A Few Thoughts on Creating Lineups for NASCAR DFS

A Few Thoughts on Creating Lineups for NASCAR DFS

I play NASCAR DFS (daily fantasy sports) on FanDuel and DraftKings.  I don’t have a gambling jones, I started playing because I was attracted to the mathematics underlying the lineup selection process.  On DraftKings, you are tasked with picking 6 drivers per lineup; on FanDuel, it is 5.  This post is not about how to pick the right drivers to make lots of money.  I want to talk about how many possible lineups there are for an individual player to choose from.  For now, we will ignore the limitations imposed by salary caps on each site.

Back in the old days, The NASCAR Cup Series had a field of 43 cars.  There were usually more cars than that trying to qualify.  The slower entrants, not fast enough to make the field, got sent home with nary a handshake.  So, let’s say that we need a single lineup of 6 drivers for DraftKings.  Any guesses as to the number of unique lineups we have to choose from?  Go ahead…take your time.

Did you come up with 6,096,454?  Unbelievable, isn’t it?  There are over 6 million possible unique lineups to choose from.  This problem, and problems like it, are known as “n choose k” problems.  Of course, there is a handy and elegant formula for us to use.

In this instance, n =  the total population to choose from and k = the number you are interested in selecting.  In our example n=43 and k=6.

Note: If you are not familiar with (!), that means factorial.  For example,

Get the idea?  For example, if you have 6 books (6!), there are 720 different ways to arrange them on a shelf.  What about 9 books? 9! = 362,880.  Astonishing, isn’t it?

Now we can talk about present-day NASCAR.  Recently, the fields have been at around 38 cars.  The high cost of participation and lack of sponsorship has led to the folding of many race teams.  Now our equation (38 choose 6) gives a still ridiculous answer of 2,760,681 possible lineups.  Good grief, that is still way beyond manageable.

Luckily, any competent DFS player can eliminate a bunch of drivers right at the start of their selection process.  There are cars referred to as backmarkers, these cars are too slow to compete.  It is very difficult for them to move forward through the field.  They tend to be the product of small, underfunded teams.  These cars ride around in the back of the pack, hoping to stay out of trouble as they cruise around the track in the hopes of a substantive paycheck.  For argument’s sake, let’s say there around 8 of those cars.

Now we are at n=30 and k=6.  30 choose 6 gives an answer of 593,775.  That is still a number way beyond what any human being could hope to tame.

What if you have a process whereby you can eliminate drivers based on any number of other factors?  Serious DFS players do this as a matter of course.  Imagine that you can whittle down your field of possibilities to 25 cars.  Now we have n=25 and k=6.  25 choose 6 = 177,100…still an outrageously large number.

There are more things to consider.  A person creating a DFS lineup just can’t pick any 5 or 6 drivers they want.  Each driver costs a certain amount, and there is a salary cap.  For our combinatorics problem, this creates some interesting issues, some easily solvable and others not.  As you will see, things get a lot more complicated when salary restraints are included in the equation.

On Draftkings, it is usually easy to split the cars into 3 different groups.  Let’s say that group 1 has 8 cars, of which you wish to choose 2 for each lineup you want to create.  8 choose 2 gives an answer of 28 different combinations.  Next would be a group of around 22 cars, of which 4 would be chosen.  22 choose 4 = 7315.  Now we have a total of 7343.  In practice, this number will be much larger due to the fact that it would be difficult to fit lineups under the salary cap using only those cars.  It is probable that some of the backmarkers would have to be included in the pool of eligible cars to create viable lineups.

On FanDuel, the salary cap restrictions are not nearly as severe.  If we go with all 38 cars in our pool, we get 38 choose 5, which equals 501,942.  If we use other methods to whittle the possible cars down to 30, we get 30 choose 5, which equals 142,506.

As of today, the most lineups one can enter in one contest is 150.  That is 150 out of possibilities ranging from the high thousands to the millions.  Obviously, the processes, mathematical and otherwise, that players employ to construct lineups are of utmost importance.  It is impossible to try to cover all bases, the math simply won’t allow it.