May the Best Team Win
By Julie J. Rehmeyer
The winner of the Superbowl or World Series is that season's best-performing team. Right?
Wrong, according to scientists. And the problem isn't just the occasional "wild card" team that unexpectedly wins, such as the Florida Marlins bagging the World Series in 2003. A recent study shows that the strongest team in the league ends up with the best record only about 30 percent of the time.
Lady Luck is the confounder. Even if a team is superb, a stray gust of wind, a bad call from a referee, or just a lousy night can make a game go awry. In fact, researchers have found that in baseball games, the team with the stronger record wins only 56 percent of the time—barely better than pure chance.
With a large dose of randomness in the outcome of any particular game, it takes lots of games to ensure that the best team compiles the winningest record. The recent study found that to give a 90 percent chance that the strongest team wins, each baseball team would have to play about 15,000 games in a season.
"That's a little unrealistic," admits Eli Ben-Naim, a physicist at Los Alamos National Laboratories in New Mexico and lead author of the study.
So Ben-Naim figured there had to be a better way. He found that a preliminary elimination round or two makes all the difference. After all the teams in a league have played a few games apiece, the weakest teams would be eliminated. The remaining teams would then play some more games to determine the top 3 or 4. Finally, those teams would play lots of games against each other to reduce the role of chance. This system would produce a 90 percent probability of the best baseball team winning, and the number of games per season would be just 150—100 times less than 15,000.
Ben-Naim points out that the use of elimination rounds to increase efficiency and accuracy is nothing new. In college admissions, for instance, most competitive colleges quickly set side the weakest applicants, and after that, spend more time poring over the stronger applicants. "Intuitively, we know this is the way to do it better," he says, "but science can prove it."
In sports, though, people don't always want the strongest team to win, notes Ben-Naim. "People don't want it to be completely random or completely predictable," he says. After all, it's exciting to have the underdog win.
Managers of sports leagues understand this and intuitively design tournaments to balance luck and skill. The researchers ran simulations in which they ranked each team's strength in advance, and then used the appropriate probabilities to model the outcome of a full season of games. In baseball, the strongest team ended up with the best record only about 30 percent of the time. Remarkably, the same is true of both football and hockey, the researchers found, which may suggest that this percentage provides an ideal balance between predictability and randomness.
The coincidence of those numbers is particularly surprising because baseball's relatively long season compared with football's would tend to make a baseball season's outcome more predictable. But when examining the records of college and professional games, the researchers found individual football games to be more predictable and less subject to chance than individual baseball games. In football, they found, the team with the stronger record wins 64 percent of the time, compared to baseball's 56 percent. The effects of game length and season length balance one another out, so that both games end up with the same seemingly magical 30 percent predictability rate.
Ben-Naim says he's a sports fan, but that's not why he studies sports. He's interested in understanding competition in all its forms, from companies struggling for market share, to scientists angling for grants, to presidential candidates trying to get elected. Sports are a particularly easy form of competition to study, because the games generate lots of data that researchers can analyze.
References:
Ben-Naim, E. and N.W Hengartner. 2007. Efficiency of competitions. Physical Review E 76(August):026106. Abstract available at http://dx.doi.org/10.1103/PhysRevE.76.026106.
Ben-Naim, E., F. Vazquez, and S. Redner. 2006. Parity and predictability of competitions. Journal of Quantitative Analysis of Sports 2(October):1. Available at http://www.bepress.com/jqas/vol2/iss4/1.
Peterson, I. 2003. Seven-game World Series. Science News Online (Oct. 25). Available at http://www.sciencenews.org/articles/20031025/mathtrek.asp.
Comments
The researchers ran simulations in which they ranked each team's strength in advance, and then used the appropriate probabilities to model the outcome of a full season of games.
So they played a bunch of Madden and called it a day?
There is a curious thing here that thinking the "best" team is some sort of defined factor. The actual thing one is looking for in the "best team that played in the current game".
This reminds me of some guy who said a football coach should, statistically, go for a fourth and 1 on their own 20 in the first quarter.
While that may be true in the world of number-crunching, it is an idiotic move in the world of bone-crunching.
You can't mathematically model every blade of grass and drop of water, and sometimes it's one of those things that changes entire seasons.
Posted by: Wah | September 13, 2007 09:11 AM
You still have to get 27 outs in baseball.
And you still have to play 60 minutes of football.
In other words, you don't just look at the game, but each play run from the line of scrimmage, each out made in an inning, each pitch made.
Posted by: AhContrar | September 14, 2007 07:19 PM
The researchers ran simulations in which they ranked each team's strength in advance, and then used the appropriate probabilities to model the outcome of a full season of games.
That method is actually OK, if they iterated over it repeatedly until they saw results that matched reality.
I'll concede that this entry probably leaves out a lot of details of the methods (but I'd love to see them, since I think this is a great topic). So it seems that their methods were lacking, but I don't know for sure. Here's what I'd do:
-- First, don't just compute the winning percentage of the "better vs. worse". Put teams in tiers based on your estimate of quality. How often does a .575 team beat a .450 team? That's different than a .525 team beating a .500 team.
-- Start with putting teams in tiers, and simulate a season based on the observed winning percentage between two teams of each tier.
-- Compare the results of such simulations (thousands of seasons in each run, of course), and see if the results match real-life -- both the distribution of teams' final records, and the head-to-head records between the various combinations of tiered teams.
-- Use an iterative model; use the data from this set of sims to vary how teams are assigned to tiers, and the winning percentages of games across tiers. Keep running sims till the results match real life.
Only after doing that would I believe the results are realistic. I hope that's what these researchers did (OK, I shouldn't say "only" -- they may have done something else clever that I haven't thought of; I'll still give them the benefit of the doubt).
That said, though, baseball has one big confounding factor: the starting pitcher. Because a team's quality depends greatly on the quality of that game's pitcher, you have variability in a team's quality. For instance, if the Pirates with Gorzelanny beat the Padres with Wells, it might actually be the better team winning. Just using constant estimates of quality will affect both the inputs and the outputs of the simulations.
Same goes for home field advantage, which wasn't mentioned in the article, either.
Posted by: vinay | September 21, 2007 03:13 AM
I just happened to be reading
John Casti's "Five Golden Rules" ( page 84) and at the end of the Brouwer fixed point section
he talks about a system of team rating based on a nonlinear algorithm developed by James Keener.
http://www.math.utah.edu/~keener/
J. P. Keener, The Perron-Frobenius Theorem and the ranking of football teams, SIAM Rev., 35, 80-93, (1993).
Roger Bagula
Posted by: Roger Bagula | September 30, 2007 03:24 AM