Sports And Math: Where Leisure And Learning Meet

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Westpoint's Brian MacDonald describes some of his hockey research at the Joint Mathematics Meetings in Boston.
Westpoint's Brian MacDonald describes some of his hockey research at the Joint Mathematics Meetings in Boston.

Hollywood loves winning streaks. And losing streaks. And hitting streaks, putting streaks, and three point shooting streaks.

ESPN and your local newspaper like streaks too. But, here's something I learned last week at the 2012 Joint Mathematics Meetings in Boston. Mathematicians don't like streaks.

"There's a narrative you have to create that says so and so clearly did this well because he's hot right now," Chris Jones, professor of mathematics at St. Mary's College of California said. "Because his wife just gave birth to a kid so he's on fire."

Fact is, says Jones, the narrative we assign to a streak is often just our brain trying to explain something that happens quite naturally.

"You can toss a coin 10 times and get six heads in a row," Jones explained. "It doesn't mean the coin was 'on fire' or 'hot' or whatever phrase you would use if it was a sports person. It just means that that happens sometimes, even if it's a 50-50 coin."

College Football Playoff?

And that's not the only narrative mathematicians say the sports world gets wrong. Certainly you've heard that the only fair way to choose a NCAA football champion would be to hold a playoff, right? You might have heard it on this very program, from Dan Wetzel of Yahoo! Sports.

[sidebar title="Death to the BCS" width="290" align="right"] Dan Wetzel feels so strongly that major reform is needed in the Bowl Championship Series, he's even written a book.[/sidebar]
"They have to do something," Wetzel said in a November 2011 interview with Bill Littlefield. "If they can make it into a four team playoff at the very least, then it would be a massive step forward for the sport."

When the commissioners of the 11 Football Bowl Series conferences met on Tuesday, they considered 50 or 60 different proposals for change, reportedly including a four team playoff, eight team playoff, and 16 team playoff.

But, the changes that need to be made to the BCS system have nothing to do with a playoff, at least not according to Mike Weimerskirch of Augsburg College in Minnesota.

As he made his presentation to the Joint Mathematics Meetings last week, Weimerskirch dropped phrases like the "CDF of the standard normal distribution." I admit, I had no idea what Professor Weimerskirch was actually proposing. I haven't taken a math class since the ever patient Mr. Lockwood got me through AP Calculus during my senior year at 29 Palms High School.

But, one thing was clear. Weimerskirch believes a playoff would be mathematically less fair than the current system.

Data is Good

"The mantra of the statistician is 'data is good,'" Weimerskirch explained. "If you have a 16 team playoff, you're deciding the national championship on the basis of 15 games and you're ignoring the 700 games that are played during the regular season."

Weimerskirch shakes his head at results that discount the regular season, and there are a lot of them. The Green Bay Packers winning last season's Super Bowl as a wild card. The St. Louis Cardinals winning the 2011 World Series…also as a wild card. And the University of Connecticut Men's Basketball team, who finished 9 and 9 in their conference, but won the 2011 NCAA Championship.

Weimerskirch likens winning six games in March Madness to that coin coming up heads six times in a row. And the proposal for a sixteen team football playoff? The one that NCAA President Mark Emmert won't support because it would require too many games? That would only require winning four games in a row.

When you boil things down to a very short lived tournament, the outcome is a lot more like flipping coins than deciding it on the football field.

Mike Weimerskirch

May the Best Team Lose?

If you need more proof that playoffs don't necessarily result in the better team coming home with the trophy, consider this. Brian MacDonald, Assistant Professor of Mathematics at the US Military Academy at Westpoint says since 2000 the team with the better regular season record in Major League Baseball and the NFL only won the playoff match-up 50-percent of the time. For the NHL, the statistic is even lower.

Billy Beane and Peter Brand reinvented the way the Oakland A's evaluated players and Brad Pitt turned their story into the blockbuster movie, Moneyball. If an NHL team sees fit to hire Brian MacDonald, he won't count wins…or even goals. He'll start by counting shots, blocked shots, and missed shots.

"I don't think there's any coaches that go into the locker room saying, 'We're playing really well. We're down 1-0. What we really need in this period is way more missed shots than we had in the previous two periods," MacDonald told a full room at the Joint Mathematics Meetings.

MacDonald says shots, missed, blocked, or successful, are indicators of some very important things in hockey, like possession and territorial advantage. And, unlike goals, they're not usually based on luck.

Quarterback Passer Rating

Here's another one. Have you heard that this is the era of the quarterback? According to the experts, a disproportionate number of the best quarterbacks in history just so happen to be playing right now. Aaron Rodgers set a new record high Quarterback Passer Rating this season, replacing Peyton Manning in the top spot for all time.

[sidebar title="Are you a Math Whiz?" width="290" align="right"] Read von Dohlen's full proposal from the Journal of Quantitative Analysis in Sports. [/sidebar]
Before this season even began, 51 of the top 100 scorers in history set their mark since 2000 and 71 since 1990, which didn't seem quite right to Paul von Dohlen of William Patterson University.

"I actually feel bad for the guys who played in a much tougher system where the rules did not favor the offense," von Dohlen explained. "They had to take a lot more hits. They weren't as protected by the rules. So, it's important to give them their due as well."

Professor von Dolen is suggesting some changes that he hopes will allow for better comparisons between quarterbacks who played under different rules. But like any good mathematician, he doesn't do so without considering the pros and cons.

"So, what are the advantages of the statistic as it is?" von Dolen asks. "Well, it's simple. At least we think it's simple."

Want in on the joke? Here's that "simple" equation.


Where's the Fun?

If all of this math seems to be spoiling the fun of sitting down and watching a game — if, like me, you're not sure you want to be a sports fan in a world where streaks mean nothing, the best team doesn't win the playoffs, and the best quarterback in history might have retired before you were born, Roland Minton of Roanoke College suggests you reconsider.

"I use the analogy of looking up at the stars," Minton said. "Some people want to see them twinkling and beautiful and that's all they want to think about. For me, knowing that behind that is a big gaseous ball and galaxies orbiting each other? That just makes the whole thing truly awesome, in the real sense of the word."

Like most of the professors who participated last week's session on Mathematics and Sports, Minton uses sports analogies to get his students excited about math. It works, he said. And he had one more sports assumption to debunk before he was through.

"I haven't exactly counted the numbers, but my experience is that it's really equally interesting and exciting for both of the genders," Minton said. "There are some people that don't like sports. Some of them are guys. Some of them are women. And I don't see any difference."

It might have taken a full day of dizzying math lectures, but finally… a statistical conclusion that I did not find to be dismaying, worrying, or even all that surprising. I guess math isn't too bad after all.

This segment aired on January 14, 2012.

Karen Given Executive Producer/Interim Host, Only A Game
Karen is the executive producer for WBUR's Only A Game.



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