Well, what about this:

We throw two dice. I, knowing, that it is the most likely outcome, pick 7. You pick 2, because that’s the number you had in little league. We roll the dice 5 times, and get 4,3,8,9,11. My educated guess turned out just as wrong as your wild one. But 7 was still a more likely score than 2 – my guess was the “right” one, regardless of the outcome. Theoretically, if we did this an infinite number of times, the dice would land on 7 more often than they would on 2. But I could never prove this like that, for obvious reasons. I could do two things:

• Convince you logically that 7 is the better pick.
• Do the test 1,000 times, and hope the results show that 7 is the better pick (not a great method, doesn’t actually prove anything).

That, IMO, is a better analogy for Carroll’s system. It should be more accurate than your “name out of a hat method”, but again, Carroll can’t prove it by just testing the two methods an infinite amount of times. He too is left with two options:

• Convince us logically that his system is worth something (would require showing us his formula, which he obviously wouldn’t want to do).
• Repeat the test many times and show us the results (even more problematic in this case – let’s say the system says Cain is a pretty big injury risk. He goes on to pitch 420 innings in the next two years, and then spends half of the third year on the DL – was the system right or wrong? We don’t know, because the system never showed a final projection, it only projected likelihood).

To my knowledge, he has done neither, which is why I’m not crazy about using his system. I think we agree on this. I hope I made myself clear.