The performance distribution is not a bell curve

In the recent post about my new car (BMW 318ti), I showed a graph of qualifying times for the BMW Compact Cup and said it looks just like every other race distribution. So let’s look at some other distributions.

Here are some virtual lap times from iRacing (Laguna Seca, MX-5 Cup).

And these come from Assetto Corsa (Brands Hatch Indy, NA Miata).

Isn’t it kind of amazing how similar they are? Real or virtual racing, performance is similarly distributed. In the real world there is car-to-car variation, but not in the virtual world. And in some series, like the iRacing one shown above, the cars have fixed setups, so EVERYTHING is identical, except for the driver. People vary a lot in their performance. But is the shape of that performance curve the same in other activities? How about we look at the finishing times at the Boston Marathon.

What the hell? It’s the same shape. Are all performance distributions the same? Forget racing, here’s the score on Exam #1 in my Winter 2019 MCB182 Genomics/Bioinformatics course at UC Davis (I’m a professor by profession if you didn’t know). The graph is in the opposite direction, but once again, it has the same shape. About 10% of the students perform really well and another 10% perform poorly, but the middle is not a bell curve, as many would want you to expect. It’s highly asymmetric.

No matter how much I try as a teacher, some people always do poorly in my class. They may have complications in their lives or some other mitigating factor. It’s okay. Not everyone shines at the same time or place. The long tail represents a lot of people who aren’t really in the game. Give them time and they may come around. On the other hand, they may not. Not everyone has to excel at racing, marathons, or academics. Let’s agree not to make fun of people who aren’t at their best.

Next, let’s talk about the people on the other end of the spectrum. Even at the elite levels of some activity, there are people who stand out above the rest. It’s kind of amazing that such talents exist. Performance at such a high level requires natural ability, a commitment to training, and usually a strong support structure around the performer.

To me, the most interesting region is the middle. Everyone eventually runs into a wall where their performance reaches a plateau. For many people, that wall is near the same place. Why do some people get beyond this and others do not? If you know it’s possible to do a marathon in 2.5 hours, why are so many people stuck at 3? Well, I’m pretty sure that I couldn’t do a 3 hour marathon if I trained for it my entire life. Is that kind of statement also true of virtual activities? While it is possible to do a 1:40 lap at Laguna Seca, are some people never going to get there no matter how much they try? And is that true of 1:41, 1:42, and other arbitrary thresholds? How much of our current limit represents a hard limit and how much is a soft limit that could be lifted with more coaching, training, practice, or support?