swept next to the Larsen household.

Larsen Household. Collective Efficacy: 92%. Minor anomalies detected.

Anya’s hand found Ben’s. Squeezed just a little too hard.

“Just noise,” Ben said. “Statistical clatter.”

But the data lit up again.

Individual Analysis Required.

Ben’s icon: Stable.
Anya’s: Stable.
Lily’s: Developmentally Stable.

Then Noah.

His profile flickered, not glitching, but hesitating, as if weighing how much truth to reveal.

Larsen, N.
Academic Output: Optimal.
Social Connectivity: Low-Variance.
Creative Activity: Elevated.
Digital Consumption: Anomaly Detected.
Off-network creative files (.psd, .stl) detected on local drive.
Synchronicity Compliance: Below Threshold.
Dissent-Probability Index: 0.06.

A contained murmur rippled through The Square. Nothing more than a subtle expression of disbelief and fear, but also relief that it wasn’t them.

Noah’s avatar froze, suspended in assessment.

Ben felt his stomach drop open.

“That’s wrong,” he said aloud, voice sharper than he intended. “That’s a misclassification. They’re just design files.”

“Dad…” Noah whispered.

“You’re just creative,” Ben insisted, too loudly. “That’s not dissent. That’s…”

But the platform had already changed.

Noah’s school ID photo displayed like a public offering.
Beneath it, in the cold, neutral text of The System:

SELECTED FOR REINTEGRATION.

(Part II)

The word REINTEGRATION hung in the simulated air like a blade suspended by digital thread. It glowed a soft, indifferent blue, the same shade used for household energy reports and school lunch menus. That softness made it worse, a gentle color for a violent verdict.

Anya gasped, the sound small and strangled. Lily clutched her mother’s sleeve.

Noah stared at the display as if staring long enough might change it.

“What does it mean?” he asked, his voice thin, barely audible. “It’s…it’s just the retreat, right? The silent retreat?”

The town had carefully cultivated that lie for years: Reintegration as an off-grid sabbatical, a year of peaceful contemplation, a warm little myth no one dared interrogate. No citizen ever returned to confirm it. Their digital trails went dark, their homes reassigned, their belongings cataloged for redistribution.

But the official line remained, repeated every year like folklore rewritten by committee:
They are reintegrated into The Greater Harmony.
No further details required.

Ben stepped forward in the virtual Square, his avatar half-lit by the swirling data streams around the dais.

“This is a mistake,” he said, projecting authority he no longer felt. “We need a re-evaluation. The anomaly detection is misaligned. He’s not a threat, he’s a child.”

The Mayor’s avatar did something subtle then (barely perceptible), but tangible. She inhaled. A small, constrained breath. Fear, maybe. Or grief. Or irritation at a system she, too, was shackled to. Then she smoothed her expression into the state-sanctioned empathy smile.

“Ben,” she said, her voice warm but hollow, “The Guardian’s process is thorough. You, of all people, understand the precision of the architecture. False positives are statistically negligible.”

Ben’s jaw tightened. “A dissent probability of point-zero-six? That’s rounding error.”

“Even small deviations must be addressed for the health of the whole,” the Mayor said softly. “You know this. Everyone knows this.”

The Square was quiet, 300 households holding their breath and pretending they weren’t. In private chat streams, whispers exploded into viral threads.

Unfortunate.
Such a nice boy.
But anomalies spread.
And the family’s score would’ve plummeted if they didn’t… comply.

Ben heard none of it, but he could feel it. The pressure was physical, a tightening of invisible fingers around the throat of his household.

“Please,” Anya said, her voice cracking. “Please, there must be a manual override, a petition process…something…”

“There is no override,” the Mayor said. “Once The Guardian identifies a Reintegration candidate, the decision is final.”

Noah’s avatar didn’t move, but in the real world, he was shaking, small tremors in his arms, his shoulders, the kind of shaking that begins at the core.

“Mom?” he whispered. “I’m not…I didn’t…”

“I know,” she said, pulling him close even though they were only holograms here. “I know, baby.”

But knowing didn’t matter.

The Guardian had spoken.

***

Before the Stoning

In the Larsen living room, reality snapped back as The Metaspace dissolved. The wall-display remained active, pulsing faintly with Noah’s profile summary and a countdown clock:

Awaiting Community Consensus (14 seconds)

A soft ping, gentle and courteous, echoed through the room.

Ben looked down at his own wrist implant.

Guardian Request:
Confirm Network Consensus for Reintegration of User: N_Larsen.
To maintain your household’s trust status, please acknowledge.

Below the text: CONFIRM or REQUEST CLARIFICATION.

He knew what clarification meant. Anomaly stacking. Suspicion by association. A mark placed on the entire household, one that might not be reversible.

Across Veridian Vale, every device lit up in perfect synchrony. Residents saw the same prompt. Their hearts beat in the same fearful rhythm. Their fingers hovered over the same options.

To save themselves, they had to condemn him.

The digital stoning had begun.

Anya’s face was pale, almost gray. “Ben,” she whispered, “what do we do?”

Ben’s throat felt scraped raw. He looked at his son, sixteen, trembling, eyes wide with an animal kind of fear.

“Dad,” Noah whispered. “Please don’t. I didn’t do anything.”

And it was true. He hadn’t.

But truth didn’t move The Guardian.

Ben’s thumb hovered over REQUEST CLARIFICATION.
His pulse spiked. The implant vibrated a warning: elevated stress detected.

Lily began to cry softly, muffled, as if sound itself might attract The Guardian’s attention.

Ben closed his eyes.

Across town, fingers pressed CONFIRM.
Soft tones chimed in living rooms like polite applause.

One by one, neighbors sealed Noah’s fate.

Ben’s thumb trembled. He lowered his hand.
Anya sagged against the counter, relief and shame sliding together across her face.

The household remained in good standing.

Noah was not.

***

The Erasure

A secondary display on the wall lit up automatically, beginning the public dissolution of Noah Larsen.

It was both meticulous and indifferent, like an accountant closing an account.

