Mathematical Model Says Ideal Baseball Season Requires Additional 100 Games

August 21, 2007

In order for the best of the best to triumph in any baseball season, the number of games that would keep a lucky-but-lousy baseball team from triumphing over a statistically superior team is 265. That's the conclusion that Eli Ben-Naim and Nick Hengartner of the Los Alamos National Laboratory come to in their article "Efficiency of Competitions."

Their case in point is the Florida Marlins, who in 2003 won the National League Championship, then defeated the far superior New York Yankees in the World Series. Each team played just 162 games in the regular season.

The study by Ben-Naim and Hengartner found that the Marlins would not have won if the season had gone another three to four months. According to the authors' statistical model, the Marlins were the worst team in 30 years to win a World Series, even if their study begs the question that some winning team had to be the "worst" in three decades.

The authors, who research random behavior in complex materials, plugged in the odds of low-seeded teams beating high-seeded ones — it happened 44% of the time in baseball over the last century — into a mathematical model covering a typical season. The more games played — this turns out not to be a surprise — the better the chances that the higher-seeded teams will become champions, according to the study.

Tournaments and one-game championships, as sports fans know, are likely to produce Cinderella winners, for the same reason. "Of course, lots of people like to see these kinds of winners," Ben-Naim told USA Today. "That's why we have March Madness." His reference is to the National Collegiate Athletic Association's annual basketball tournament.

But if the desire is to have the best Major League Baseball team come out on top, a longer World Series of, say, 11 games, would be mathematically appropriate and do the trick. "The same is true for other competitions in arts, science, and politics," the researchers wrote.

"The world of sports provides an ideal laboratory for modeling competition because game data are accurate, abundant, and accessible," the authors noted. "Even after a long series of competitions, the best team does not always finish first."

A more efficient competitive process, the authors suggest, would be to schedule a preliminary series of competitions to cull the obviously bad teams, followed by a longer season pitting the better teams against each other.

Nonetheless, "baseball actually isn't doing too bad a job compared to other leagues," Ben-Naim said. "Probably the worst is the National Football League with only 16 games in a season."

"In real life, we have to compete all the time — rank people, rank proposals and other things," he added. The study proposes devoting time and energy to evaluating "only the few obviously best ones."

Source: USA Today, July 31, 2007; "Randomness in Competitions."