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Monday, July 27, 2009

The Book Blog: mgl: Most people still don’t understand the concept of regression toward the mean…

Dig, it!

There is a thread on BTF about Sabathia’s “numbers,” particularly his BB and K rates, being down this year, as compared to last year, although he is still pitching very well of course.

While the quality of the posts on BTF is nowhere near that of this blog (although they beat us easily in quantity), there are some reasonably intelligent regulars on that site (if anyone interprets that as a dig, it is).

...The thing that people don’t understand (actually one of the things) about regression toward the mean in baseball is that the reason any above or below average player will always regress, on the average, towards average, is that they were not really as good or bad as we thought in the first place, based on any of their stats.  That goes for Sabathia, Halladay, Bonds, Chipper Jones, etc., etc.  Chipper Jones is not as good as his career stats tell us, even after you do all the appropriate adjustments.  Same for Halladay.  And Sabathia.  And everyone else who has been above average and we think has true talent X.  When I say “as we think” I mean as their stats suggest, not as we think based on a credible projection which already does the regression.  And of course, there is some chance that any given player is better than his prior stats - it is just that the chances of him being worse is greater than the chances of him being better.  That is ALWAYS the case, as long as we properly define the mean for that player.

That is the KEY to understanding regression toward the mean and is what most people don’t understand, even if they think they understand the concept.

Repoz Posted: July 27, 2009 at 12:19 PM | 244 comment(s) Login to Bookmark
  Tags: baseball geeks, projections, sabermetrics, site news

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   1. Coot Veal and Cot Deal's cols=“100” rows=“20” Posted: July 27, 2009 at 12:30 PM (#3268129)
Throughout my years of lurking, this guy has consistently impressed me as one of the most insufferable, self-important jerks around...
   2. Edmundo got dem ol' Kozma blues again mama Posted: July 27, 2009 at 12:34 PM (#3268132)
I thought regression to the mean referred to the change in mgl's attitude if you don't accept his truths on faith. :)
Seriously, the guy may be a brilliant analyst but dummies like me can never tell because he has no ability or desire to write in a way that is understandable to the masses.
   3. vern_fuller_brushback Posted: July 27, 2009 at 12:43 PM (#3268141)
You guys mean he keeps regressing and is getting meaner and meaner?!
   4. Best Regards, President of Comfort, Esq. Posted: July 27, 2009 at 12:46 PM (#3268144)
If your apartment had burned down, you'd know how mean mgl isn't.
   5. Chris Needham Posted: July 27, 2009 at 12:48 PM (#3268147)
So that means that the quality of comments here are better than he's observing, and the quality there is less, right?
   6. Jeff K. Posted: July 27, 2009 at 12:49 PM (#3268149)
####, if my apartment burns down, I'm looking at him first. Then Szymborski. Then Keefe.
   7. RJ in TO Posted: July 27, 2009 at 12:55 PM (#3268155)
####, if my apartment burns down, I'm looking at him first.


You should look slightly to the north.

The people of the vestigial tails are looking for vengeance.

On a more thread related note, while I've never had any run ins or direct interactions with mgl, and while I'm sure that he can be quite a nice guy (as evidenced by whatever he did to help out Larry), his writings (or at least those that I've read) frequently come off as arrogant, insulting, and often unwilling to answer whatever question was posed in anything approaching a useful way. While that may be useful in a "baseball as theory" manner, it's not terribly useful in an actual "baseball as an actual event" manner.
   8. Coot Veal and Cot Deal's cols=“100” rows=“20” Posted: July 27, 2009 at 12:56 PM (#3268156)
If your apartment had burned down, you'd know how mean mgl isn't.


Granting that this sort of basic kindness is a good thing, I don't see how it buys him a pass on his wholly obnoxious public persona... lots of people lend a helping hand to their fellow man each and every day without spewing mgl's completely unnecessary crap.

screw him and his oh-so-intelligent blog.
   9. Rickey! On a blog from 1998. With the candlestick. Posted: July 27, 2009 at 12:57 PM (#3268157)
Reading MGL makes me reconsider the "geeks in their mother's basement" assessment. I'm sure he's a whiz with the math and all, but boy needs a personality adjustment in the worst way.
   10. Jeff K. Posted: July 27, 2009 at 01:06 PM (#3268165)
Canada has fire now? Good for you guys!

Also on-topic: Look, I understand the point being made. But quite frankly, Chipper Jones is exactly as good as his career stats with adjustments tell us. There comes a point when belaboring the sample size issue is overly done, and a career of that length, with no ridiculousness, is past that point. Yes, even with a guy who has hit exactly .300 every year for 10 years (neutral everything contextual), we should project a little below that. But saying we don't know that guy is a true-talent .300 hitter, or worse, saying that he's not one, which is what "Chipper Jones is not as good as his career stats tell us, even after you do all the appropriate adjustments" says, is the definition of belaboring the point.
   11. Slivers of Maranville descends into chaos (SdeB) Posted: July 27, 2009 at 01:08 PM (#3268169)
I have never been entirely comfortable with the Platonic assumption adopted by many sabermetricians that a player has an unchanging "True Talent," and any and all fluctuations in his performance are due to random error or statistical fluctuation. At some level it is clearly not true: Alex Rodriguez did not have the same True Talent at age 8 as he did at age 28, players get injured, etc. All sabermetricians would concede that. Still, maybe it is true for small slices of a player's career, assuming he stays healthy. Then again, perhaps not. I can see the adoption of the idea of "True Talent" as a simplifying assumption, but in a lot of writing it seems to be referred to as an unchallengeable axiom. Has it ever been demonstrated, empirically or mathematically?

Alternately, we could define True Talent as the average performance of a player over his career. In that case, as Jeff K. notes, a player's True Talent could not, by definition, deviate from his career statistics.
   12. Shooty Survived the Shutdown of '14! Posted: July 27, 2009 at 01:09 PM (#3268170)
So, separating the personal insults from the point he's trying to make...what is his point and does it have merit? An above average player is not as good as his stats? Is he arguing that there is no such thing as an established level X if X is above average? Or below X is we're discussing Tony Pena Jr.? I admit, I'm not one of the few reasonably intelligent people around here, so could someone help a bother out?
   13. RJ in TO Posted: July 27, 2009 at 01:09 PM (#3268171)
Canada has fire now? Good for you guys!