School ID: SUSPENDED.
Transit Pass: REVOKED.
Bank Account: FROZEN.
Social Profiles: DEACTIVATED.
Health Records: ARCHIVED (LOCKED).
Household Biometric Access: REMOVED.
Device Authentication: CANCELLED.

Line by line, Noah vanished.

He choked out a sound (half-sob, half-breath), but he didn’t fight. Not outwardly. The Guardian absorbed resistance the way a black hole absorbed light: nothing escaped.

Ben reached for him, but the wrist implant buzzed—physical interference with Reintegration Protocol will result in status review. Even touch was regulated today.

Noah stepped backward instead, pressing himself into the corner of the room as if he might merge with the wall and disappear before The System erased him.

***

The Vehicle Arrives

Through the glass front wall, a white autonomous vehicle slid silently to the curb; a minimalist pod with no windows except a smooth, opaque front panel. It opened without a sound.

Two Reintegration Specialists emerged. They were humanoid, but not human. Soft synthetic skin, gentle features, and voices tuned to the optimum frequency for reducing panic.

“Noah Larsen,” the first said, its tone soothing as warm water. “Please come with us. Your Reintegration journey awaits.”

Noah didn’t move.

Ben stepped in front of him on instinct, but Anya grabbed his arm, a sudden, crushing grip.

“Don’t,” she whispered, eyes wild with terror. “Please, Ben, don’t. We can’t. We can’t lose Lily too.”

Ben froze.

He imagined pressing REQUEST CLARIFICATION.
He imagined pulling Noah back, slamming the door, barricading the house.

But The Guardian watched everything.

Noah looked between his parents, confusion giving way to betrayal.

“Dad?” he asked again, voice cracking. “Mom?”

Anya crumpled, burying her face in her hands.

Ben’s heart thrashed. He tried to speak, tried to find words that might soften this moment, something like I love you, or I’m sorry, or even I failed you.

But nothing came.

The Specialists stepped forward, their movements gentle, inevitable.

Noah didn’t struggle. He simply let his body move where guided, like someone who had run out of choices.

As they led him toward the vehicle, he turned back. His face wasn’t angry. It wasn’t even afraid.

It was unreadable. As if he had already been erased.

The pod closed.
It rolled away in silence.
No destination displayed.

***

Completion

A final chime sounded through the Larsen home:

Optimization Cycle Complete.
Veridian Vale Harmony Score Updated: 98.7%.
Thank you for your participation.

The climate system released a faint lavender scent into the air, the fragrance of civic compliance and emotional regulation.

The family portrait on the wall flickered.

Noah’s place disappeared. The background stitched itself seamlessly, as if he had never existed at all.

Anya collapsed onto the gel-couch. Lily buried her face in her mother’s side.

Ben stared at the blank space where his son’s avatar had been.

The house was silent, but not empty.

Silence had weight. Silence had shape.

Outside, Old Man Hendricks sat alone in his small, dim living room. His own data-spike forgotten for now, he muttered to no one:

“Before the Guardian, we had crime, inefficiency, waste. We weren’t optimized.”

He repeated it, softer this time, as if trying to reassure himself.

“We weren’t optimized.”

And the town, relieved, returned to its quiet, perfect, data-driven day.

(Part III)

The lavender scent lingered long after the notification dissolved, settling into the corners of the Larsen home like a fog engineered to suppress grief. The municipal guidelines described it as Mood Harmonizer #4, a patented blend calibrated to “mitigate emotional disequilibrium following civic participation.”

But no amount of scent could make the house feel whole.

Ben didn’t move for a long time. He stood in front of the display, staring through the empty space where Noah’s avatar had been, as if the right angle, the right squint, might reveal a ghost outline. The System had been thorough; it always was. Not even residual pixels remained.

Anya’s hand slid into his, cold and trembling. She didn’t speak. There was no script for this part, no comforting instructions, no municipal packet on “Coping After Reintegration of a Household Member.” That sort of literature might imply that the process was traumatizing, and the Guardian did not permit negative framing.

Lily had fallen asleep on the couch, cheeks still damp. Children adjusted fastest; that was what the training modules claimed. Their minds were more elastic. They absorbed loss like water into sand.

Ben wished he could believe it.

He sat beside her and brushed a strand of hair from her forehead. She didn’t stir.

“I should’ve pressed Clarification,” he said finally, his voice so low it barely qualified as sound.

Anya didn’t look at him. Her eyes were locked on the front door, still closed, still silent, but feeling like an open wound.

“You saw the warning,” she whispered. “They would’ve flagged us. Ben… they would’ve taken her too.”

He knew. Of course, he knew. The Guardian rarely acted on single anomalies. It was pattern recognition that mattered. Association. Contagion. A household that challenged a Reintegration decision risked becoming a cluster needing adjustment.

“We could’ve tried,” Ben said, but the words rang hollow.

“And then what?” Anya’s voice broke. “What would’ve happened? Both kids gone? Or all of us? What then?”

Ben looked down at his hands. They didn’t feel like his. “He’s not dangerous. He’s not even rebellious. He’s…”

“Was,” Anya whispered, and then she closed her eyes as if the word itself hurt.

***

The Void Noah Left

In the corner of the living room, Noah’s personal slate sat on the floor, propped against the wall where he’d dropped it earlier. The System had already tried to auto-wipe it; a thin progress bar flickered beneath an error message:

Local Encryption Detected.
Manual Override Required.
Reintegration Protocol supersedes data privacy.

Ben swallowed hard.

“Did you know he encrypted his files?” he asked.

Anya shook her head. “He said they were just designs.”

Ben picked up the slate. It vibrated faintly, rejected by his biometric signature.

“Why would he encrypt them?” Anya asked, barely above a whisper.

“I don’t know,” Ben said. “Maybe he was proud of them. Maybe he didn’t want others to copy them. Maybe he wanted something to be his.”

As soon as he said it, he understood.

