If you were starting a team today......

[TanksAndSpartans]

As an outsider on the baseball side, its interesting to me that I haven't noticed a single argument that used sabermetrics. My understanding is that field devalues most traditional statistical measures like RBI in favor of new ones like WAR. Philosophically, I've even heard it argued that there is no such thing as clutch. I would have thought there would be some crossover between collecting and sabermetrics especially among those posting in this thread on a non-collecting topic.

[darwinbulldog]

Originally Posted by TanksAndSpartans

As an outsider on the baseball side, its interesting to me that I haven't noticed a single argument that used sabermetrics. My understanding is that field devalues most traditional statistical measures like RBI in favor of new ones like WAR. Philosophically, I've even heard it argued that there is no such thing as clutch. I would have thought there would be some crossover between collecting and sabermetrics especially among those posting in this thread on a non-collecting topic.

I try it from time to time, but it never seems to change anyone's mind. The paper that debunked the hot-hand phenomenon in basketball applies to baseball as well. The other interesting thing that becomes clear from the data is that baseball is only a team sport in the trivial sense. The game within the game is almost all there is to the game in terms of predicting victories. And I have written a bit about the "clutch" phenomenon, more as a theory paper than with sabermetrics. Most people here didn't like what I had to say on the matter, but maybe you would, and I stick by it. https://www.psychologytoday.com/us/b...e-and-more?amp

[TanksAndSpartans]

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?

[darwinbulldog]

Originally Posted by TanksAndSpartans

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.

[nat]

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.

[darwinbulldog]

Originally Posted by nat

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.

[CurtisFlood]

Mays.

[packs]

Originally Posted by darwinbulldog

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.

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

[Peter_Spaeth]

Originally Posted by nat

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.

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.

[nat]

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.