But it is not clear to me that his incentives aren’t “right,” and that under the alternative de Novo review he has “exactly the right incentives”. Yes, he will more heavily weight what he believes to be true under de Novo review. But incorrect definitive calls cannot be corrected by replay while incorrect non-calls can be; thus type 1 errors may impact the outcome of the game while type 2 errors will not (because they are overturned).

So if we want refs to minimize the total number of errors they make, then de Novo review is the better mechanism. If we instead want refs to minimize the number of errors that may change the outcome of the game, the present system is the best mechanism, and we actually want refs to set their threshold probabilities to one. Of course, this would dramatically slow down the pace of the game (as most plays would be reviewed). So I think the best thing for football is the present system, where type 1 errors are induced to be more costly than type 2 errors, but not infinitely so. Maybe induce a threshold probability of 60-65%. Personally, I think this mechanism induces “the right” incentives in referees.

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