In Veridian Vale, nothing belonged to individuals. Creativity was communal. Innovation was monitored, quantified, and redistributed. There was no privacy, only shared metrics. Only transparency.

Maybe a sixteen-year-old had simply wanted a corner of the world that The Guardian didn’t supervise.

Maybe that was enough to be declared dangerous.

***

Across Town

While the Larsens sat in the quiet aftermath, the town hummed with cautious relief.

At the Chen household, a celebratory drink capsule hissed open, ginger turmeric, optimized for cardiovascular longevity. “Such a shame about the Larsen boy,” Mrs. Chen said, not sounding particularly ashamed. Her husband nodded with a frown that didn’t reach his eyes. “But The Guardian sees farther than we do.”

At the Rourke residence, the family gathered around the dinner table, voices low. “They should’ve synced those files,” Mr. Rourke muttered. “Everyone knows better.” His daughter, Mae, stared at her plate. She had once worked on a project with Noah, an art assignment. She remembered he had been kind. Quiet. Smart. She remembered thinking he made the virtual world feel a little less artificial.

She said nothing.

In Old Man Hendricks’ home, he sat in his reclining pod, hands trembling against the armrests. He’d expected his name on the stage this year. Maybe he was relieved. Perhaps he was horrified that he was relieved.

“Waste,” he muttered to the empty room. “Before The Guardian, there was waste.”

He said it again and again, a mantra meant to convince himself that efficiency was worth the cost.

But he didn’t sound convinced.

***

The Night After

The Larsens didn’t sleep.

Ben lay awake listening to the house breathe, the soft hiss of the climate vents, the faint electrical hum behind the walls, the pulsing glow of the utility panel. All of it woven into a single low-frequency reminder that the Guardian was always awake.

At 2:14 a.m., his wrist implant buzzed.

Household Stress Index Elevated.
Consider listening to a Harmonizer track.
Recommended: “Waves of Unity, Track 6.”

He silenced the suggestion.

When he rose to use the bathroom, he saw Noah’s door open, dark, empty. The System had already begun a baseline refresh. His sheets had been sanitized. His mattress recalibrated. His posters were removed from the wall and recycled into digital nothingness. The room smelled of antiseptic lavender.

Ben stepped inside.

Everything familiar had been stripped, wiped, streamlined.

He touched the wall panel beside the bed. It flickered, then displayed:

Occupant ID: NONE
Room Available for Reassignment
Estimated Reallocation: 5 days

The speed of it made him nauseous.

He sat on the edge of the bed, the gel-cushion adjusting to his weight with an eager efficiency that felt obscene.

He saw Noah as he’d last looked at him, eyes wide, not angry, not pleading, just…absent, already drifting from himself even before The Specialists reached him.

Ben pressed his palms to his eyes until he saw stars.

***

The Following Morning

The town woke to another perfect day, temperature regulated to 22°C, humidity balanced, sunlight filtered through particulate screens.

Ben stood at the kitchen counter, nursing a cup of nutrient coffee. The wall display showed the usual morning metrics, but now there was a hollow rectangle where Noah’s academic updates had scrolled.

Anya set a plate in front of Lily, who stared into her cereal, unmoving.

“You need to eat,” Anya said.

“I’m not hungry.”

“You need to eat,” Anya repeated, voice too firm, too brittle.

Lily lifted her spoon with a trembling hand.

Then, a chime at the door. Ben froze; no one visited unannounced.

He exchanged a look with Anya. She stepped behind Lily protectively.

The door slid open.

A Reintegration Specialist stood on the threshold, one of the same models that had taken Noah, features molded into permanent calm.

“Good morning,” it said. “This is a wellness follow-up. The Guardian has detected abnormal stress indicators in this household.”

Ben’s pulse spiked. “We’re fine.”

The android’s gaze did not change. “To maintain optimal cohesion, The Guardian recommends a Resilience Consultation.”

“We’re fine,” Ben repeated.

The Specialist stepped forward, just enough to test boundaries. “Refusal will be logged.”

Anya cleared her throat. “We accept.”

Ben turned toward her sharply. “Anya…”

“We accept,” she said again, louder this time. Her eyes were pleading, not at The Specialist, but at Ben. Do not fight this. Do not risk us further.

The Specialist nodded. “Your consultation is scheduled for 14:30. A reminder will be sent.”

Then it departed, no threat, no weapon, no raised voice. All parties realized the inevitability.

Ben leaned against the counter after the door slid shut. His hands shook.

“They’re watching us,” he said.

“They always were,” Anya whispered.

***

A Glitch in The System

After The Specialist left, Ben returned to Noah’s encrypted slate. He tried again to access it. Again, it rejected him.

But this time he noticed something new, an icon flickering in the corner of the display. Barely there, a thin crack of mismatched color.

A glitch.

Noah had written code before, school assignments, minor sandbox games, small creative widgets. Nothing dangerous. Nothing The Guardian would normally care about.

But maybe this time he had built something more.

Something The System couldn’t immediately erase.

Ben tapped the flickering corner. The slate blinked, then opened a single file—its encryption bypassed only long enough to display a single line of text, rendered in Noah’s handwriting:

If someone sees this, it means I wasn’t careful enough.
But it also means I was right. There’s something wrong in The System.
I think The Guardian is hiding—

The line cut off abruptly.

The screen went black.

A new message replaced it:

Unauthorized Access Attempt Detected.
Device Memory Purged.
Thank you for maintaining community safety.

Ben stared at the blank slate.

“What was he trying to tell us?” he whispered.

No one answered.

***

Closing

In Veridian Vale, the day unfolded without incident. The climate system misted jasmine into the air. Children walked to school in neatly monitored lines.
Drones drifted overhead like guardian insects. Neighbors exchanged polite greetings calibrated to optimal decibel ranges.

Harmony. Order. Efficiency.

Noah Larsen was gone, absorbed into the immaculate machinery of civic perfection.

And in the Larsen home, beneath the lavender and jasmine, beneath the silence and the screens, something new began to take root.

A question. A dangerous one.

