Ender wrote:Sorry I wasn't talking about PECOTA attrition rates, I was talking about pitchers in general. Pitchers are riskier than hitters without any doubt at all in my mind. The odds of Santana getting hurt this year and missing significant time is much higher than the guys picked in the early first round (except maybe Pujols).

And no what happened isn't the best way to decide whether a pick was good or not. If you had drafted Ryan Braun in the 3rd round last year it would have been a terrible pick, yet he put up better value than that. If you drafted Pujols #1 it wasnt' a bad pick but he wasn't a top 20 player because of the injuries. If you picked Chris Carpenter in the 9th round it was still a steal even though he got hurt right away. The results ignore all of the risk and upside that goes into draft position.

Again, sure. But just presenting the concept of risk as an amorphous thing doesn't solve, indeed it worsens, your complaint for non-objectivity of measures. You have to quantify it, or at least approximate it, to make the concept of risk useful. Simply stating that this risk exists so this player isn't worth it doesn't work.

Additionally, it ignores the other side of a projection function. For all things, be they cards, baseball player, or oil wells, the proper formula is:

Expected Value = Sum of: Probability of Outcome 1 (P1) * Value of Outcome 1 (V1) + P2*V2 + ... + PnVn.

To continue with your initial example, even a 2-8 becomes playable if you're getting 4-to-1 odds on your money in a heads-up situation. So it's not enough to simply declare by fiat that a probability exists to arrive at the conclusion of a certain player's value.

Pitchers have high variance in their performance, even if you exclude the injury risk. The thing that makes Santana so appealing is that the performance variance in his career has been very low. He's been incredibly, incredibly consistent. So, in my mind, his high level of performance and his low beta on performance variance puts him into a category of pitcher by himself, worth a 1st round pick. You can certainly disagree. But I don't think you're being as theoretically rigorous as you think you are.

As far as the question of how you evaluate a pick after the fact.... again, the probabilities are unknowable since each season is a singular, unrepeated event. It has some robustness as a sample size of a certain # of ABs or certain # of starts but it's still a singular event if you're evaluating it at a season level. So we can't say after the fact what the entire universe of P's and V's are: we can only say what actually happened. So the best we can do is look at past performance to project out and then see how the data fits. I'm not sure how else you would do it.

You can think of this as rolling a dice and a 6 comes up. Now, off of that one event, is the probability of rolling a 6 one-sixth? It could be. Or it could be a weighted die where the probability of rolling a 6 is one-half or one-third or three-quarters or whatever. Based off of one rolling of the die, you can't extrapolate out the probabilities with any kind of certainty. But if you observe it and a 6 comes up four times in a row, you might think that maybe you're not dealing with random chance so you project that it's going to come up a 6. What you're saying is that if you say, "I think it's going to be a 6" and it comes up a 6 again that has nothing to do with the probability ahead of time. And there I disagree. You made an observation (it's coming up 6 a lot), you projected out (I think it's going to be a 6 again) and then you observe the results (whatever comes up). The actual event plays a role in the ex-post evaluation of your initial projection because you don't actually know the existant probabilities in the same way that you do with theoretical coin flips or card games so every data point, including the one you're projecting, becomes a factor in the analysis.

Me, I think Santana comes up 6's a whole lot and is worth a top-5 pick this year.

0-3 to 4-3. Worst choke in the history of baseball. Enough said.