# Power Has a 28% Chance of Winning Watkins Glen or Sonoma

The IndyCar championship is down to just two races: Watkins Glen, where the series hasn’t raced since 2010, and Sonoma. Will Power is trailing Simon Pagenaud by 28 points right now and most people say he’ll need a win to have a shot at the championship. His rival has been very good at finishing races this year, so banking on another DNF from him isn’t a worthy strategy.
Using a binomial distribution — which gives the chance of a certain number of successes (in our cases wins) occurring in a given number of trials (races) — I calculated the odds of both Pagenaud and Power winning zero, one, or both of the races remaining. Their expected win probability was based off of their winning percentage from 2014 through Texas 2016. Here’s what I found:

Both drivers are more likely than not to go winless over the last two races, which hurts the chaser more than the leader. Power has slightly better than a one in four chance of picking up a win. Securing two wins has less than a five percent chance of occurring for both drivers.

The result of this quick analysis reaffirms the idea that Power really does have to go out and take control of these races if he wants to win the title. Pagenaud will be more focused on finishing the race high up the field but not necessarily winning, opting to try and stay out of trouble instead. He’ll know the odds of Power winning one of the races is pretty low and that he just needs to keep a cool head on the track to take home a nice trophy.

Update — 3:51 p.m., 8/31
One caveat of using a binomial distribution that I failed to mention is that a binomial distribution assumes all trials are independent. That is, the probability of winning one race doesn’t affect the probability of winning a future one. After Watkins Glen, the respective win probabilities for both drivers will change because they will have either won a race or not in the time frame we are looking at. The only part of our analysis that is truly affected by this is the probability of winning two races. If a driver wins the first one, their probability of winning the last race too will go up.

by Drew

# The Qualifying Lap That Could Have Been: Belgium 2016

Vettel’s best qualifying lap for the Belgian Grand Prix was 1:07.108. His theoretical best lap time was almost a full tenth faster at 1:07.013.

Wait what? His theoretical best time?

A driver’s theoretical best time takes his best time from each of the three sectors throughout the qualifying session, no matter what lap or round they came in, and adds them together. This new theoretical best (from now on referred to as TB) is the best time the driver could have hoped to achieve if he ran all of his best sector times on the same lap.

Now, this isn’t a perfect indication of what could be done by the driver. For example, perhaps the reason one driver has such a low sector one time (helping his TB) is because he braked for the corner that began sector two way too late and ran off the track. That sector one time he posted will still be included in his TB, but it’s important to note that he could never complete a full lap while posting such a fast sector one time. So his TB time will be slightly above what you could actually expect from him if he were to qualify again at the track.

The Top Ten at Spa

Here’s a look at the data in full from Belgium for the top ten drivers who qualified. The light blue column shows where the driver would have started if the grid was set using TB lap times. I’ve also included a driver “TheoBest” in red whose time is the best sector times of the session not necessarily from the same driver. For this race TheoBest is made up of Rosberg for sectors one and three and Verstappen for sector two.

If a driver’s difference between actual qualifying time and ultimate (TB) qualifying time is zero, that means he ran all three of his best sector times on the same lap.

 Click to enlarge

Some Quick Takes on the Results

• Raikkonen had the most to gain from stringing together his three best sectors on the same lap. He would have shaved two tenths off of his time and jumped from the second row to first on the grid.
• Massa had the greatest difference between his actual and TB times with a 0.823 second difference. Even with such a large difference though, he would have only gained two spots and move into eighth place on the grid.
• Rosberg was 0.264 seconds off of our made up driver, “TheoBest.” The only sector he lost time on “TheoBest” was sector two.
If you’re interested in getting updates on ultimate qualifying laps for future grand prix let me know in the comments below.
by Drew

# We’re Experiencing The Most Top-Heavy Championship Since 2011

It looks to me like we are having an unusual year of two strong title contenders followed by a big drop off. The gap between first and second place in the championship is 28 points with two races remaining. Kanaan is 113 points away from the leader in third place.
To see if this is actually unusual or simply the norm, I went back to all seasons 2009 and on and checked how many points per race the top two contenders were averaging together with two races remaining. I adjusted to account for double points races by making them count for two races.
Here’s what I found:
Power and Pagenaud are averaging 68.7 points per race together this year, the most by any championship-leading duo since 2011. These two drivers are running away with the championship and are the strongest in the field by a wide margin. You have to go back to the 2011 season led by Franchitti and Power to find a stronger pair of leaders. The two years preceding 2011 were also particularly strong, perhaps a sign of IndyCar increasingly becoming more competitive in recent years?
So what exactly does this mean for the championship? For one it means that whoever wins the championship out of Power and Pagenaud will be a worthy recipient. Both of these drivers blitzed the field this year with four wins a piece as of writing. The last time multiple drivers won four or more races in a season was (you may have guessed) 2011.
Power will need to try and improve on his personal PPR (currently at 33.4) and get another race win — preferably at the double points Sonoma finale — or bank on a poor race from Pagenaud if he wants to snatch the title from his teammate.
by Drew