Friday, April 11, 2014

The Chances of Seeing 16 Unique Winners Reach the Chase

With Joey Logano's win at Texas, we now have 7 unique winners through 7 races. This matters a lot in 2014, because the eligibility for the 16 Chase spots is primarily based on wins, and secondarily on points. If there are at least 16 unique winners after 26 races, then all winless drivers (except possibly the overall points leader) will be eliminated from joining the Chase. Right now that list of winless drivers still includes champions like Jeff Gordon, Matt Kenseth, Jimmie Johnson, and Tony Stewart.

Specifically, the number of winners will affect how teams strategize in the next 19 races: if there will end up being exactly 16 winners, you'll need to gamble to get a win. If there won't be enough winners, you'll need to be consistent to stay at the top of the points. If there are 17 or more winners, you'll need to gamble for a win and be high enough in points to qualify. That's why the topic is important: the number of winners -- or projected winners -- will dictate team strategy as we approach the Chase.

We've seen this topic already debated heavily in the press, for example Nate Ryan at USA Today, Bob Pockrass at the Sporting News, and David Caraviello at NASCAR.com.

Today we look at the probability of seeing 16 unique winners by the time the checkered flag waves at Richmond. First, we use our base assumptions of historical winning percentages during the 2009-2013 seasons:


The final column uses the binomial distribution to calculate the probability of each driver winning one race out of the next 19, given their historical win rates. For example, drivers like Jeff Gordon and Kasey Kahne win 4% of their races, which translates to a 53% chance of winning one race out of 19. Compare that to Matt Kenseth, whose 8% historical average translates to an 85% chance of winning one race in the next 19.

The highlighted drivers are the 2014 winners, and the cutoff line shown is after the 16th driver, indicating that Dale Earnhardt, Jr. and Joey Logano have taken spots that mathematically were more likely available to others. Based on that data, we can see the likelihood of unique winners throughout the season. Here's what it was at the start of the season, before the Daytona 500:


The outcomes are based on 1 million trials of race outcomes: at the start of the year, the chance of 16 unique winners was small: only about 5 percent, with an additional 2% for all totals above 16.

After the first six races saw six unique winners, the percentages obviously increased. Heading into our most recent at Texas, the likelihood of ten additional (or 16 total) winners before the Chase had shifted closer to 20%. Remember the calculations take into account the specific drivers who are still without wins: it knows that drivers like Johnson are definitely due to get one. 


After Logano's win at Texas, the numbers moved even further towards the 16+ camp. We now have a 17% chance of seeing exactly 9 more winners (to reach 16 total), with an additional 10 percent for all numbers above that. In total, there is now a 27% chance of seeing at least 16 unique winners before the Chase starts.


That means the likelihood of having at least 16 winners is now a reasonable one. It's not the most probable scenario for now, but it does suggest that Chase spots are filling up fast. Worrying about points should not be the most important thing on the minds of teams.

In the most likely scenario, we will probably end up with 7-8 more winners, reaching a total of 14-15 uniques, leaving only 1-2 spots for drivers to get in on points. For almost all drivers, getting one win through good luck or a smart gamble will be easier than keeping the consistency necessary to be a top-2 non-winner in the points standings.