Once you have the concept of a drafting error in hand, and a fairly large one at that, you can ask questions that have almost Murphy’s Law implications for hoary old theories such as BPA. Consider this scenario: you have three players in the middle rounds you are considering, whose “true career value” is about the same. We’ll assume drafting is an efficient market for now, so our estimation of the value of these picks is a normally distributed estimate whose mean is based off their true career value. Which one of these men do we draft? We draft the player whose value we have overestimated the most. Consequently, we draft the player most likely to underachieve our expectations.
Since in most drafts there are very few times a true BPA falls into the lap of teams (i.e. players where one is wildly superior to all other candidates), it would seem that BPA is a way of optimizing how heartbroken a team will be over the draft choices it actually picks. Though this approach would appear to gather the best athletes, in a draft with a large error, and multiple situations where you’re picking from nearly equivalent athletes, perhaps all BPA will get you is maximally suffering from buyer’s remourse.
Update: Brian Burke, on the blog Advanced NFL Stats, talks about exactly the same issue, except with free agents. This issue has a name, the “Winner’s Curse” and is a well documented problem with auction style transactions.