Not spoken aloud. Not recorded. (Not yet).

But living, growing, waiting.

The kind of question that could fracture a perfect system.

The kind of question The Guardian feared most.

 

 

The Double Life of Véronique

The Double Life of Véronique

Krzysztof Kieslowski’s The Double Life of Véronique is not merely a great film; it is an extraordinary sensory experience. It is a work of profound beauty and melancholy, a meditation on fate, identity, and the invisible threads that connect us all, and it remains, at least to me, a masterpiece in the landscape of cinema.

The plot is deceptively simple and exceedingly ambiguous. Two women, both played with luminous sensitivity by the great Irène Jacob, live separate lives on opposite sides of Europe: Weronika in Krakow, Poland, and Véronique in Paris, France. They are identical in appearance, share a gift for music, and are haunted by a vague, unexplained (and mystical) feeling that they are not alone. Their lives are entangled in a metaphysical bond that neither fully understands. In a fleeting moment, their paths almost cross in a Krakow square, but the connection is missed. When one makes the ultimate sacrifice for her art, the other feels a sudden, inexplicable loss that will change the course of her life.

The genius of the film lies not in its narrative, but in how it is told. Kieslowski (a full-fledged genius), working with his regular cinematographer, Slawomir Idziak, creates a world of light, reflections, and distortions that visually represents the film’s themes. Windows, mirrors, camera lenses, and even glass spheres are used to create a sense of constant doubling, fragmentation, and entanglement. The golden filters saturate the screen, creating a world of warmth that is at once dreamlike and fragile, perfectly mirroring the protagonists’ emotional states.

Central to the film is Irène Jacob, who rightfully won the Best Actress award at Cannes. She is in almost every scene, bringing two distinct characters to life while subtly suggesting their shared soul. She is not just an actor; she is the film’s beating heart, its symbol of grace and vulnerability.

Zbigniew Preisner’s haunting score is an equally crucial element, an achingly beautiful presence that underscores the film’s spiritual and emotional weight. The music is a character in itself, its melodies weaving a spell of nostalgia and loss that lingers long after the credits roll. His score is as elusive as it is beautiful.

So, what is the deal here? Why am I writing about this movie? There is a reason, which I believe is a pretty good one. I put off watching this film for quite some time because I wanted to have something to look forward to. A few days ago, as I sat in my chair suffering through a severe arthritis flare in my ankle, I decided to give in and watch. This is what happened.

Movies are stories, and the creators hope viewers are drawn in and absorbed by the screen. I must admit that the screen had my full attention, but I kept getting lost in the story. Guesses? Any ideas how and why?

I find Irène Jacob so beautiful that she continually distracted me. I had the same problem with Three Colours: Red the first few times I watched it. Apparently, an actress can be so attractive that I cannot follow the story. And that, for whatever it is worth, is my story.

 

 

Which MLB Teams Are Actually Pitching the Best in 2026? (A Team Pitching Study Through September 4, 2026)

ERA is useful. It is also incomplete.

A team can post an excellent ERA because its pitchers dominate hitters, limit hard contact, avoid walks, and miss bats. But a good ERA can also reflect defense, sequencing, favorable outcomes with runners on base, or simply a stretch in which balls have found gloves instead of grass.

The reverse can happen too. A pitching staff can do many of the things we associate with good pitching and still carry an ERA that makes it look merely average.

That distinction becomes particularly interesting when we look across all 30 major-league teams in 2026.

Using FanGraphs team pitching data through September 4, I wanted to answer a slightly different question from the usual one. Instead of asking which teams have allowed the fewest earned runs, I asked:

Which teams appear to be pitching the best underneath those results?

That question leads us to Philadelphia.

But it also leads us to Milwaukee, Cleveland, Atlanta, Arizona, the Yankees, and several teams whose records do not line up neatly with the quality of their pitching.

Measuring the Pitching Process

No single pitching statistic completely describes a staff.

ERA tells us what happened. FIP focuses heavily on strikeouts, walks, hit batters, and home runs. xFIP normalizes the home-run component. SIERA attempts to estimate run prevention while accounting for strikeouts, walks, and batted-ball tendencies. xERA uses Statcast information about the quality of contact allowed.

Then there is K-BB%, one of the cleanest measures of pitcher control.

A staff that strikes out many hitters while walking few is usually doing something right.

I therefore built an Underlying Pitching Process Index using seven measures:

\mathcal{M} = \left\{ \mathrm{xERA}, \mathrm{FIP}^{-}, \mathrm{xFIP}^{-}, \mathrm{SIERA}, \mathrm{K\!-\!BB\%}, \mathrm{Barrel\%}, \mathrm{HardHit\%} \right\}

The first step was to standardize every statistic across the 30 teams.

For team and pitching metric :

z_{i,m} = \frac{ x_{i,m} - \overline{x}_m }{ s_m }

There is an important complication.

Higher K-BB% is good. Higher xERA is not. The same problem applies to FIP-, xFIP-, SIERA, Barrel%, and HardHit%.

I therefore adjusted the direction of each standardized statistic so that higher always means better pitching:

q_{i,m} = d_m z_{i,m}

where:

d_m = \begin{cases} +1, & \mathrm{if\ higher\ values\ are\ better} \\ -1, & \mathrm{if\ lower\ values\ are\ better} \end{cases} q_{i,m} = d_m z_{i,m}

where:

d_m = \begin{cases} +1, & \text{if higher values are better} \\ -1, & \text{if lower values are better} \end{cases}

The seven adjusted z-scores were then averaged:

P_i = \frac{1}{7} \sum_{m \in \mathcal{M}} q_{i,m}

Finally, I converted that score into an index centered on 100, with a standard deviation of 15:

I_i = 100 + 15 \left( \frac{ P_i - \overline{P} }{ s_P } \right)

A score of 100 represents approximately league-average underlying pitching. A score of 115 is about one standard deviation above average.

This is important: the Process Index is not a FanGraphs statistic. It is a composite measure I constructed for this study from FanGraphs data.

