Poker: November 2007 Archives
I hope Tyler Cowen will forgive me for using a variation on the title that he often uses for posts on Marginal Revolution.
I've said it before, the markets in professional sports are very inefficient. Even in some cases where some smart guys have figured stuff out, most of the pundits refuse to believe it. This can be because they don't want to accept that some academic who never played the sport might know more about strategy than players and coaches who have lived and breathe it their whole lives. Or it might be as simple as the human tendency to believe one's own eyes and ears rather than abstract data about what the best course of action is.
Take David Romer's conclusions about when to go for it on fourth down. Basically, he's figured out you go for it a lot, and even in your own half of the field. The data back him up, and even Bill Belichick believes him. Yet the vast majority of coaches, players, pundits and fans ignore him and continue to believe that the right thing to do is to "play it safe". This situation reminds me of poker.
Say you're an NFL coach, your team is on the opponents 35, its 4th and 1, and you estimate that you have a 50% chance of success if you go for 1st down. If you kick a field goal, your chance of success is 80%. Should you go for it?
Going for the field goal is worth 3*.8 = 2.4 points. What's a first down worth? Well, you have three possibilities:
1) You go one to score a touchdown (7 pts; most teams have an extra-point success rate sufficiently high to disregard the chance of a missed PAT)
2) You go on to kick a field goal (3 pts)
3) You go on to lose the ball (0 pts)
So going for a first down is worth p(1)*6 + p(2)*3 + p(3)*0. Of course, this simplifies to p(1)*6 + p(2)*3. Now, let's remember that IF we determine that going for the first down is higher higher expected value than kicking a fiield goal right now, p(2) isn't going to be possible unless it is at least 4th and 2 (because we'd go for it again on 4th and 1). So p(2) is a relatively tricky number to figure out, and of course p(1) and p(2) are NOT mutually exclusive, because both really depend on how efficient you are at picking up first downs, and whether your strategy accounts for your risk tolerance (you might run more often on 3rd and 4 because you know you are going to go for it on 4th and 1, for example). Let's assume that p(3) is 5%, and that it includes missed field goals. This is a high field goal success rate, but obviously chances are you will be more successful from closer in.
And of course, I'm negating the opponent's expected-value for all our actions. That is, our expected value is a combination of how many points each action scores for us (on average) and how many each action scores for the opponent (on average). To illustrate, going for it on 4th and 1 and throwing an interception that the defense runs back is effectively worth -7 points, from your team's perspective, so this probability must also be accounted for somewhere (even if it's small).
But let's make the thought exercise simple. After all, David P did all this analysis, and this isn't the point I am trying to make. Let's pretend the only factors are how often do you go on to score a touchdown/field goal if you make a first down. Let's say you'd score a TD 50% of the time. So, 50% of the time you'd get a field goal. Well, going for it has a value of 50%*((50%*7) + (45%*3)) = 50%*(3.5+1.35) = 2.425. In other words, going for it has a higher expected value than kicking a field goal (2.4).
But, of course, even in our fantasy world where the factors are that simple (and in which I fudged the numbers to make going for it +EV), most people wouldn't agree that you should always go for it. Most humans aren't wired to think of average probabilistic outcomes. You keep going for it on 4th down, you fall short half of the time, and the angry mob will be lining up with pitchforks and torches to drive you out of town! "You keep going for it on 4th down even though we lose the ball half the time, coach! What the HELL?"
Just like poker. Just because you are not likely to win the pot doesn't mean that you shouldn't call the bet. It's not how often you win the pot (erm...score), it's how much money you win (erm...points you score).
I've said it before, the markets in professional sports are very inefficient. Even in some cases where some smart guys have figured stuff out, most of the pundits refuse to believe it. This can be because they don't want to accept that some academic who never played the sport might know more about strategy than players and coaches who have lived and breathe it their whole lives. Or it might be as simple as the human tendency to believe one's own eyes and ears rather than abstract data about what the best course of action is.
Take David Romer's conclusions about when to go for it on fourth down. Basically, he's figured out you go for it a lot, and even in your own half of the field. The data back him up, and even Bill Belichick believes him. Yet the vast majority of coaches, players, pundits and fans ignore him and continue to believe that the right thing to do is to "play it safe". This situation reminds me of poker.
Say you're an NFL coach, your team is on the opponents 35, its 4th and 1, and you estimate that you have a 50% chance of success if you go for 1st down. If you kick a field goal, your chance of success is 80%. Should you go for it?
Going for the field goal is worth 3*.8 = 2.4 points. What's a first down worth? Well, you have three possibilities:
1) You go one to score a touchdown (7 pts; most teams have an extra-point success rate sufficiently high to disregard the chance of a missed PAT)
2) You go on to kick a field goal (3 pts)
3) You go on to lose the ball (0 pts)
So going for a first down is worth p(1)*6 + p(2)*3 + p(3)*0. Of course, this simplifies to p(1)*6 + p(2)*3. Now, let's remember that IF we determine that going for the first down is higher higher expected value than kicking a fiield goal right now, p(2) isn't going to be possible unless it is at least 4th and 2 (because we'd go for it again on 4th and 1). So p(2) is a relatively tricky number to figure out, and of course p(1) and p(2) are NOT mutually exclusive, because both really depend on how efficient you are at picking up first downs, and whether your strategy accounts for your risk tolerance (you might run more often on 3rd and 4 because you know you are going to go for it on 4th and 1, for example). Let's assume that p(3) is 5%, and that it includes missed field goals. This is a high field goal success rate, but obviously chances are you will be more successful from closer in.
And of course, I'm negating the opponent's expected-value for all our actions. That is, our expected value is a combination of how many points each action scores for us (on average) and how many each action scores for the opponent (on average). To illustrate, going for it on 4th and 1 and throwing an interception that the defense runs back is effectively worth -7 points, from your team's perspective, so this probability must also be accounted for somewhere (even if it's small).
But let's make the thought exercise simple. After all, David P did all this analysis, and this isn't the point I am trying to make. Let's pretend the only factors are how often do you go on to score a touchdown/field goal if you make a first down. Let's say you'd score a TD 50% of the time. So, 50% of the time you'd get a field goal. Well, going for it has a value of 50%*((50%*7) + (45%*3)) = 50%*(3.5+1.35) = 2.425. In other words, going for it has a higher expected value than kicking a field goal (2.4).
But, of course, even in our fantasy world where the factors are that simple (and in which I fudged the numbers to make going for it +EV), most people wouldn't agree that you should always go for it. Most humans aren't wired to think of average probabilistic outcomes. You keep going for it on 4th down, you fall short half of the time, and the angry mob will be lining up with pitchforks and torches to drive you out of town! "You keep going for it on 4th down even though we lose the ball half the time, coach! What the HELL?"
Just like poker. Just because you are not likely to win the pot doesn't mean that you shouldn't call the bet. It's not how often you win the pot (erm...score), it's how much money you win (erm...points you score).
