Thursday, June 13, 2013

Denny Hamlin's 42% Chance of Getting 2 Wins Before the Chase

(This is a cross-post with BSports Stats Insights)

Based on my models, the cutoff place for 20th place after 26 races will be about 670 points. Denny Hamlin has 285 points right now.  He would need 385 more points in the next 12 races. That's an average of 32.1 points per race (or an average finish of 11.9 or better in the next 12 races). You can review myprevious article about predicting Chase cutoffs to see how I approach this.

Just achieving this 11.9 average finish will be a challenge for Hamlin: his average finish so far this year is 16.2. Hamlin will need to step his game up and avoid crashes to get there. Needless to say, he doesn't have much room for error. That’s just the first step.

If he does get into the top 20, he will need to be among the two drivers with the most wins (of drivers ranked 11th through 20th).

In the past years of this format, a driver with 2 or more wins has always been guaranteed a spot in the Chase. Drivers with 1 win may or may not make it. Right now, of drivers ranked 11 through 20, Tony Stewart has a single win. The other nine drivers have 0 wins.

All this data suggests that Hamlin will need two wins to make it. What are the probabilities of him getting that pair of wins?

Here's what we know:
  • We have completed 14 races so far this year.
  • There are 12 more before the Chase: races through 15 through 26.
  • In the past 5 years, if you only look at races numbered 15 through 26, Hamlin has won 7 out of those 60 total races, for a winning percentage of 11.7%.
Note that 11.7% is the winning percentage for each individual race. The real question is how do we figure out his ability to get multiple wins in this same time period?

Our tool for answering this question is the binomial distribution. You can use the binomial distribution to answer questions like "If a coin flip comes up heads 50% of the time, and I flip my coin 12 times, what's the chance I get 2 heads in those 12 flips?"

Or…we can ask the exact same question, but applied to winning races: "If Denny Hamlin wins a race 11.7% of the time, and he races 12 times, what's the chance he gets 2 wins in those 12 races?"

Here's what the binomial distribution tells us, given Denny’s historical winning percentage:

What’s the probability of Denny winning 2 or more races? It’s simply the sum of the probabilities for the numbers of 2 or more wins. That’s how we arrive at a 42% chance.

Now take the same approach, and apply that to everybody else outside the top 10.

If you look at this table, you’ll see that Denny has significantly better prospects than *anyone* ahead of him. It bodes well for Hamlin that none of the drivers ahead of time are strong threats to win multiple races before the Chase starts.  (Remember that Tony Stewart is halfway there with his first win. He has a 56% chance of winning at least one more time before the Chase starts, to get to two total wins.)

There you have it: using some math and historical data, we can see that Denny Hamlin has a 42% chance of getting those two wins.

If anything, given his racing performance this year, getting the 2 wins might be more doable than getting into the top 20 in points. We’ll definitely be keeping an eye on Denny to see how he does over this final stretch.