Of course we have fire. If we didn't, how would we survive in this frozen wasteland?

And I agree with everything else in your post. While we can never know the "true" talent level of a player, we can (after enough at bats) get a close enough approximation of that true talent level to be comfortable enough with the increasingly small difference between actual performance and "true" talent level.
   14. JoeHova Posted: July 27, 2009 at 01:12 PM (#3268175)
I like mgl. He can be a gigantic ass but he seems so oblivious to that tendency of his that it's almost cute.
   15. BFFB Posted: July 27, 2009 at 01:15 PM (#3268178)
on average towards the average.

that statement right there is the entire ####### problem with applying regressions to specific players under specific circumstances. it's great for approximating how a group will behave but goes funky if you apply it to a single player because it doesn't contain enough information about that player.

i guess what i'm saying is that the thing people don't understand with regressions is when they are useful and when they may be useful or useless.

I have never been entirely comfortable with the Platonic assumption adopted by many sabermetricians that a player has an unchanging "True Talent," and any and all fluctuations in his performance are due to random error or statistical fluctuation.


you shouldn't be. it's a false assumption.
   16. Rickey! On a blog from 1998. With the candlestick. Posted: July 27, 2009 at 01:15 PM (#3268179)
He may be cute, but he's also trolling for web hits by taking swipes at supposedly inferior sites.
   17. Shooty Survived the Shutdown of '14! Posted: July 27, 2009 at 01:15 PM (#3268180)
I like mgl. He can be a gigantic ass, but he seems so oblivious to it that it's almost cute.

For some reason, he doesn't push my buttons, either. At least he's intelligent and, seemingly, true to himself. (Also, he makes me chuckle.) It's the idiots without a sense of humor who write in a patronizing tone that get me fired up.
   18. 6 - 4 - 3 Posted: July 27, 2009 at 01:19 PM (#3268184)
At some level it is clearly not true: Alex Rodriguez did not have the same True Talent at age 8 as he did at age 28,


True. But Wieters did. The fact of the matter is that Wieters possessed more true talent as a tadpole in God's scrotum than any other player has or ever will have.

What you charlatans don't seem to understand is that MGL is the Wieters of baseball analysts. Even if you think that you understand his greatness, the fact is simply that the universe haven't experienced a sufficient sample size to make any conclusions since the rest of the world is regressing to the mean, which in the long-run of the cosmos is inanimate matter. This whole human civilization thing is just a statistical anomaly that will ultimately regress back to the mean of nothingless.

But you can't be expected to understand all that. Only MGL truly understands the secrets of the universe. And of course Wieters.
   19. Coot Veal and Cot Deal's cols=“100” rows=“20” Posted: July 27, 2009 at 01:20 PM (#3268186)
It's the idiots without a sense of humor who write in a patronizing tone that get me fired up.


aside of "idiot", this is a perfect description of the gentleman in question...
   20. 6 - 4 - 3 Posted: July 27, 2009 at 01:23 PM (#3268188)
If your apartment had burned down, you'd know how mean mgl isn't.


And yet he'd chastise your gratitude for being based on an insufficent sample.


For some reason, he doesn't push my buttons, either. At least he's intelligent and, seemingly, true to himself. (Also, he makes me chuckle.) It's the idiots without a sense of humor who write in a patronizing tone that get me fired up.


+1. There's no reason to take it personally, he's just trying to be funny and also has grown tired of having the same conversation with people 1000x. I enjoy his work, even when he's calling me an idiot.
   21. Shooty Survived the Shutdown of '14! Posted: July 27, 2009 at 01:23 PM (#3268189)
aside of "idiot", this is a perfect description of the gentleman in question...

Yeah, but one out of three ain't bad!
   22. pkb33 Posted: July 27, 2009 at 01:23 PM (#3268190)
Putting aside the meta-commentary...

What I think is unfortunate is how many confuse regression to the mean with the 'gambler's fallacy'

A lot of people are trying to use 'regression to the mean' to refer to things other than what it is, here and elsewhere.
   23. Jeff K. Posted: July 27, 2009 at 01:25 PM (#3268193)
FWIW, I like mgl too. I'm certainly no one to judge others for being a jerk.
   24. RJ in TO Posted: July 27, 2009 at 01:27 PM (#3268197)
FWIW, I like mgl too. I'm certainly no one to judge others for being a jerk.


Why not? Your expertise in the manner would surely make you an excellent judge.

As Canadians go, I suspect that I'd qualify too.
   25. Rickey! On a blog from 1998. With the candlestick. Posted: July 27, 2009 at 01:29 PM (#3268203)
has grown tired of having the same conversation with people 1000x

If you have this much difficulty conveying your thoughts and findings to a general audience you might consider improving your ability to communicate to a general audience. Or stop trying to communicate outside of specialized audiences. If one listener fails to understand something it may not be your fault. If many listeners fail to understand, repeatedly, it's probably not their fault.
   26. Biff, highly-regarded young guy Posted: July 27, 2009 at 01:35 PM (#3268210)
And yet he'd chastise your gratitude for being based on an insufficent sample.

Primey.
   27. The importance of being Ernest Riles Posted: July 27, 2009 at 01:40 PM (#3268213)
I have never been entirely comfortable with the Platonic assumption adopted by many sabermetricians that a player has an unchanging "True Talent," and any and all fluctuations in his performance are due to random error or statistical fluctuation.

Not a single serious sabermetrician makes this assumption.

Questions of personality aside (if you ever met mgl, you would think him a perfectly reasonable human being), mgl is dead right in this regard. Given a certain sample of performance, it is more likely than not that the player is closer to average than to the extremum suggested by his stats. Note the emphasis. It is possible that Pujols is better than what he has shown, but it is unlikely. That's why we regress to the mean, but not all the way to the mean.

Given the general misconceptions about regression to the mean and sabermetrics in general, even at a place like Primer (mgl's dig at which I find disagreeable but hilarious), his crankiness should not be surprising.

