[StanFanFam13]

The problem with the above analysis is the assumption that fouls are a random variable. They clearly are not. Some teams foul more than others. Some teams foul more in some games and less in others. It depends on a lot of non-random things, like what the defense is trying to play and how the offense is attacking it. Fouls are supposed to be called based on what actually happened. Expecting that fouls should be equally distributed between the two teams clearly makes no sense.

I understood M T to be saying that the fouls should be roughly evenly distributed between refs, not teams. "Each official should see approximately the same number of fouls" doesn't imply that those fouls are split evenly between teams. M T further says that those fouls should logically be similar in ratio across officials (i.e. if Team 1 is fouling twice as much as Team 2, then each official should probably be calling a fouls on those teams at a 2:1 ratio, rather than one official calling most of the fouls on Team 1 and another calling most of the fouls on Team 2). Definitely valid to point out that in today's game, that was far from the case.

Thanks for the thorough and interesting analysis, M T. As you recognize, there is unfortunately the outstanding and largely un-quantifiable factor of uncalled fouls. I attended the game in person, and while I didn't love some of the fouls called on us, I was much more bothered by the lack of fouls called on Colorado. There was a significant amount of under-the-basket jockeying off-ball that the refs seemed not to acknowledge, and Sherrod's physicality resulted in what to my (admittedly untrained) eye were several reach-arounds and shoves that were at least equivalent to what Stanford players got called for. I was honestly shocked that she didn't foul out.

[StanFanFam13]

The problem with the above analysis is the assumption that fouls are a random variable. They clearly are not. Some teams foul more than others. Some teams foul more in some games and less in others. It depends on a lot of non-random things, like what the defense is trying to play and how the offense is attacking it. Fouls are supposed to be called based on what actually happened. Expecting that fouls should be equally distributed between the two teams clearly makes no sense.

I understood M T to be saying that the fouls should be roughly evenly distributed between refs, not teams. "Each official should see approximately the same number of fouls" doesn't imply that those fouls are split evenly between teams. M T further says that those fouls should logically be similar in ratio across officials (i.e. if Team 1 is fouling twice as much as Team 2, then each official should probably be calling a fouls on those teams at a 2:1 ratio, rather than one official calling most of the fouls on Team 1 and another calling most of the fouls on Team 2). Definitely valid to point out that in today's game, that was far from the case.

Thanks for the thorough and interesting analysis, M T. As you recognize, there is unfortunately the outstanding and largely un-quantifiable factor of uncalled fouls. I attended the game in person, and while I didn't love some of the fouls called on us, I was much more bothered by the lack of fouls called on Colorado. There was a significant amount of under-the-basket jockeying off-ball that the refs seemed not to acknowledge, and Sherrod's physicality resulted in what to my (admittedly untrained) eye were several reach-arounds and shoves that were at least equivalent to what Stanford players got called for. I was honestly shocked that she didn't foul out.