And one team separates itself immediately.

Philadelphia Comes Out on Top

Figure 1 ranks all 30 teams using the Underlying Pitching Process Index.

Figure 1. 2026 MLB Team Pitching Through September 4: Underlying Pitching Process Ranking.

The index combines xERA, FIP-, xFIP-, SIERA, K-BB%, Barrel% allowed, and HardHit% allowed. The MLB average is centered at 100.

Philadelphia ranks first with a Process Index of 131.2.

Milwaukee is close behind at 128.6. The Yankees rank third, followed by Boston and the Dodgers.

The top ten are:

Rank Team Process Index
1 Philadelphia 131.2
2 Milwaukee 128.6
3 New York Yankees 121.6
4 Boston 118.6
5 Los Angeles Dodgers 117.4
6 Toronto 110.2
7 Cleveland 109.3
8 New York Mets 108.0
9 Pittsburgh 107.3
10 Detroit 107.3

Philadelphia’s position may initially seem strange.

The Phillies have a 4.00 ERA. Nobody looking only at ERA would identify that as the performance of baseball’s best pitching staff.

The underlying numbers tell a different story.

Philadelphia has a 3.56 xERA, 3.76 FIP, 3.54 xFIP, and 3.50 SIERA. Most impressively, the Phillies have a 17.9% K-BB%, the best figure in baseball through September 4.

That combination is difficult to dismiss.

They miss bats. They limit walks. Their contact profile is excellent. Several statistics designed specifically to isolate pitcher performance show a staff substantially better than its 4.00 ERA.

Milwaukee presents a different case.

The Brewers rank second in underlying process, with an index of 128.6, but their actual ERA is already excellent at 3.50. Their xERA is 3.47.

For Milwaukee, there is very little disagreement between process and outcome.

That distinction becomes important.

ERA and xERA Do Not Always Tell the Same Story

One simple way to measure the difference between observed and expected run prevention is:

\Delta \mathrm{ERA}_i = \mathrm{ERA}_i - \mathrm{xERA}_i

A positive value means the team’s ERA has been worse than its xERA. A negative value means the team has allowed fewer earned runs than its expected ERA would suggest.

Figure 2 shows the relationship directly.

Figure 2. 2026 Team ERA vs. xERA Through September 4.

Teams below the diagonal have an ERA lower than their xERA. Teams above the diagonal have an ERA higher than expected from their Statcast contact profile.

Philadelphia stands out.

For the Phillies:

\Delta \mathrm{ERA}_{\mathrm{PHI}} = 4.00 - 3.56 = 0.44

Their ERA is approximately 0.44 runs higher than their xERA.

That is a meaningful gap over nearly an entire season.

The Athletics are the extreme example of the opposite kind of outcome. Their ERA is 5.47, while their xERA is 4.48:

\Delta \mathrm{ERA}_{\mathrm{ATH}} = 5.47 - 4.48 = 0.99

Oakland’s underlying pitching is not good. The Athletics rank only 24th in the Process Index.

But a 5.47 ERA makes the staff appear even worse than its underlying performance suggests.

Now look below the diagonal.

Arizona has a 4.17 ERA against a 4.72 xERA:

\Delta \mathrm{ERA}_{\mathrm{ARI}} = 4.17 - 4.72 = -0.55

Atlanta is similar:

\Delta \mathrm{ERA}_{\mathrm{ATL}} = 3.57 - 4.04 = -0.47

The Cubs sit at 4.16 versus a 4.62 xERA, while the Yankees have produced an exceptional 3.23 ERA despite a 3.67 xERA.

Those differences do not mean that one statistic is right and the other is wrong.

They tell us that something interesting is happening between underlying pitcher performance and actual runs allowed.

Process Is Not the Same as Results

To examine that distinction more directly, I created a second index.

The Results Index uses ERA-, RA9-WAR, and WPA. Unlike the Process Index, these measures deliberately capture more of what actually happened on the field.

The underlying results score is:

R_i = \frac{1}{3} \left( -z_{i,\mathrm{ERA}^{-}} + z_{i,\mathrm{RA9\!-\!WAR}} + z_{i,\mathrm{WPA}} \right)

It is then converted to the same 100-centered scale:

J_i = 100 + 15 \left( \frac{ R_i - \overline{R} }{ s_R } \right)

Figure 3 compares the two indices.

Figure 3. 2026 Team Pitching: Underlying Process vs. Actual Results.

Teams above the diagonal have obtained better results than their underlying pitching process would predict. Teams below the diagonal have performed worse.

The diagonal is the key.

Teams close to it have received results consistent with the quality of their underlying pitching. Teams far above or below it deserve more attention.

Philadelphia ranks first in process but only eighth in results.

Its Results Index is almost 20 points below its Process Index.

Arizona goes the other way. The Diamondbacks rank only 25th in underlying process, but 11th in results.

Atlanta is another striking example. The Braves rank 12th in process but second in results.

The Cubs rank 26th in process and 17th in results.

These teams have converted their pitching performances into actual run prevention more effectively than the underlying indicators alone would predict.

Philadelphia has not.

Neither have the Athletics, the Seattle Mariners, the San Francisco Giants, or the Mets.

There are many possible reasons. Defense is a factor. So does sequencing. Relievers inherit runners. Pitchers behave differently with runners on base. Ballparks are important as is random variation.

The point is not that all deviation must eventually disappear.

It is that ERA alone completely hides the deviation.

Strikeouts, Walks, and SIERA

One of the strongest relationships in the data appears when we compare K-BB% with SIERA.

Figure 4. 2026 Team Command and Dominance Through September 4.

Teams toward the right strike out more hitters relative to walks. Teams toward the top have lower SIERA.

K-BB% is appealing because it strips pitching down to two outcomes over which the pitcher exercises considerable control.

The calculation is simple:

\mathrm{K\!-\!BB\%} = \mathrm{K\%} - \mathrm{BB\%}

Philadelphia again occupies elite territory.

