Luck or skill: Bronco's record in close games

[Top Ute]

Prophetic?

Since this thread was started, BYU has lost two games decided by 7 points or less. With an offensive line that can't block and an unsettled QB matter, but a dominant defense, I wouldn't be surprised to see BYU double that number by season's end. Outside of Hawaii, NMSU and Idaho, the rest of BYU's games -- yes, Notre Dame included -- are ripe for sweat-inducing finishes.

[pelagius]

Since this thread was started, BYU has lost two games decided by 7 points or less.

And those two games are actually really important in terms of updating inferences. Before, based on the setup I had Bronco at

P(U|W=18) = 0.00018*0.99/(0.00018*0.99 + 0.1369*0.01) = 11.5%
P(S|W=18) = 0.1369*0.01/(0.00018*0.99 + 0.1369*0.01) = 88.5%

One should update again based on the fact that Bronco lost twice in two close games and two loses are going to be important because if a coach is as highly skilled as I model it is just really highly unlikely that he/she would lose two in a row like that (relative to the alternative hypothesis that it is just random):

P(U|L=2) = 0.25*0.115/(0.04*0.885 + 0.25*0.115) = 45%
P(S|L=2) = 0.04*0.885/(0.04*0.885 + 0.25*0.115) = 55%

You still should think it is more likely that he is skilled than unskilled but not be much. One issue, of course, is the way I set it up there are only two options: unskilled (random) and high skilled (80%). Between those two options, the last two games were very informative. However, if you did it more realistically with more granular options (I didn't do that to try to keep things simple but still capture the essentially luck vs skill issues from a probability stand point) for coach skill the last two games wouldn't be as informative. Also, even though it is in the background what you assume about the commonness of close game coach skill in the cross-section is going to drive a lot of this (as I tried to show originally).