[YOhio]

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 (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 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.

Someday I'll explain the Scoreboard Rule to you Professor.