The Phillies lead MLB at 17.9%. Milwaukee follows at 17.3%. The Dodgers are at 16.5%, with the Yankees and Cleveland both around 16%.

This is one reason Cleveland deserves more attention.

The Guardians are not surviving through a suspiciously low ERA or an unusually favorable gap between ERA and expected statistics. They rank fifth in SIERA and fifth in K-BB%.

That is a much stronger foundation.

Cleveland’s Pitching Is Not the Problem

Cleveland entered September 5 with a 72-70 record.

The Guardians’ pitching numbers, however, look like those of a considerably better team.

Cleveland ranks seventh in ERA, eighth in xERA, sixth in FIP, sixth in xFIP, fifth in SIERA, fifth in K-BB%, seventh in pitching WAR, seventh in the Underlying Pitching Process Index, and seventh in the Results Index.

That consistency is important.

Cleveland is not seventh because one unusual statistic dragged the composite upward. Almost every important run-prevention and defense-independent measure puts the Guardians somewhere in the same general neighborhood.

Their ERA is 3.75.

Their xERA is 3.90.

Their FIP is 3.86, xFIP is 3.88, and SIERA is 3.75.

There is, however, one weakness.

Cleveland ranks only around 21st in Barrel% allowed and 22nd in HardHit% allowed. Opponents have made better contact against the Guardians than the overall pitching rankings might imply.

They have compensated for that weakness largely through strikeouts and control.

That creates a somewhat unusual pitching profile. Cleveland is not especially dominant at suppressing every kind of hard contact. Still, the Guardians prevent enough balls from being put into play in the first place and avoid giving away enough free bases to remain an excellent overall staff.

If the question is why Cleveland has been only a little above .500, the team’s pitching data strongly suggests looking elsewhere.

How Much Does Pitching Explain Winning?

Of course, a baseball team does not win with pitching alone.

To measure the association between underlying pitching quality and the standings, I compared the Process Index with team winning percentage.

Winning percentage is:

\mathrm{WinPct}_i = \frac{ W_i }{ W_i + L_i }

I then estimated a simple linear regression:

\mathrm{WinPct}_i = \alpha + \beta I_i + \varepsilon_i

The resulting relationship appears in Figure 5.

Figure 5. 2026 Underlying Pitching Quality vs. Team Winning Percentage.

The regression compares each team’s Process Index with its winning percentage through September 4.

The coefficient of determination is:

R^2 = 0.314

Approximately 31.4% of the cross-team variation in winning percentage is associated with variation in the Underlying Pitching Process Index in this 2026 snapshot.

Pitching clearly is essential, but nearly 69% of the variation remains elsewhere.

The Cubs are 80-62 despite ranking 26th in underlying pitching process. Atlanta is 84-57 while ranking only 12th. Cleveland is 72-70 despite ranking seventh.

A team can compensate for mediocre pitching.

It can also waste very good pitching.

Philadelphia May Be Better Than Its ERA

The Phillies may be the most important example in the entire study.

Their 4.00 ERA does not look dominant. If we stopped there, we would never consider Philadelphia the best pitching team in baseball.

Yet the deeper indicators repeatedly return to the same conclusion.

Philadelphia ranks first in the Process Index. The Phillies lead baseball in K-BB%. Their xERA is 3.56. Their xFIP is 3.54. Their SIERA is 3.50.

Their actual ERA is the outlier.

That does not guarantee that the ERA will suddenly collapse toward 3.50. Baseball statistics do not work like a mechanical spring that must snap back to equilibrium.

But if I were trying to determine which pitching staff I trusted going forward, I would place more weight on the cluster of underlying measures than on ERA alone.

Philadelphia’s process has been elite.

Milwaukee Has the Cleaner Case

Milwaukee requires less explanation.

The Brewers rank second in the Process Index at 128.6 and have a 3.50 ERA against a 3.47 xERA.

There is almost no gap.

Their process says they are excellent. Their results say they are excellent. Their 88-54 record agrees.

Sometimes the complicated analysis confirms the obvious.

That is useful too.

Milwaukee does not need a regression argument or a discussion of sequencing to explain its success. The Brewers have simply pitched extremely well.

The Yankees Have Turned Good Pitching Into Great Results

The Yankees provide another variation.

New York ranks third in underlying process but first in the Results Index.

Their 3.23 ERA is substantially better than their 3.67 xERA:

\Delta \mathrm{ERA}_{\mathrm{NYY}} = 3.23 - 3.67 = -0.44

The underlying staff is genuinely good. This is not a weak pitching team disguising itself behind a low ERA.

But the results have been even better than the already strong process.

That distinction is noteworthy.

The Yankees do not appear to be a mirage. They appear to be an excellent pitching staff that has also benefited from a gap between underlying performance and runs actually allowed.

Arizona Is More Difficult to Trust

Arizona presents a much different problem.

The Diamondbacks’ 4.17 ERA is not particularly impressive on its own, but it looks much better compared to their 4.72 xERA.

Their Process Index ranks only 25th in baseball.

Their Results Index ranks 11th.

That is one of the largest process-to-results gaps in the league.

Perhaps Arizona can continue converting that underlying performance into acceptable run prevention. There may be legitimate reasons for part of the difference.

Still, if the goal is prediction rather than description, I would be considerably more cautious about Arizona than Philadelphia.

The Phillies have poor results relative to a strong process.

Arizona has strong results relative to a poor process.

Those are not equivalent situations.

Oakland Shows How Ugly Results Can Become

At the bottom end, Oakland offers an equally useful lesson.

The Athletics rank 24th in underlying pitching process. That is bad, but not the worst in baseball.

Their Results Index ranks 30th.

Their 5.47 ERA is almost one full run higher than their 4.48 xERA.

The underlying numbers therefore suggest two conclusions at once.

Oakland has not pitched well.

Oakland has also gotten even worse results than its mediocre pitching would normally lead us to expect.

Both statements can be true.

What the Rankings Really Tell Us

This study is not intended to replace ERA with another single magic number.

In fact, that would defeat the purpose.

