I weep for America

[pelagius]

Really because of its education system. Doesn't anyone teach Bayes Rule? People, if you believed that Texas was a better team than Texas Tech before then played, it still may be perfectly rational (and correct from a subjective probability sense which is all we have absent an experimental setting) to still believe that Texas is better than Texas Tech (meaning that Texas is more than 50% likely to beat Texas Tech if they play on a neutral field. Remember games have a random component (bad bounces, it wasn't Texas' day, etc), the best team doesn't alwways win and things like home field advantage needs to be taken into account

Let's use the Vegas rankings as an example. The spread was 4 points (Texas favored by 4). That implies on a neutral field Texas would have been favored by about 7. Lets suppose this means that the oddsmakers believed that there was a 70% chance that Texas was better than Texas Tech (a little of slight of hand here but I really just want a prior that favors Texas which Vegas really did). Let me simplify it a bit so there are only two possibilities

Let P(A1) = 0.70 Probability that Texas is 4 points better than Texas Tech in expectation iwhen playing at Texas Tech

Let P(A2) = 0.30 Probability that Texas Tech is 6 points better than Texas in expectation when playing at home

Let's suppose this the preceeding is what Vegas believed before the game (this is their Bayesian prior).

Now for the conditional probabilities (B= 6 point win by Texas Tech):

Let P(B|A1) = 25% (just a guess but reasonable) . This is Probability that Texas loses by 6 or more at Texas Tech given they are 4 points better in expectation (ie., they have a bad game but are better)

Let P(B|A2) = 50%. Probability that Texas Tech wins by 6 or more if Texas Tech is 6 points better than Texas in expectation when playing at home.

After Texas Tech wins the game this is how you should compute the probability the Texas is better than Texas Tech given the outcome of the game:

Using Bayes Rule:

P(A1|B) = P(B|A1)*P(A1)/(P(B|A1)*P(A1) + P(B|A2)P(A2))

P(A1|B) = 0.25*0.70/(0.25*0.70 + 0.50*0.30) = 0.54

Thus after the game you still think that Texas is probably better than Texas Tech. You are much less confident and you think there is a much higher probability than before that Texas Tech is better but you still think Texas is more likely to be better. This is rational. This is how you update under uncertainty. The Vegas poll update looks perfectly consistent with Bayesian updating. As long as you believed with some confidence (not a ton of confidence) before the game that Texas was better than Texas Tech, you should still believe that Texas is better than Texas Tech after the game. This is for a specific calibration of numbers but the principle will hold more generally.

[jay santos]

Originally Posted by pelagius

Really because of its education system. Doesn't anyone teach Bayes Rule. People, if you believed that Texas was a better team than Texas Tech before then played, it still may be perfectly rational (end correct from a subjective proability sense which is all we have absent an experimental setting) to still believe that Texas is better than Texas Tech (meaning that Texas is more than 50% likely to beat Texas Tech if they play on a neutral field. Remember games have a random component (bad bounces, it wasn't Texas' day, etc), the best team doesn't alwways win and things like home field advantage needs to be taken into account

Let's use the Vegas rankings as an example. The spread was 4 points (Texas favored by 4). That implies on a neutral field Texas would have been favored by about 7. Lets suppose this means that the oddsmakers believed that there was a 70% chance that Texas was better than Texas Tech (a little of slight of hand here but I really just want a prior that favors Texas which Vegas really did). Let me simplify it a bit so there arel only two possibilities

Let P(A1) = 0.70 Probability that Texas is 4 points better than Texas Tech in expectation if when playing at Texas Tech

Let P(A2) = 0.30 Probability that Texas Tech is 6 points better than Texas in expectation when playing at home

Let P(B|A1) = 25% (just a guess but reasonable) . This is Probability that Texas loses by 6 or more at Texas Tech given they are 4 points better in expectation (ie., they have a bad game but are better)

Let P(B|A2) = 50%. Probability that Texas wins by 6 or more if Texas Tech is 6 points better than Texas in expectation when playing at home.

