Another 24 Hour Lap Time Post!

I'm still working on getting the full lap data for Great Glen, because I'm sure there's a lot of cool stuff in there.  In the meanwhile, someone sent me this email that was too well done not to post (with his permission, of course), which answered some of the "but what's the statistical certainty???" questions that were posed in the comments last week.  Enjoy.

"Hi Colin,
Don’t know if you remember me.  I’m [explanation of how we know each other redacted].  Anyways, I enjoyed your cheater writeup.  You’re probably done with comments about this whole deal, but I was bored at work this morning and took a look at some of the lap data.  Some of the comments were asking about statistical certainty of Sam Anderson’s night lap times being fake.  The short answer is “oh my god, yes”.

I looked at the lap times from the top 10 teams from the 2011 24hogg.  I discarded the first lap (running) and then averaged every rider’s laps started before 8 pm and called those day laps, and averaged every rider’s laps started between8 pm and 5 am and called those night laps.  So from the top 10 teams, we have a population of 32 riders, and I added Sam Anderson’s laps to the data set.  When you plot them, you get this graph:

The dashed blue line represents even lap times day and night.  As you would expect, every legit racer is, on average, at least 2 minutes slower in the dark.   If you look at the ratio of night:day for the 32 riders, you find with 99.9% confidence that all riders should run lap times 1.078 to 1.147 times slower at night compared to day.  And this makes intuitive sense as a good rider running 40 minute day laps and going 8% slower at night would run 43 minute laps.

So onto Sam’s night:day ratio of 0.998.  If you run a t-test to determine if his lap ratio is significantly different from a normal person's, you find that there is 99.999999999% confidence that his is an outlier.  This translates to a 1 in 1.3 million shot of his lap times happening without some outside influence (cheating, mechanicals, whatever).  

You made a great case that something fishy was going on with his lap times.  Just though you should know statistics is on your side.