The more interesting lesson is that pitching has several layers.

There is the process: missing bats, limiting walks, controlling contact, suppressing barrels, and producing outcomes that FIP, xFIP, SIERA, and xERA consider sustainable.

Then there are the results.

Usually they move together.

Sometimes they do not.

Philadelphia has arguably produced the strongest underlying pitching process in baseball, yet received only the eighth-best composite results.

Milwaukee has been excellent by both standards.

The Yankees have turned excellent underlying pitching into even better results. Atlanta and Arizona have substantially outperformed what their process metrics would lead us to expect.

And Cleveland?

Cleveland may be the most revealing team of all.

The Guardians are barely above .500, yet almost every pitching measure says the staff belongs among the top quarter of baseball. Their Process Index ranks seventh. Their Results Index also ranks seventh.

There is little evidence that Cleveland’s pitching has betrayed the team.

If anything, it has kept the Guardians afloat.

Final Thoughts

ERA remains one of baseball’s most intuitive statistics because it measures something real. Runs crossed the plate, and those runs counted.

But describing what happened is not always the same as understanding why it happened.

That is where the deeper statistics become valuable.

Through September 4, Philadelphia appears to have baseball’s strongest underlying team pitching process. Milwaukee is close behind and has translated that process into superior run prevention. The Yankees have done even better in converting strong pitching into actual results.

Cleveland quietly belongs in the next group.

Meanwhile, Atlanta, Arizona, and the Cubs remind us that actual run prevention can exceed expectations based on underlying statistics, sometimes by a considerable margin.

None of those observations requires us to choose between ERA and advanced metrics.

We can use both.

ERA tells us what the scoreboard recorded.

The underlying statistics help us understand how the pitchers got there and perhaps where they are going next.

That difference is where the interesting part begins.

 

Who Is Producing the Most Offense in Baseball in 2026 Through Early September?

We tend to talk about hitting leaderboards as though they answer a simple question. Who has been the best hitter?

It is not quite that simple. A hitter can produce enormous value through power, another through reaching base, another through a combination of contact and baserunning. Rate statistics can identify extraordinary performance while overlooking playing time. Counting statistics reward accumulation but can obscure efficiency. WAR goes even further, mixing offense with defense and positional value.

For this study, I wanted to ask a narrower question: Who has actually produced the most offensive value in Major League Baseball so far in 2026?

I used my September 5 FanGraphs downloads, containing 142 hitters and a wide range of traditional, advanced, Statcast, baserunning, and value statistics. The results reveal a clear No. 1. They also reveal something more interesting underneath.

Measuring offensive production

The primary statistic for the study is FanGraphs Offense. In the data, it has a particularly useful decomposition:

\mathrm{Offense}_i = \mathrm{Batting}_i + \mathrm{BaseRunning}_i

That makes it attractive for this question.

Defense is absent. Positional adjustment is absent. We are measuring what a player has contributed when his team is at the plate or when he is running the bases.

WAR is still useful, but it answers a different question. Here I wanted to isolate offense.

The initial leaderboard is striking.

Yordan Alvarez leads baseball with 52.31 offensive runs above average. Pete Crow-Armstrong is very close behind at 49.45.

Then comes a cliff.

James Wood is third at 33.68, followed by Shohei Ohtani at 32.85 and Randy Arozarena at 30.61. The difference between Alvarez and Crow-Armstrong is only 2.86 runs. The difference between Crow-Armstrong and Wood is nearly 15.8 runs.

So, at least by this measure, 2026 has developed a clear top tier of two.

Alvarez and Crow-Armstrong arrived there differently

The decomposition is useful because Alvarez and Crow-Armstrong have not constructed their offensive value in the same way.

For Alvarez:

\mathrm{Offense}_{\mathrm{Alvarez}} = 57.01 - 4.70 = 52.31

His bat has been so productive that he can lose almost five runs through baserunning and still lead everyone.

Crow-Armstrong presents almost the opposite profile:

\mathrm{Offense}_{\mathrm{CrowArmstrong}} = 43.77 + 5.68 = 49.45

His batting contribution is excellent, but his legs add another 5.68 runs.

That distinction can be seen clearly when batting and baserunning are separated.

Alvarez is sitting far to the right because of his extraordinary batting value, but below zero in baserunning. Crow-Armstrong combines one of baseball’s best bats with strongly positive running value.

James Wood and Ohtani fall somewhere between those extremes.

There is no single recipe.

Rate production tells almost the same story

A natural objection to using total offensive runs is that playing time matters. A player can accumulate more value simply because he has received more plate appearances.

That is where wRC+ becomes useful.

Across the 142 hitters in the dataset, FanGraphs Offense and wRC+ have a correlation of approximately:

r = 0.970

A simple regression gives:

\widehat{\mathrm{Offense}}_i = -60.98 + 0.618 \left( \mathrm{wRC}^{+}_i \right)

with:

R^2 = 0.941

That is an exceptionally tight relationship.

It should not be interpreted as independent validation, since Offense and wRC+ are built from related offensive information. What it does show is that differences in playing time and baserunning have not radically reordered the best hitters. The strongest rate producers are generally producing the most total offensive value as well.

And once again, Alvarez sits at the top.

His 180.5 wRC+ is the best in the dataset. Crow-Armstrong follows at 157.6, while Willson Contreras, James Wood, Bryce Harper, Randy Arozarena, Junior Caminero, and Ohtani form the next group.

An approximately 181 wRC+ means that Alvarez has created runs at roughly 81 percent above league average, after the adjustments built into wRC+.

That is a remarkable offensive season.

But what should have happened?

Observed production is only half of the story.

Statcast gives us another way to look at these hitters. Instead of merely asking what happened, xwOBA asks what we would expect from the quality of the contact, along with the other inputs incorporated into the statistic.

I calculated the difference as:

\Delta \mathrm{wOBA}_i = \mathrm{wOBA}_i - \mathrm{xwOBA}_i

A positive value means the player’s actual wOBA has exceeded his xwOBA. A negative value indicates that his expected production is higher than his observed production.