Or stop trying to communicate outside of specialized audiences.

That's what the Book Blog is for. It's not his fault that Primer keeps linking to it.
   28. Shooty Survived the Shutdown of '14! Posted: July 27, 2009 at 01:44 PM (#3268220)
It is possible that Pujols is better than what he has shown, but it is unlikely. That's why we regress to the mean, but not all the way to the mean.

Isn't this what most people understand as regressing to the mean to be? I didn't read the CC Sabathia thread, but now I'm completely flummoxed as to what MGL's beef is.
   29. BDC Posted: July 27, 2009 at 01:46 PM (#3268224)
any above or below average player will always regress, on the average, towards average


It's time for me, after a string of intelligent posts in the past month, to regress toward the stupid, but: the statement above is certainly a general truth. However, it's a factor, not a law. Other factors are health, experience, and aging. There are bunches of below-average players who don't regress towards average, for instance. They get older and older, or they get less and less healthy, or their inability to learn to hit the curveball leaves a wedge for the league's pitchers to increasingly exploit.

If the concept is instead that players regress toward their true talent, which is itself a moving target based on multiple factors, that's probably a better way of thinking about what a player is going to do next year.
   30. The importance of being Ernest Riles Posted: July 27, 2009 at 01:47 PM (#3268228)
Isn't this what most people understand as regressing to the mean to be? I didn't read the CC Sabathia thread, but now I'm completely flummoxed as to what MGL's beef is.

I didn't read the thread, so I'm not sure what his beef is (or whether it is justified in this particular case).
   31. Chris Needham Posted: July 27, 2009 at 01:47 PM (#3268230)
If you have this much difficulty conveying your thoughts and findings to a general audience you might consider improving your ability to communicate to a general audience. Or stop trying to communicate outside of specialized audiences.

In fairness, hasn't he pretty much stopped trying to communicate to general audiences? Isn't 99.9% (warning: not regressed) of his writing only done on his blog at this point?
   32. Shooty Survived the Shutdown of '14! Posted: July 27, 2009 at 01:48 PM (#3268231)
If the concept is instead that players regress toward their true talent, which is itself a moving target based on multiple factors, that's probably a better way of thinking about what a player is going to do next year.

Exactly. Which is why no one expects Marco Scutaro to perform in the second half the way he did in the first. He may do it, but no one here would bet on it. Again, I just don't get the controversy here.
   33. Edmundo got dem ol' Kozma blues again mama Posted: July 27, 2009 at 01:49 PM (#3268232)
Given a certain sample of performance, it is more likely than not that the player is closer to average than to the extremum suggested by his stats. Note the emphasis. It is possible that Pujols is better than what he has shown, but it is unlikely. That's why we regress to the mean, but not all the way to the mean.
Sid, would you please give your friend mgl* some writing lessons? Your explanation is crystal clear to this dummy.

*My original snark was mainly to have fun with words. And with mgl's writerly personna to poke some fun at, how could I resist?
   34. Slivers of Maranville descends into chaos (SdeB) Posted: July 27, 2009 at 01:52 PM (#3268241)

Not a single serious sabermetrician makes this assumption.


Well mgl uses the term "true talent" in the sample above, and it evidently refers to something other than a player's actual performance. What, then, does it mean?
   35. The importance of being Ernest Riles Posted: July 27, 2009 at 01:53 PM (#3268242)
Sid, would you please give your friend mgl* some writing lessons? Your explanation is crystal clear to this dummy.

*My original snark was mainly to have fun with words. And with mgl's writerly personna to poke some fun at, how could I resist?


Hey, buddy, this is the internet! Snark is the lingua franca!

Funny though, we primates can dish it but we have a hard time taking it.
   36. BFFB Posted: July 27, 2009 at 02:01 PM (#3268254)
If the concept is instead that players regress toward their true talent, which is itself a moving target based on multiple factors, that's probably a better way of thinking about what a player is going to do next year.


That is the way it should be looked at. A modelled "true talent" with standard deviations to each side like ZiPS does. Which is absolutely not what the excerpted passage stated, which goes back to the poor communication thing. And if you're trying to do it in season you should look at putting more weight towards most recent performance because baseball is a complex emergent system and something may have changed
   37. Benji Gil Gamesh Rises Posted: July 27, 2009 at 02:03 PM (#3268259)
If your apartment had burned down, you'd know how mean mgl isn't.


I sent you some money too (probably much less). Doesn't mean I'm not an ass at times.
   38. Rickey! On a blog from 1998. With the candlestick. Posted: July 27, 2009 at 02:04 PM (#3268260)
That's what the Book Blog is for. It's not his fault that Primer keeps linking to it.

Uh....horseshit. He explicitly calls out BTF and the level of commentary here. He may be blogging at his book site to avoid the lumpen proles in the Primer-verse, but he's clearly in need of BTF acknowledgement of his work. Else he wouldn't make the call back. And seriously, if you're writing a book for the mass consumer market, you're trying to communicate to a general audience. It's not like he's submitting his work to peer reviewed statistical analysis journals.
   39. Backlasher Posted: July 27, 2009 at 02:06 PM (#3268264)
which is what "Chipper Jones is not as good as his career stats tell us, even after you do all the appropriate adjustments" says, is the definition of belaboring the point.

Right, he could be better, especially if one considered the speed he possessed prior to the ACL injury. That is a difficult concept to get our hands around. A concept we can get our hands around much better (but one that we know for sure) is his value over that time period.

I will not speak for mgl, but what I agree with in his assertion, is that if you re-ran Chipper Jones career from the beginning its safter to presume that he would not have as good a performance as he has exhibited. Consequently (even if you don't factor in age), its safer to presume that he will not do as well going forward.

We may be entering an age where there are more metrics available to us, to where you can make even safer and better presumptions to end up with better forcasts.


I admit, I'm not one of the few reasonably intelligent people around here, so could someone help a bother out?

You really aren't that big of a bother.

Anyway, I didn't participate in the Sabathia thread, and I don't know if trying to search for it would be helpful in understanding mgl's exact complaint.

