The swimming psychology paper

In the previous post, I wrote about a paper (gated) that showed an anomaly in team swimming relays. It turned out that the first swimmer's times were roughly equivalent to his times in individual events -- but the second through fourth swimmers had relay times are significantly faster than their individual times.

The paper concluded that this happens because people put more effort into group tasks than individual tasks. They do this because other people are depending on their contributions. However, the leadoff swimmer's time is seen to be less important to the team's finish than the other three swimmers' times, and that explains why swimmers 2-4 are more motivated to do better in the team context.

My point was not really to criticize that individual paper, but to make a broader point -- that just because the results are *consistent* with your hypothesis, doesn't necessarily mean that's what's causing them. In this case, I agreed with an anonymous e-mailer, who speculated that it might have to do with reaction times. The first swimmer starts by a gun, while the other swimmers start by watching the preceding swimmer touch the wall. I said that I didn't know whether the authors of the paper considered this or other possibilities.

Commenter David Barry kindly sent me a copy of the study, and it turns out the authors *did* consider that:

"We corrected both performance times for the swimmer's respective reaction time by subtracting the time the athlete spent on the starting block after the starting signal (also retrieved from [swimrankings.net]). ... Please note, however, that previous research did not find any differences between the individual and relay competition after a swimming distance of 10m. Thus, faster swimming times for relay swimmers are unlikely to be merely due to differences in the starting procedure."

Fair enough. But ... well, the effect is so strong that I'm still skeptical. Could it really be that swimmers, who have trained their entire lives for this one Olympic individual moment, are still sufficiently unmotivated that they can give so much more to their relay efforts?

Here are the results for the four relay positions. (Times are an average of 100m and 200m):

#1: individual 78.19, team 78.38. Diff: -0.19
#2: individual 87.30, team 86.92. Diff: +0.38
#3: individual 87.73, team 87.39. Diff: +0.34
#4: individual 87.40, team 86.66. Diff: +0.74

It seems to me that the 2-4 differences are *huge*. Are the #4 individual swimmers so blase about the Olympics that they swim almost three-quarters of a second slower than they could if they were just more motivated? My gut says: no way.

One thing I wonder, following Damon Rutherford's comment in the previous post: could it be that correcting for the swimmer's reaction time to the starting gun isn't enough? Mr. Rutherford implies that the first swimmer's reaction time is for him to *start moving*. But he implies that subsequent swimmers are already well into their diving motions when the previous swimmers touch the wall. That could explain the large discrepancies, if the reaction time correction only compensates for part of the difference.

Is there anyone who knows swimming and is able to comment?

Oh, and there's one more issue with the differences, and that's a selective sampling issue. The authors write,

"We focused our analysis on the data from the semi-finals to obtain a reasonable sample size. If a swimmer did not advance to the semi-finals in the individual competition, we included his/her performance time from the first heats."

That means the individual times are going to be skewed slow: if the swimmer did poorly in the heats, his unsuccessful time is included in the sample. But if the swimmer did *well* in the heats, his successful result is thrown away in favor of his semi-final time.

That would certainly account for some of the differences observed.