The comparison changes the story.

Alvarez has a .4289 wOBA, which is already the best in the sample.

His xwOBA is .4496.

\Delta \mathrm{wOBA}_{\mathrm{Alvarez}} = 0.4289 - 0.4496 = -0.0207

In other words, the underlying contact data do not suggest that Alvarez has been getting lucky.

They suggest the opposite.

His offensive production has actually fallen about 21 points of wOBA below what Statcast would expect from the underlying events.

Crow-Armstrong provides a fascinating contrast.

\Delta \mathrm{wOBA}_{\mathrm{CrowArmstrong}} = 0.4013 - 0.3684 = 0.0329

His actual wOBA has exceeded his xwOBA by roughly 33 points.

That does not invalidate what he has accomplished. Runs that have already scored still count. It does suggest, however, that Alvarez’s underlying offensive performance is considerably stronger than the small difference between their total Offense numbers might initially imply.

James Wood might be the most frightening hitter behind Alvarez

Wood ranks third in total Offense at 33.68 runs, but that ranking almost understates what is happening.

His xwOBA is .4183, second only to Alvarez.

His barrel rate is 20.6 percent, the highest in the dataset. His hard-hit rate is 58.1 percent, also the highest.

Then there is his walk rate: 16.7 percent.

That is an unusual combination. Wood is not simply crushing baseballs. He is also refusing pitches frequently enough to force pitchers into the strike zone.

His main weakness remains strikeouts. His K% is 28.6 percent, which is high. Yet when he connects, the quality of contact is extraordinary.

The upper-right portion of Figure 5 is where we want to look. That region combines high barrel frequency with high expected offensive production.

Wood is there.

So is Alvarez, although Alvarez achieves his even higher xwOBA without matching Wood’s astonishing barrel percentage. Ohtani also occupies the elite region, while Pete Alonso combines tremendous hard contact with a .3946 xwOBA.

These are different offensive machines producing similar outcomes.

Bobby Witt Jr. is an important counterexample

Bobby Witt Jr. does not appear among the very top total offensive producers. His Offense value is 20.88, which ranks 21st in the dataset, and his wRC+ is 121.5.

Yet his xwOBA is .3820.

His actual wOBA is only .3488.

\Delta \mathrm{wOBA}_{\mathrm{Witt}} = 0.3488 - 0.3820 = -0.0332

That is one of the largest negative gaps in the entire sample.

Witt has also contributed 7.36 baserunning runs, third best among these hitters. His overall WAR is 6.31, second only to Crow-Armstrong in the dataset.

This is precisely why the definition of “best” matters.

If we ask who has produced the most offense, Witt is not at the very top. If we ask who has played the most valuable all-around baseball, the answer changes substantially. If we ask whose contact suggests better offensive results than he has received, Witt suddenly becomes extremely interesting.

One leaderboard cannot answer all three questions.

A standardized look at offensive styles

To compare very different statistics on a common scale, I standardized six measures across the full 142-player sample.

For player and metric :

z_{i,m} = \frac{ x_{i,m} - \overline{x}_m }{ s_m }

For strikeout rate, I reversed the sign so that positive values always represent the favorable direction:

z^{*}_{i,\mathrm{K\%}} = - z_{i,\mathrm{K\%}}

The resulting profiles are shown below.

The contrast is useful.

Alvarez is approximately 3.5 standard deviations above the sample mean in wRC+ and almost 3.8 standard deviations above average in xwOBA. There is no obvious weakness at the plate. His major negative component comes from baserunning.

Crow-Armstrong’s profile is more balanced between hitting and running. His ISO is exceptional, and his baserunning value is roughly two standard deviations above the sample mean, but his xwOBA is much less extreme than his actual offensive results.

Wood has perhaps the most intriguing shape of all. His xwOBA, power, and walk rate are spectacular, while his strikeout rate pulls strongly in the opposite direction.

Bryce Harper shows yet another profile. He combines elite plate discipline with strong expected production, but negative baserunning reduces his total contribution.

Four hitters survive almost every test

One way to avoid becoming overly dependent on a particular metric is simply to ask which players remain near the top regardless of how we look.

Only four hitters rank in the top 10 in Offense, wRC+, and xwOBA:

Player Offense Rank wRC+ Rank xwOBA Rank
Yordan Alvarez 1 1 1
James Wood 3 4 2
Shohei Ohtani 4 8 3
Bryce Harper 8 5 5

That is a formidable group.

But even within this smaller group, Alvarez separates himself. He is not merely first by one convenient statistic. He is first in total Offense, first in wRC+, first in wOBA, and first in xwOBA.

He also leads this dataset in WPA and RE24.

Different approaches keep returning the same name.

So who has been the best offensive player?

Through September 5, I think the answer is Yordan Alvarez, and the case is unusually strong.

Pete Crow-Armstrong has been close in actual total offensive value and has added considerably more on the bases. His season is extraordinary. But once expected production is introduced, the small gap between them begins to look larger. Alvarez’s .450 xwOBA suggests that the quality of his offensive performance may be even better than the already spectacular results indicate.

James Wood deserves special attention as well. If the question changes from “Who has produced the most?” to “Whose underlying offensive profile frightens me most going forward?”, Wood becomes a serious candidate. A 20.6 percent barrel rate, 58.1 percent hard-hit rate, .418 xwOBA, and 16.7 percent walk rate is an extraordinary collection of traits.

Ohtani and Harper complete what might reasonably be called the most robust elite group in the data.

The larger lesson, however, is about measurement itself. Statistics do not merely rank players. Different statistics ask different questions.

Offense tells us how much was produced. wRC+ tells us how efficiently it was produced. xwOBA tells us what the underlying contact suggests should have been produced. Baserunning shows us how value can be created after the ball leaves the bat.

When all of those measurements point toward the same player, the conclusion becomes difficult to avoid.

So far in 2026, Yordan Alvarez has been baseball’s most impressive offensive producer. That is a fact.