Nevertheless, I would agree with a statement that you can't just look at Sabathia's rates of output and make a determinitive conclusion that Sabathia has lost skill. (I also do not agree that there is a platonic True Talent. At most, there is a median projection of performance based on taking a lot of assumptions).

Where I may disagree is whether or not you can use those rate outputs as warning signals for possible changes in skill. We do need indicators for changes of skill. Those indicators should require you to investigate further. What I don't know, and mgl may know, is whether a higher BB walk is just a "Check Engine" light or a "low oil" light. Does it give you any significant information as to a possible problem? I gather from the tone of mgl's article, that he thinks a higher BB rate, particularly with the difference of Sabathia, gives you about as much information as a backseat passenger telling you that you don't have a smooth ride. That does nothing, unless you say it to JP Ricciardi, who will demote you to the minors.
   40. The importance of being Ernest Riles Posted: July 27, 2009 at 02:06 PM (#3268267)
Well mgl uses the term "true talent" in the sample above, and it evidently refers to something other than a player's actual performance. What, then, does it mean?

"True talent" refers to a player's ability at a particular moment in time.

"True talent" refers to a player's ability (a "projection" or more properly an estimate) at a given moment, incorporating a) his past performance sample and b)regression to the mean (or you can call it "the performance sample of other similar players"). With each new plate appearance (for hitters), our estimate of his true talent will change because we have more data. However, his true talent ALSO changes from PA to PA, usually due to aging (or injuries). So when we estimate true talent, we are estimating a moving target, which makes the exercise difficult (but not intractable).

I wrote this a few years ago, I think the first paragraph is a decent if not thorough explanation.

http://www.hardballtimes.com/main/article/the-running-of-the-monkeys/
   41. Best Regards, President of Comfort, Esq. Posted: July 27, 2009 at 02:06 PM (#3268268)
I sent you some money too (probably much less). Doesn't mean I'm not an ass at times.
Everybody sent me much less, though the contributions were all generous. mgl's was... over the top generous.
   42. Tom Nawrocki Posted: July 27, 2009 at 02:08 PM (#3268271)
The thing that people don’t understand (actually one of the things) about regression toward the mean in baseball is that the reason any above or below average player will always regress, on the average, towards average, is that they were not really as good or bad as we thought in the first place, based on any of their stats.... And of course, there is some chance that any given player is better than his prior stats - it is just that the chances of him being worse is greater than the chances of him being better.


So the thing to understand about regression is that every player will regress toward the mean, except for those players who regress the other way. Right? In other words, every player is likely to be better or worse than his numbers have indicated before.

I must be missing something, because I don't understand why this concept is useful or important.
   43. The importance of being Ernest Riles Posted: July 27, 2009 at 02:09 PM (#3268275)
That's what the Book Blog is for. It's not his fault that Primer keeps linking to it.

Uh....horseshit. He explicitly calls out BTF and the level of commentary here. He may be blogging at his book site to avoid the lumpen proles in the Primer-verse, but he's clearly in need of BTF acknowledgement of his work. Else he wouldn't make the call back. And seriously, if you're writing a book for the mass consumer market, you're trying to communicate to a general audience. It's not like he's submitting his work to peer reviewed statistical analysis journals.


Well, that's one assessment of the situation. We'll agree to disagree; I'd rather not guess at mgl's intentions behind his dig (which, as I said, I find disagreeable but simultaneously hilarious).
   44. Shooty Survived the Shutdown of '14! Posted: July 27, 2009 at 02:12 PM (#3268280)
What we need is a mini-softball tournament between the staff/members of the community at ESPN, B-Pro, The Book Blog and BBTF. The winners get beer and the losers have to spend a week in a basement.
   45. The importance of being Ernest Riles Posted: July 27, 2009 at 02:13 PM (#3268281)
So the thing to understand about regression is that every player will regress toward the mean, except for those players who regress the other way. Right? In other words, every player is likely to be better or worse than his numbers have indicated before.

I must be missing something, because I don't understand why this concept is useful or important.


I think you are missing something. That's not how I read the portion you excerpted at all, although I will say it is confusing. Try the following re-wording:

The thing that people don’t understand (actually one of the things) about regression toward the mean in baseball is that the reason any above (or below) average player will always regress, on the average, towards average, is that they were not really as good (or bad) as we thought in the first place, based on any of their stats.... And of course, there is some chance that any given above average player is better than his prior stats - it is just that the chances of him being worse is greater than the chances of him being better. Similarly, there is some chance that any given below average player is worse than his prior stats - it is just that the chances of him being better is greater than the chances of being worse.
   46. The importance of being Ernest Riles Posted: July 27, 2009 at 02:14 PM (#3268282)
The winners get beer and the losers have to spend a week in a basement.

So if we win, we get to continue to drink, but we're required to come out of the basement? Can I just stay in my basement and continue to drink?
   47. Hang down your head, Tom Foley Posted: July 27, 2009 at 02:15 PM (#3268284)
This makes me think of somebody watching Kirk Gibson's home run off Eckersley and yelling "Small sample size! This means nothing!" at the TV. Or yelling it at the spreadsheet where he'd read about it.
   48. Shooty Survived the Shutdown of '14! Posted: July 27, 2009 at 02:16 PM (#3268286)
So if we win, we get to continue to drink, but we're required to come out of the basement? Can I just stay in my basement and continue to drink?

Hmm. Would you be offended if we made you team statistician? It's important!
   49. RJ in TO Posted: July 27, 2009 at 02:18 PM (#3268288)
Can I just stay in my basement and continue to drink?


Since I'm going to stay in my basement and continue to drink no matter what, why should I bother even worrying about the game?
   50. The importance of being Ernest Riles Posted: July 27, 2009 at 02:19 PM (#3268289)
Hmm. Would you be offended if we made you team statistician? It's important!

This is like the time in high school when the wrestling coach asked me to join the team...as the announcer.

Just so you know, Shooty, I do play softball with my coworkers. I'm like Jason Kendall: I catch, I hit at the bottom of the order, and everybody is shocked when I punch the ball into the outfield once a year.
   51. Mister High Standards Posted: July 27, 2009 at 02:20 PM (#3268291)
MGL - go #### yourself.
   52. Backlasher Posted: July 27, 2009 at 02:22 PM (#3268295)
Again, I just don't get the controversy here.


