It’s almost unfortunate that the men’s performances shadowed the women’s race. As I was watching the race on Monday, I was electrified by Kim Smith’s solo in the first half and then the exciting duel between Desiree Davila and Caroline Kilel, but obviously the running world went crazy by seeing the impressive time of 2:03:02 by Geoffrey Mutai, and discussions about that world-record-that-wasn’t ensued.

Many have pointed out that, had the wind been such a big advantage, Kilel would have broken the world record set by Paula Radcliffe at 2:15:25 in 2003. It’s a good point, but it falls short: one doesn’t compare pears and apples, and the men’s and women’s race on Monday couldn’t have been more different. But it’s still a good point and I tried to analyze it following the same, generic lines of yesterday’s post.
The conclusions I drew are the same as in yesterday’s post: Mutai’s time is a statistical outlier.

I want to stress again that this statement isn’t about Geoffrey Mutai: he is a truly exceptional athlete who will be likely to reserve us many surprises in the years to come. My point here is to explain why — statistically speaking — Boston 2011 was “excessively aided.”

Cherop, Kilel, and Davila round the corner onto Hereford St in Boston - photo credit: Michael Dwyer, AP

Before starting discussing the statistical significance of the women’s race, I want to comment on an analysis, that appeared on Friday and received some attention.

[the arrs analysis] The Association of Road Racing Statisticians (ARRS) published an analysis whose conclusions are that Boston was “not excessively aided.” I read the article about the analysis (I couldn’t find the actual paper on the web) and I think their reasoning is flawed on statistics and physics. (For more, you could read Ross Tucker’s commentary at the Science of Sport.)

The observed times were roughly 2.4 sec/km faster than expected for the 43 elite runners making up the time comparisons. Hence, one could conclude that the wind aid was sufficient to balance out the effect of the hills (such as they are).

“To balance out the effect of the hills” seems to suggest that Boston was de facto a flat course on Monday as the wind counterbalanced the uphills. This statement makes no sense: even assuming that the tailwind nullified the effect of the uphills, the wind is still blowing on the downhills hence adding speed on those stretches, therefore their reasoning seems to lead to the opposite conclusion. Plus, the Boston course has a net elevation loss and it was the combined effect of a strong tailwind and the net downhill to create the perfect storm.
On the statistical viewpoint, they use a seemingly arbitrary cutoff of 5 sec/km to suggest “excessively aided” races and include bits like “faster than expected,” which seems to suggest that every runner is sort of expected to improve their performance on every race — at the very least, this sounds a bit odd.

[the women’s field] Following the same analysis I wrote about yesterday, I will analyze the statistical significance of the course records in Boston and London compared with their respective winning times over the last 20 years.

London Marathon: Plot of woman winner’s times in the last 20 years. The arrow shows the current course record.

The graph shows the winning times for the London Marathon since 1990; the average is 2h 23m 53s and the standard deviation 4m 12s. (For an explanation of the statistics, [1])
Paula Radcliffe’s course and world record of 2:15:25 falls two standard deviations away from the average: as I described, this gives an ‘unlikability’ of roughly 3% fairly larger than the 0.1% of Mutai’s time and completely in line with all the other records.
Honestly, this result surprised me a bit: when compared with all women’s fastest times, Paula Radcliffe’s stands apart — her time is 3 minutes faster than the second best set by Catherine Ndereba; in comparison, there are roughly 30 runners who ran within 3 minutes of Haile Gebrselassie’s world record. Still, the analysis seems sound and Paula Radcliffe’s world record is not an extreme outlier when compared to other winning times in London.

Boston Marathon: Plot of woman winner’s times in the last 20 years. The arrow shows the current course record.

Boston women’s times look a bit more sober, especially when compared to the men’s times. The average is 2h 25m 03s and the standard deviation 2m 28s. The course record (2h 20m 43s) was set by Okayo in 2002: it is 1.77 standard deviations away from the average — once again in the same range of statistical significance as the other records.

Caroline Kilel’s time on Monday falls within one standard deviation from Boston’s average: it does seem odd that the men’s race had been favored by weather conditions so much more than the women’s race, but as I said earlier, the two races were extremely different — Kim Smith.
The New Zealander athlete dominated the race for the first half, but she didn’t set the pace, instead she took off with a 40 seconds lead over the pack. On these conditions, I suspect that the elite women ran a much more conservative race and only when Kim Smith had to quit because of injury their race really started. On the other hand, the men’s race had Ryan Hall leading for the first half but still on sight, basically he paced the race and the men took a less conservative approach.