Thursday, December 13, 2007

Sports and The Weakest Link

I'm a game show junkie, and one of my favorites is The Weakest Link. For those of you who've never watched the show, it combines trivia questions with a Survivor-style vote to eliminate the weaker contestants. This eventually whittles the team down to one member who collects the entire prize pool for himself.

What does any of this have to do with pro sports, you ask?

- The Voting

Players are encouraged to vote off the opponent who answered the fewest questions correctly. However, this is very rarely the case in practice. In fact, the show's host will regularly point out when the contestants have voted "incorrectly".

Usually, they will vote for someone who missed one prominent question, often one the voter considers to be "obvious". Frequently a voter will explain that, as a history teacher, he can't excuse his opponent not knowing the answer to a World War II question.

I can think of two obvious parallels to the world of sports analysis. First, scouts and fans often argue that statheads don't really understand baseball, because they don't watch enough games. In fact, this is reportedly why Rob Neyer and Keith Law were not given Hall of Fame votes. But the players on the show--who observe their opponents firsthand the whole time--constantly get the vote wrong. When you ignore the numbers and simply follow your observations, your opinion is bound to be biased.

Also, if American sportswriters and Alex Rodriguez played The Weakest Link together, A-Rod would be voted off the first time he got a question wrong about the playoffs, even though he had aced all the others. It's not like he needs the money anyway, right?

- "Banking"

As with most game shows, The Weakest Link allows the players to "bank" the money they have earned rather than risk it to try and make more. However, there is a strong added incentive to bank on this show: If you don't bank, then get your question wrong, you are very likely to be voted off the team. Often, gambling is +EV for the team but -EV for the individual, so he will choose to bank rather than go for it.

Similarly, most NFL coaches would do far better if they pursued a more aggressive approach, particularly on fourth downs and late in games when the other team has the lead. However, the coach's first priority is to make sure that he will not be fired. If a coach plays by the book and his team loses, the players get the blame; if he makes an unusual decision and the team loses, the coach becomes the scapegoat.

So while every pro and college team would win more games by cutting down on punts, it wouldn't be the best strategy for the coaches, who have to explain their strategies to team officials that will never begin to grasp them.

- The Final Round

The final round of the show is a best-of-5-questions format. This, much like the playoffs in any major sport, is designed for entertainment and not to determine which player is actually the best. As in a baseball playoff series, the underdog in any reasonable scenario will never have less than about a 25% shot to win.

This isn't a problem, so long as we understand that the best team is not always the one that wears the crown. I find it funny that the 2001 Patriots, who at the time were considered a Cinderella story, are now viewed as the beginning of a dynasty. The Pats have been the best franchise in football since 2001, but that year's team got lucky. If they were better than the Rams, they wouldn't have been 14 point underdogs.

2 comments:

Karl said...

I'd love to see the numbers behind this:
"So while every pro and college team would win more games by cutting down on punts"

j holz said...

Here are some treatments of the subject:

http://www.footballoutsiders.com/2006/08/10/ramblings/stat-analysis/4059/

http://mathforum.org/library/view/61478.html

Looking at the issue from an expected value standpoint, the following inequality usually holds:

EV(Punt) < EV(Conversion) * P(Conversion) + EV(Turnover) * (1-P(Conversion))