The controversy is how much information people are pulling from output statistics TO USE AS A FORECASTING MECHANISM.

If people are saying that Sabathia is declining as a pitcher because of an X% change in walk rate then that is likely erroneous.

There is a y% of change for some populations of X and Z that would probably indicate a change in skill of Sabathia; however (1) Its not going to tell you whether its a permanent change or temporary change (such as injury) and (2) y, X, and Z are pretty big.

What those real sabermetricians do is a good concept of y, X, and Z and the size they need to extract meaning with their models.

A problem with those models is the size needed for y, X, and Z to get any good projective information. Consequently, as fans, we are going to try to see if we can't use the information we have in a more fuzzy manner to get to conclusions.

Pitch f/x data may change that. We may be able to do more with analytics that we previously did with our eyes, and BE ABLE TO MAKE REAL TIME AND ANYTIME decisions from these models. Tango and mgl probably have the acumen to do that. Many of the people that just use classical statistics are going to lost.
   53. Shooty Survived the Shutdown of '14! Posted: July 27, 2009 at 02:22 PM (#3268297)
Just so you know, Shooty, I do play softball with my coworkers. I'm like Jason Kendall: I catch, I hit at the bottom of the order, and everybody is shocked when I punch the ball into the outfield once a year.

We don't ahve a softball team at work and my local doesn't have a team, either. I really wish Primer had a team to play in the Central Park league. <sigh>
   54. John DiFool2 Posted: July 27, 2009 at 02:32 PM (#3268312)
Wouldn't major-league players tend to regress towards replacement level? That is, given that major-league baseball players represent the far right slice of the talent curve, that they will tend to get pulled back to the overall average (which lies quite a bit further to the left of major-league replacement level)? [i.e. the average of all baseball players in the world, from semi-pro leagues and high school/college level on up] Just throwing that out there...
   55. Shooty Survived the Shutdown of '14! Posted: July 27, 2009 at 02:34 PM (#3268319)
The controversy is how much information people are pulling from output statistics TO USE AS A FORECASTING MECHANISM.

Yeah, but this will always be a moving target, even with fx data. The argument seems one of application more than conception so it's not surprising there are disagreements about it. (As a sidenote, what may be really interesting in the future is if you could combine fx data with a biomechanical model of a pitcher when he was at his best. That is, have video of Gio Gonzales on Saturday when he shut down the Yankess and then compare that with his form when he gave up a gazillion runs to the Twins in a previous start and then have the computer analyze the differences in his delivery to try to pinpoint what goes right or wrong. You could then use that as a training tool or even as an in-game predictor of whether your starting pitching has his "stuff" or not.)
   56. SouthSideRyan Posted: July 27, 2009 at 02:36 PM (#3268321)
####, if my apartment burns down, I'm looking at him first. Then Szymborski. Then Keefe.


I know who burnt down Larry's apartment, but I'm not allowed to say who.
   57. Tom Nawrocki Posted: July 27, 2009 at 02:36 PM (#3268322)
That's not how I read the portion you excerpted at all, although I will say it is confusing.


Your rewrite clarifies that above-average players are more likely to need regression downward, and below-average players are more likely to need regression upward. That doesn't really disagree with what I said; it just adds a layer of complexity.

And is the second half even really true? Is there any reason to think that Anderson Hernandez needs to have his stats regressed toward the mean (that is, upward)? Baseball is not a bell curve, as Bill James pointed out many years ago. It seems just as likely that the worst players aren't as good as their numbers indicate, and that Anderson Hernandez will be playing for the Surf Dawgz this time next year.

EDIT: John DiFool wrote post 54 while I was writing this. That's another way of saying what I'm getting at here.
   58. Backlasher Posted: July 27, 2009 at 02:36 PM (#3268323)
"True talent" refers to a player's ability at a particular moment in time.

"True talent" refers to a player's ability (a "projection" or more properly an estimate) at a given moment, incorporating a) his past performance sample and b)regression to the mean (or you can call it "the performance sample of other similar players"). With each new plate appearance (for hitters), our estimate of his true talent will change because we have more data. However, his true talent ALSO changes from PA to PA, usually due to aging (or injuries). So when we estimate true talent, we are estimating a moving target, which makes the exercise difficult (but not intractable).


Stating it like that does absolutely nothing to rebut the MAIN point in this objection:

I have never been entirely comfortable with the Platonic assumption adopted by many sabermetricians that a player has an unchanging "True Talent," and any and all fluctuations in his performance are due to random error or statistical fluctuation.


In fact, I find all the problems attributed to mgl in that post. You are not attempting to discuss or debate or even understand the objection. You are treating everyone that objects to the concept as "not understanding" and trying to "explain it to them." I much prefer mgl's "F''ed, here it is, understand it if you can" approach. than being patronized like this.

There is no "true ability" even if you isolate it at a point in time. First, as you mentioned a players individual skill does move with time. Consequently, if you isolate the time down to a small enough interval where you didn't have such changes, the output becomes pretty binary: Hit or No Hit, etc. which makes any projection not an indicator of "true talent" but a probability of output (e.g. that is, he has a 33% chance of reaching base, not that he is "going to have a .330 OBP). More important, if you bring things down to such small time intervals, there are much more specific stimulus to use.

If you expand the time interval to get the .330 OBP, then you have a projected level of output NOT A TRUE TALENT BECAUSE AS YOU HAVE ADMITTED, THAT CHANGES OVER TIME.

When you increase the data you have on a players output, you are not finding some cosmic truth, you are just having a more refined ability to project future performance. Those data points are not "samples of true talent" they are just outputs that have THE THEN CURRENT PHYSICAL SKILL AS ONE OF THE CAUSAL ELEMENTS.

