Game Theory: Proof That Football, Baseball, and Hockey Are All Better Than Basketball

I get a lot of crap out here at Duke because I love football and I'm going to a basketball school. Hoops rule around here and pigskin is an afterthought. But recently my dislike of basketball has been vindicated, and by the most unlikely of heroes. Turns out you can explain why football is the better sport in mathematical terms using a little discipline called Game Theory.

Game theory is a mathematical study of strategic decision-making based on limited information. I'm no good - no good at all, frankly - at higher-level mathematics, but Jesus Christ game theory is awesome.

One of the tenants of game theory is that you become more interested in something if that thing has a higher chance of being the determining factor in a contest. We see this in voting rhetoric and behavior:

In national elections, many people believe (statistically correctly, by the way) that their vote for President doesn't matter, as it's one of a hundred million or more. What they mean when they say "matter" is that their vote has a chance to be the deciding vote; i.e., after 100+ million votes have been cast for John Q Democrat and Percy H Republican there will be a dead even split, and their vote will decide the election. That's a 1 in 100 million chance, so its not likely that your vote will be the deciding factor.

Now take a committee vote. Let's assume there are 5 committee members. Now your vote has a 20% chance of being the deciding vote; i.e., your vote "matters."


I am convinced this also plays out in sports, and it's why I can say quantitatively what I have believed for years: compared to football, baseball, and hockey, basketball sucks.

Game theory would say that basketball is not as cool a sport because its scoring system is too diluted. In a typical game somewhere near 200 points will be scored. That means that one basket, one drive, one all-out-for-the-win score has only a 1% chance of making the difference in the game. It makes the scoring unimportant: any particular hoop likely won't decide the game. It also makes it seem random: any measly score that is only worth 1% of the game's total output can decide a win or a loss. Flipping coins is more interesting if you ask me.

Football, baseball and hockey are awesome precisely because scoring is more rare, and therefore more important: each score "matters."

Baseball and hockey games average combined scores of around 8, meaning each point matters a lot: it represents about 13% of the total score and has about a 1 in 8 chance of deciding the game. Scores are important, and a game decided by one score doesn't seem like a meaningless difference. After all, the winning team put up 13% more on the board.

Football is the best. Similar to baseball and hockey, most games have around 10 scores (TDs and FGs combined) between the two teams. Unlike baseball and hockey, however, those scores can have significantly different values: a TD and the PAT are worth more than twice what a FG is worth. Assigning multiple points to each score and then having an over 100% differentiation between different types of scores (as opposed to basketball's 2 vs. 3 point shots, where 3's are vastly rarer and make for a mere 50% difference) allows for higher point totals where games can still be decided by one point, but not at the insane highs of basketball scores. This allows for an added layer of strategy to be injected into the game, while still making each score have about 10% chance of being the deciding factor. This makes a 1 point difference in football still important, rather than making a 1 point win seem random and meaningless like in basketball.

So there you have it. It's a mathematical fact that football is awesome and basketball sucks. Don't agree? Take it up with game theory.