Thanks Glenn - good article - so which player would you take? A quick Google search told me Ruth had the highest WAR. Wouldn't he be the player I want assuming the goal of the team would be to win as many games as possible i.e. the sabermetric approach rather than citing "clutch performance" and "best I ever saw" type arguments to chose a player?

The OP didn't offer Ruth as a choice, so I went with Mays, but if I could take any player from the history of the game, yes, Ruth is the one.

It really depends how this counterfactual is spelled out. Let me make it a bit more specific and then offer an answer.

I'm going to assume:

(1) We've got the player starting their rookie year.
(2) We don't know what their career is going to be like in our imaginary world, but:
(3) we do know what their career was like in the real world.

Without (3) you're really asking about which player had the best tools - you're looking for scouting reports on these guys as 20 year olds. But given that we do know what their careers were like in the real world, I think my first cuts to the list will be Griffey and Mantle. Both were injury prone, and Mantle had problems with alcohol. In real life, both were great players. But the probability that if Mantle played his career out again his knees would give out before they did, or his alcoholism would get severe enough that he couldn't play at a top level, are too high for me to be comfortable picking him. (Ditto for Griffey wrt to the injuries. He also just wasn't as great of a player as the others.)

That leaves Aaron, Mays, and Trout. Now, let's assume (as seems reasonable) that a player's possible performances form a normal distribution, with the mean determined by their talent level. That is: if they each replayed their career a zillion times, of the outcomes they generate, 66% of them will fall within one standard deviation of the average outcome, a further 33% will fall within an additional standard deviation of the average, and then there are a few outliers. We are, in effect, being asked to take a chance on one of those zillion possible careers, it's just that we don't know which one.

Now, we do know that in the actual world Aaron and Mays put together superlative careers. That is, we've already picked one possible outcome out of the bag, and it turned out to be a good one. Given that these outcomes form a normal distribution, it is extremely likely that their actual career was relatively close to the expected outcome. (99% probable that it's within two standard deviations, 66% within one.) It's possible, but not terrifically likely, that their actual career was one of the extreme outliers. So we can be reasonably confident that if we picked Aaron or Mays, we'll again get something reasonably close to the career that they actually produced. Now, this still involves quite a bit of uncertainty - that 99% confidence interval covers four standard deviations after all - but it's pretty good.*

Trout, despite being both my favorite Angel and my favorite fish, doesn't allow this kind of confidence because we haven't seen the rest of his career yet. He certainly could end up beating Mays or Aaron, but he hasn't done it yet. Which means that, given our information, the range of possible outcomes on Trout's career is greater than it is for the other two. One way to think about this is that the bell curve of possible careers for Trout is flatter than it is for Mays or Aaron. So, given the additional risk involved in picking him, my second cut would be to eliminate Trout.

It then comes down to which player you think had the better career: Mays or Aaron. I'll pick Mays, but if you want to go with Aaron I'm not going to argue too much.



* Can we be 99% confident that their actual careers are within two standard deviations of their mean career, given that we know that they had great careers? Maybe not. If not, let me given an additional argument. Given that they actually had great careers, their mean performance, whatever it is, has got to be pretty high. And so even if their actual careers were unlikely outliers, their expected career is still going to be good. And, more to the point for this exercise, if we have grounds to think that Aaron's or Mays' career was actually an outlier, we have the same grounds for thinking that Trout's career (so far) is as well. And, given that we know more about Aaron's career than about Trout's, we can still infer that the distribution of possible careers for Trout is flatter than it is for Aaron and Mays.

Good stuff, but in a normal distribution over 4% (not just 1%) of outcomes deviate from the mean by more than two standard deviations. What I would focus on though are the standard errors of the means, which become tiny with all of the data in a 20-25 year career.

Naturally there's going to be some regression toward the mean, as you allude to in your footnote, but that doesn't have any impact on the rank ordering of where you expect the players' careers to end up if you replayed them under slightly different circumstances. Sure, it's possible that Don Mattingly would end up having the best career in MLB history, but it's more likely that Griffey would, more likely still that it would be Mantle, and even more likely that it's Mays.

Mays.

I would say it's equally possible that Griffey never becomes Griffey because he sustains an injury earlier in his career.

I am probably just not well-versed enough in statistics etc. to understand this fully, but it seems like a somewhat inconsistent mix of ex ante and ex post. If you were analyzing it purely ex ante you would have absolutely no idea beyond speculation about how any of their talents would ultimately translate into a career, no? History is full of guys with enormous talent who go bust.

There are lots of ways the counterfactual situation of picking a young player to start a team could be spelled out. You could go just from scouting reports of the guys when they were 20 (this is the first possibility that I mentioned).

But the assumption that I made for the exercise was that we know how their careers actually turned out. Since it's all counterfactual anyway, we can give ourselves that knowledge if we want. And why not? We do, in fact, know how they turned out. Now, given that their careers turned out one way, it doesn't guarantee that they will turn out that way again - which is why this question isn't just "which player in fact had the greatest career". But it does give us some indication of how we should expect them to turn out if they played their careers again, and what my post was doing was trying to figure out what we should expect from them if they went back in time and played their career out again.

Think about it this way: imagine that we have exact replicas of Mays, Mantle, Trout, etc. as young men. Up until the age of 20 (or whatever) both nature and nurture have, for these clones, been exactly the same as they were for the real Mays, Mantle, etc. We don't know what they're going to do with their respective careers. But we do know what their exact duplicates did with their careers, and that should tell us something about what to expect from the young ball players that we have to choose between.

It's beyond me why, if we know how they turned out, we would even ask how would they turn out if they started again. As I said, this seems an odd mix of ex ante and ex post, why not just do one or the other?

I agree with your point but Ford could not have started game seven because he pitched a complete game in a must win the day before. Stengel's mistakes re: Ford, IMO were:
1) Not starting him until game three in favor of Ditmar & Turley.
2) Keeping him in the entire sixth game which should have been handed over to the bullpen as it was a blowout.
3) As you noted not using Ford in game seven even with the game six CG under his belt.

Other debatable pitching moves in game seven were not using Ryne Duren, who had a poor season but an excellent WS up to that point, at all & leaving Bobby Shantz in for five innings after an entire season in short relief.

I've seen sources give Stengel a lot of credit for the way he used platooning which he apparently learned under McGraw.

"why not just do one or the other?"


Pure ex post is boring. Just get a list of players, order it by your favorite measure of value, and then give Trout a bonus of however much your favorite projection system puts him at. (With some tweaks for possible ranges of outcome, but whatever tweaks you put on it, Trout + projection-for-the-rest-of-his-career isn't going to be a contender here.)

Pure ex ante is hard to do (since we don't, that I know of, have scouting reports for a young Hank Aaron), but also unnecessarily restrictive. We know that Hank Aaron is capable of having the career that he, in fact, had. Why discard that information?

But perhaps more to the point: it's just a game, and you can play it however you want. If you want to project players just based on their amateur scouting reports, fine, that's one way to play the game. The OP didn't give us much guidance on how this game was to be played, so I picked one way to play it that sounded like fun to me. There are lots of other ways to do it too.

OK fair enough I just wanted to make sure I wasn't missing something. I am guessing the OP was just asking who do you think the best player was in so many words, which sounds ex post. Thanks for clarifying.

I'm just waiting for someone to start regurgitating Gordon Wood, talking about ya know, the Pre-Revolutionary utopia and the capital forming effects of military mobilization.