Somewhere, somebody decided the like the sound of "True Talent" As a result, the phrase has stuck, but it belies what is really being done. I presume its ok if everyone who needs to understands what it means, but its now getting into the territory of "luck" When somoene has a direct objection as to its use because of its connotation; the result is not to inartfully "explain" to them the situation and use false attributions.
   59. The importance of being Ernest Riles Posted: July 27, 2009 at 02:40 PM (#3268331)
Wouldn't major-league players tend to regress towards replacement level? That is, given that major-league baseball players represent the far right slice of the talent curve, that they will tend to get pulled back to the overall average (which lies quite a bit further to the left of major-league replacement level)? [i.e. the average of all baseball players in the world, from semi-pro leagues and high school/college level on up] Just throwing that out there...

This is a very important point.

When we regress to the mean, we regress toward a population mean. Choosing the correct population is critically important. The group should be large enough that you have good data, but small enough that it represents a population to which your belongs.

For Travis Buck, that might be a) major leaguers b) minor leaguers c) tall players d) hot players e) American men f) players with a history of wrist injuries, etc. That's your call to make as the estimator, and it is in this regard that most projection systems are different. Marcel regresses to the mean of all major leaguers. Other systems regress to the mean of similar players as weighted by a similarity score.
   60. JJ1986 Posted: July 27, 2009 at 02:41 PM (#3268333)
I'm still waiting for Cliff Lee to go back to being replacement level.
   61. Shooty Survived the Shutdown of '14! Posted: July 27, 2009 at 02:44 PM (#3268340)
I'm still waiting for Cliff Lee to go back to being replacement level.

Patience my friend. Replacement Level is like death and taxes.
   62. Slivers of Maranville descends into chaos (SdeB) Posted: July 27, 2009 at 02:45 PM (#3268341)

"True talent" refers to a player's ability at a particular moment in time.


Fine, but you're still talking about abstract 'ability' rather than actual performance, no? And I understand the point that true talent fluctuates, but the use of the singular absolute (as well as the way in which it is used in reasoning like mgl's), implies that it doesn't, or at least not much over small segments of time. Otherwise it isn't really 'true,' not as that term is generally used.

Backlasher I think points out the flaws in that approach.

It seems to me it's a metaphysical argument. Maybe Neifi Perez had the true talent of Barry Bonds, but unfortunately for him only during the moments when he wasn't at the ballpark. Nothing wrong with metaphysical arguments, but it seems odd to see them given such a prominent place within a statistical analysis.
   63. Best Regards, President of Comfort, Esq. Posted: July 27, 2009 at 02:47 PM (#3268345)
I know who burnt down Larry's apartment, but I'm not allowed to say who.
He dead.
   64. SoSH U at work Posted: July 27, 2009 at 02:48 PM (#3268347)
I'm still waiting for Cliff Lee to go back to being replacement level.


I'll bet you $50 zillion he will. If you don't take that bet, it proves I'm right.
   65. The importance of being Ernest Riles Posted: July 27, 2009 at 02:53 PM (#3268359)
And I understand the point that true talent fluctuates, but the use of the singular absolute (as well as the way in which it is used in reasoning like mgl's), implies that it doesn't, or at least not much over small segments of time.

That it doesn't change much over a small segment of time is an approximation that you have to make to get any practical information.

It's not a metaphysical argument, just one of probability. Maybe Neifi Perez had the true talent of Barry Bonds, and maybe it was just bad timing. However, Given the performance data we have, we can say that Bonds>Perez. But we can only say that with some degree of confidence (in your example, probably upward of 99.99% or something).

In fact, if you gave Marcel a sample size of one PA for each and asked it to guess who was better, it would regress to the mean and come to the conclusion that they were both average. That's why you need more sample data. That's why sophisticated projection systems incorporate phenotypic characteristics. That's why you need...scouts.
   66. DCW3 Posted: July 27, 2009 at 02:55 PM (#3268361)
Everybody sent me much less, though the contributions were all generous. mgl's was... over the top generous.

That's a very small sample of his generosity, though. His true generosity level is almost certainly less than that.
   67. The District Attorney Posted: July 27, 2009 at 02:56 PM (#3268362)
I'll bet you $50 zillion he will.
Is that in money dollars?
   68. Portia Stanke Posted: July 27, 2009 at 02:57 PM (#3268365)
Based on his tone and lack of self-awareness, I would not be surprised if MGL were mildly autistic.
   69. Tango Posted: July 27, 2009 at 02:57 PM (#3268366)
So that means that the quality of comments here are better than he's observing, and the quality there is less, right?


Brilliant!

***

MGL has his public persona, however it is that it is taken. I'd also like to point out regarding those who says that he never explains anything in a useful manner, to look at his responses on our wiki. There is some 80 responses from him. There has to be at least one that is useful and clear, no?

***

I have never been entirely comfortable with the Platonic assumption adopted by many sabermetricians that a player has an unchanging "True Talent,"...


Not only should you not be comfortable, you should outright reject it. Players are humans, not machines, and therefore, have an ever-changing true talent level, by the second.

This is why we can't look at a player's career, without weighting his more recent seasons more. It is because they are not unchanging machines. Aging, conditioning, etc, are all part of the human condition.

If someone wants to say "If Chipper weren't human", then yes, look at his career total, and presume he's the well-oiled machine that doesn't need any maintenance. Otherwise, you have to:
a. presume he's human
b. accept that sample observed performances, no matter how many you think is enough, is never enough

***

For some reason, he doesn't push my buttons, either. At least he's intelligent and, seemingly, true to himself. (Also, he makes me chuckle.) It's the idiots without a sense of humor who write in a patronizing tone that get me fired up.


That's a well-considered point-of-view.

The opposite is, of course, just as reasonable.

***

If you have this much difficulty conveying your thoughts and findings to a general audience you might consider improving your ability to communicate to a general audience. Or stop trying to communicate outside of specialized audiences.


I believe MGL stopped posting at primer a long long time ago, and posts almost exclusively at our blog. So, he's done exactly as you said, and it doesn't seem to matter.

Otherwise he can't post anywhere as he wishes.

***

However, it's a factor, not a law. Other factors are health, experience, and aging.


The "mean" is not the single league-average mean, but the mean of the population you are drawing the player from. Therefore, his health, experience and aging are all part of the regression equation.

***

Funny though, we primates can dish it but we have a hard time taking it.


