Justin Gatlin's 100-meter world record time of 9.76 was changed to 9.77 after it was determined that it was timed to be 9.766, which officially should have been rounded up to 9.77, the previous world record. Perhaps they do that to eliminate human error, but I'm wondering why, in a sport where hundreths of a second matter tremendously, they can't extend the recorded times to at least thousandths of a second. Perhaps the previous world record holder ran a 9.774 -- it seems that the .008 difference might be noticeable or meaningful.
The same observation goes for a quirk I've noticed in some major fantasy leagues providers. In these categorical rotisserie leagues, batting average, ERA, and WHIP (as well as FG% and FT% in basketball) are all rounded -- ERA and WHIP to the nearest hundredth, batting average (also FG% and FT%) to the nearest thousandth. And why shouldn't they be? That's the metric we see in the newspaper; how awkward would it be to see that Ted Williams batted .4057 in 1941, not .406?
The problem comes when these rounded totals tie. Over the course of a season, a team in a weekly league starting 14 batters might accumulate somewhere around 7000 at-bats. After a while, the marginal base hit doesn't affect the team's cumulative average as much as it did earlier in the season. The law of large numbers implies that the average of a random sample from a large population is likely to be close to the mean of the whole population. Taking the whole population to be all major league baseball players' batting averages, and taking the random samples to be each owner's team (if everyone knows what they're doing, which isn't always the case in your average (pardon the pun) home league or public league), every owner's team batting average will tend to regress to the mean by the end of the season. The basic result of these unnecessary statistical observations is this: in categorical rotisserie leagues, where the very basis of accumulating the stats is to rank each team in relation to each other, why should my team be tied be tied with the next when they've batted 1991-for-7000 (.2844) and the other has batted 1985-for-7000 (.2835)? Do those six hits count for nothing?
In baseball leagues, the same goes for ERA, and especially WHIP (walks+hits per inning pitched, for baseball newcomers). Taking the season-ending stats from the 2005 RotoWire Staff Keeper League, the mean of all team WHIPs was 1.3076 and the standard deviation was .0599. Assuming a normal distribution of baseball batting averages, this means that 95 percent of team WHIPs should fall within two standard deviations from the mean, which in this case is a paltry 0.1198 (Indeed, only one team's WHIP out of 18 fell out of that range, leading to 94.4 percent falling within; my team barely made it in at 1.3967, mostly thanks to the antics of Orlando Cabrera, Bruce Chen, and Brandon Backe). This means (again, pardon the pun) that the team WHIP values are so clustered that there will be plenty of collisions when rounding to the nearest hundredth, as many major fantasy providers do. Thank goodness we used RotoWire MLB Commissioner to host the league, as it either doesn't round or rounds WHIP to the nearest ten-thousandth, which is enough to distinguish almost any two fractions divided by about 1250 (the innings cap for some leagues, and the denominator for the WHIP calculation). Looking at the RotoWire Staff Keeper League, the following pairs of teams (each denoted by the WHIP ranking they actually received using four decimal places) would be tied if WHIP was rounded to the nearest hundredth: {(3,4), (5,6), (7,8), (9,10), (13,14)}. That's a lot of unnecessary ties as when using the pure stats, which are readily available, each of the higher-numbered of those ordered pairs can be objectively judged to have a lower WHIP than the other. With a few more or less hits and walks, three or four teams easily could have been tied if WHIP was rounded to the nearest hundredth in this league.
The basic thesis of this whole rant is this: wouldn't it be too simple for your typical fantasy league provider to throw a few extra decimal places on these stats? In some of these leagues, in which a friendly gentleman's wager may or may not be on the line, the extra half point you may gain or lose in the "average" categories your league uses (AVG, SLG, OPS, ERA, WHIP, XBA, etc.) might make a material difference. So what if your team batting average of .2778 or ERA of 3.8781 looks a little funky. Getting it right is what matters. As for Gatlin's 100-meter dash time, I hope they have mechanisms that allow for the uniform timing of all races across the statistical population of all 100-meter times ever recorded (especially with today's modern technology), but if they don't, I don't see why his 3.766 time can't stand. A couple hundredths of a second less and he would have had his name alone in the record books (at least until it gets broken next year). Pull out your stopwatches and find out how short that actually is.
Posted by Bret Cohen at 5/17/2006 9:16:00 AM