After Texas Tech wins the game this is how you should compute the probability the Texas is better than Texas Tech given the outcome of the game:

Using Bayes Rule:

P(A1|B) = P(B|A1)*P(A1)/(P(B|A1)*P(A1) + P(B|A2)P(A2))

P(A1|B) = 0.25*0.70/(0.25*0.70 + 0.50*0.30) = 0.54

Thus after the game you still think that Texas is probably better than Texas Tech. You are much less confident and you think there is a much higher probability than before that Texas Tech is better but you still think Texas is more likely to be better. This is rational. This is how you update under uncertainty. The Vegas poll update looks perfectly consistent with Bayesian updating. As long as you believe was some confidence (not a ton of confidence) before thaa game that Texas was better than Texas Tech, you should still believe that Texas is better than Texas Tech after the game. This is for a specific calibration of numbers but the principle will hold more generally.

They're lawyers. Just forget it.

[il Padrino Ute]

Originally Posted by jay santos

They're lawyers. Just forget it.

I'm not a lawyer.

I'm just a guy that went to school to play baseball.

Whatever it is that you and Pelagius are talking about is like me looking for a fastball and having a curveball hit the outside corner.

[pelagius]

Originally Posted by il Padrino Ute

I'm not a lawyer.

I'm just a guy that went to school to play baseball.

Whatever it is that you and Pelagius are talking about is like me looking for a fastball and having a curveball hit the outside corner.

Il Pad, not problem. I didn't see you make a statement like the Vegas consultant poll made no sense with regard to Texas and Texas Tech. However, if one is inclined to make such statements I am suggesting you should consul Bayes Rule before you decide it can't make any sense.

[pelagius]

Originally Posted by jay santos

They're lawyers. Just forget it.

You're right ... but I must continue my one person quest to correct cognitive biases in decision making under uncertainty. Its a underappreciated quest.

[il Padrino Ute]

Originally Posted by pelagius

Il Pad, not problem. I didn't see you make a statement like the Vegas consultant poll made no sense with regard to Texas and Texas Tech. However, if one is inclined to make such statements I am suggesting you should consultant Bayes Rule before you decide it can't make any sense.

Got it.

The only kind of Bayes rule that I'm familiar with is that there are 90 between each.

[Archaea]

Originally Posted by pelagius

You're right ... but I must continue my one person quest to correct cognitive biases in decision making under uncertainty. Its a underappreciated quest.

If you stating that Bayes rule shows if somebody played 100s of times, how many times somebody might prevail, and that's why Vegas oddsmakers stick to a formula which doesn't reflect who actually won on any given date, I understand your point.

Some of those predictions look odd though.

[pelagius]

Originally Posted by Archaea

If you stating that Bayes rule shows if somebody played 100s of times, how many times somebody might prevail, and that's why Vegas oddsmakers stick to a formula which doesn't reflect who actually won on any given date, I understand your point.

Some of those predictions look odd though.

Bayes rule shows you how you should update what you believe based on new information under uncertainty. It shows you how to do it optimally. The cognitive physcology literature finds strongly in experimental settings that people overreact and change their beliefs too much in the face of information that is new and dramatic (the Texas vs Texas Tech game fits the bill nicely). People are fighting against a fairly strong congitive bias when they see a poll that still ranks Texas ahead of Texas Tech.

[pelagius]

Just a note, Bayes Rule should be used in some legal applications (So yes there should be a class on Bayesian statistics in law school). For example, in criminal law regarding DNA testing. A DNA test actually tells you the following:

Pr(DNA match| innocent)

In words, a DNA test tells you the probability of a DNA match given the person is innocent (1 million to one or whater). However, that's not what you want or need to know to asses guilt properly. You need the following:

Pr(innocent|DNA match)

In words, you want to know the probability of innocence given the evidence (the fact that the DNA matches). The only way to get to that probability is Bayes Rule (any other way is wrong).

[Jeff Lebowski]

Thank you, Pelagius. Well done.

Are you paying attention, SU?