You think?!?

Though, I'm not sure that Primates are disproportionately ornery compared to the population at large.

***

...but he's clearly in need of BTF acknowledgement of his work. Else he wouldn't make the call back. And seriously, if you're writing a book for the mass consumer market, you're trying to communicate to a general audience. It's not like he's submitting his work to peer reviewed statistical analysis journals.


1. I don't think MGL cares about any acknowledgement from anyone.

2. MGL has helped more people directly than any other saberist around.

3. The Book is a tough read, but it is readable. I don't see the need to presume that his blog writing style equals his book writing style. If you want to take a passage from The Book that you think was poorly communicated, please highlight it. Otherwise, no need to make blanket assertions.

4. The peer-review we get from the general saber audience is far better than the peer-review we'd get from academia. When it comes to subject matter experts (SME), the hardcore baseball fan trumps the barely-a-baseball-fan academician. Ideally, you have someone like Andy Dolphin, Ted Turocy, or Walt Davis. But, those are the exceptions.

Otherwise, though I'd like to hear from both of them, I'd place a lot more weight on Chris Dial than Rodney Fort.

***

"True talent" refers to a player's ability at a particular moment in time.


Correct!

***

mgl's was... over the top generous.


MGL is extremely generous with his time. He also donated all his profits from The Book to Retrosheet.

So, his "need" to write The Book (meaning spending hundreds of hours writing, the never-ending and grueling editing sessions we went through, etc to provide a tight, hopefully timeless book) was done strictly on an educational basis.

***


I must be missing something, because I don't understand why this concept is useful or important.


The Book is available for free reading from Amazon's Look Inside. I suggest reading the last few pages of Chapter 1. After you do that, let me know if you have more questions.
   70. Edmundo got dem ol' Kozma blues again mama Posted: July 27, 2009 at 03:01 PM (#3268376)
Since I'm going to stay in my basement and continue to drink no matter what, why should I bother even worrying about the game?
Because nature abhors an empty spreadsheet.
   71. SoSH U at work Posted: July 27, 2009 at 03:04 PM (#3268381)
Is that in money dollars?


I'm not putting up money dollars, though I will wager some dollar bucks.
   72. Tango Posted: July 27, 2009 at 03:11 PM (#3268393)
This makes me think of somebody watching Kirk Gibson's home run off Eckersley and yelling "Small sample size! This means nothing!" at the TV. Or yelling it at the spreadsheet where he'd read about it.


The correct response is how it was called by the announcer: "I don't believe what I just saw". It is not anything more than that. It doesn't push Gibson or Jack Morris in his game 7 above any line beyond where they already were before that point in time.

These moment-in-time performances should be enjoyed and absorbed for what they were, and not try to be explained beyond that.

***

Wouldn't major-league players tend to regress towards replacement level?


Albert Pujols would not get regressed to that point, because replacement level players do not get the amount of playing time Pujols has gotten in his career. You would regress say Willie Bloomquist to that point. The number of games you play is part of the regression equation.

***

I'll bet you $50 zillion he will. If you don't take that bet, it proves I'm right.


Well-played.

***
   73. Bring Me the Head of Alfredo Griffin (Vlad) Posted: July 27, 2009 at 03:13 PM (#3268396)
Thanks for stopping by, Tango.
   74. Rickey! On a blog from 1998. With the candlestick. Posted: July 27, 2009 at 03:21 PM (#3268408)
I don't think MGL cares about any acknowledgement from anyone.

I suspect he would claim as much as well, and I strongly suspect that both you and he would be wrong. Behavior belies motivation.
   75. Shooty Survived the Shutdown of '14! Posted: July 27, 2009 at 03:23 PM (#3268412)
For some reason, he doesn't push my buttons, either. At least he's intelligent and, seemingly, true to himself. (Also, he makes me chuckle.) It's the idiots without a sense of humor who write in a patronizing tone that get me fired up.


That's a well-considered point-of-view.

The opposite is, of course, just as reasonable.


I'm not sure what the opposite would be!
   76. BFFB Posted: July 27, 2009 at 03:35 PM (#3268430)
he's a moron lier who tells bad jokes and it's the smart people with a sense of humour who write in a level tone that get you fired up!
   77. Nineto Lezcano needs to get his shit together (CW) Posted: July 27, 2009 at 03:39 PM (#3268435)
Of course Canada has fires. Why else would they have all those firefighters?
   78. caprules Posted: July 27, 2009 at 03:39 PM (#3268436)
Based on his tone and lack of self-awareness, I would not be surprised if MGL were mildly autistic.


mgl appeared once on a local radio sports show in Milwaukee. He couldn't have been nicer or more "normal" when answering questions.
   79. The importance of being Ernest Riles Posted: July 27, 2009 at 03:40 PM (#3268437)
it's the smart people with a sense of humour who write in a level tone that get you fired up!

It's like hating JoePo.
   80. The District Attorney Posted: July 27, 2009 at 03:41 PM (#3268439)
I'm not putting up money dollars, though I will wager some dollar bucks.
D'oh! That's what I meant.
   81. Backlasher Posted: July 27, 2009 at 03:53 PM (#3268458)
That it doesn't change much over a small segment of time is an approximation that you have to make to get any practical information.

That is not an "approximation" That would be an assumption or other form of control.

Maybe Neifi Perez had the true talent of Barry Bonds, and maybe it was just bad timing.

If you isolate the time period down to just before a hanging curve ball crosses the plate in Neifi Perez's hot zone, any meaningful number that you come up with will show them being about the same.

If you stretch it out over a more elongated time period with varying stimuli, then you can get a different between those numbers.

That is why the explanation is not responsive to the objection.

Given the performance data we have, we can say that Bonds>Perez. But we can only say that with some degree of confidence (in your example, probably upward of 99.99% or something).

Who do you think doesn't know this (at least on any meaningful measure. I would bet there were time intervals when Perez > Bonds for playing SS. I'd also bet that Perez > Bonds on most offensive outputs while Bonds was undergoing surgery and during most of his recovery time)?
   82. Nineto Lezcano needs to get his shit together (CW) Posted: July 27, 2009 at 03:53 PM (#3268461)
So the thing to understand about regression is that every player will regress toward the mean, except for those players who regress the other way. Right? In other words, every player is likely to be better or worse than his numbers have indicated before.


When we say that players regress to the mean, we're being very inexact with our words (one could say wrong, if they were being uncharitable). Populations regress to the mean. Since the population is nothing but a group of players, it stands to reason that most players will behave in this fashion. But there's no reason to think that all players will. It's just that prior to things actually happening, we don't know what players will defy the population tendencies.
   83. Slivers of Maranville descends into chaos (SdeB) Posted: July 27, 2009 at 03:56 PM (#3268465)
Maybe Neifi Perez had the true talent of Barry Bonds, and maybe it was just bad timing. However, Given the performance data we have, we can say that Bonds>Perez. But we can only say that with some degree of confidence (in your example, probably upward of 99.99% or something).


See, this is part of my problem. In this world, the only world that matters, we know Bonds was better then Perez. He performed better, period. There's no 99% about it.

What you are arguing is that both Bonds and Perez had some invisible but real "True Talent" of which their actual performances are but a reflection -- a pretty good reflection, but just a reflection. What is your evidence for that proposition?

I mean, I could understand the question: Given their careers to date, who is likely to have the better overall career stats? But when their careers are finished, the question becomes moot.
   84. 6 - 4 - 3 Posted: July 27, 2009 at 04:02 PM (#3268474)
"See, this is part of my problem. In this world, the only world that matters, we know Bonds was better then Perez. He performed better, period. There's no 99% about it."

To a statistician, 99.99...% is the same thing as 100% is to a non-statistician. There is no attainable level of absolute certainty when you're working with sample data.
   85. Phenomenal Smith Posted: July 27, 2009 at 04:15 PM (#3268492)
Tango and mgl are evil.
   86. Tango Posted: July 27, 2009 at 04:20 PM (#3268499)
Bonds 100% performed better than Neifi. We are 99.9999% sure that he was in fact better than Neifi.

Suppose you have 100 coins, one of which you know is weighted, and the other 99 you know are not. You pick out one coins at random. You flip it 1000 times. You get 600 heads (which is 6.3 SD from the mean if you presume all coins are fair). You flip a second coin, and you get 485 heads. You flip more coins: 520 heads, 490, 530, 495, 515, etc, etc.

How certain are you that the coin that came out with 600 heads is in fact the weighted coin? Are you 100% certain, or are you Bonds-is-truly-better-than-Neifi certain?
   87. Shooty Survived the Shutdown of '14! Posted: July 27, 2009 at 04:21 PM (#3268503)
Tango and mgl are d-i-c-k-s.

What's the point of this? Maybe you're a dick. Dicks shouldn't point their dicks at other dicks lest their own dick be turned against them.
   88. SoSH U at work Posted: July 27, 2009 at 04:22 PM (#3268505)
If anything can get a detractor to rethink his position on mgl, it could be standing side-by-side with ol' Phenomenal.
   89. Tango Posted: July 27, 2009 at 04:28 PM (#3268517)
What you are arguing is that both Bonds and Perez had some invisible but real "True Talent" of which their actual performances are but a reflection -- a pretty good reflection, but just a reflection. What is your evidence for that proposition?


Perfectly said. The evidence should be self-evident: Bonds comes to bat 4 times (if they let him) over a 3-hour time span. If you would let Bonds bat once every 2 minutes (or however long a PA lasts), and let him bat continuously without him getting tired 7/24/365, then you'd have 5 million PA in his career. And STILL you can't have 100% certaintly, because it is still 5 million observations.

This is what we deal all the time: we simply do not know the true of anything, and we rely on observations, of manifestations of their efforts, and how they interact with their environment, however uncontrolled that is.
   90. Best Regards, President of Comfort, Esq. Posted: July 27, 2009 at 04:29 PM (#3268519)
If you isolate the time period down to just before a hanging curve ball crosses the plate in Neifi Perez's hot zone, any meaningful number that you come up with will show them being about the same.
That's not true. The hanging curve ball has an impact on the results, not the talent.
   91. Slivers of Maranville descends into chaos (SdeB) Posted: July 27, 2009 at 04:31 PM (#3268522)

To a statistician, 99.99...% is the same thing as 100% is to a non-statistician. There is no attainable level of absolute certainty when you're working with sample data.


What, though, are we sampling? If you respond "true talent," then that begs the question. A sample implies a subset of a larger population. What is the population here?


How certain are you that the coin that came out with 600 heads is in fact the weighted coin? Are you 100% certain, or are you Bonds-is-truly-better-than-Neifi certain?


Coins have weight. That is empirically determinable. What is the empirical demonstration of the existence of true talent?

Perfectly said. The evidence should be self-evident: Bonds comes to bat 4 times (if they let him) over a 3-hour time span. If you would let Bonds bat once every 2 minutes (or however long a PA lasts), and let him bat continuously without him getting tired 7/24/365, then you'd have 5 million PA in his career.


How is describing an imaginary version of Bonds any form of evidence?
   92. AROM Posted: July 27, 2009 at 04:31 PM (#3268523)
If Sabathia was having a subpar season due to a .350 babip or a high hr rate, regression should be a big issue. For a pitcher's strikeout rate you can regress 50% to the mean after only about 17 innings. So after 120 or so it's much more likely a real change in performance than any other stats we focused on.
   93. Alex meets the threshold for granular review Posted: July 27, 2009 at 04:33 PM (#3268528)
I would just like to add that MGL gave an interview with a forum I post on and was very gracious and amiable when it came to answering our questions. I don't doubt he's arrogant, but I don't think that makes him a dick.
   94. Tango Posted: July 27, 2009 at 04:38 PM (#3268535)
Coins have weight. That is empirically determinable.


Presume someone else weighed them, and you didn't. That person told you that one is weighted, and the other 99 aren't.

How certain are you that the coin that came out 600 heads was the weighted coin?
   95. Tango Posted: July 27, 2009 at 04:40 PM (#3268542)
And, yes, I should have said if you can give Barry Bonds one million PA in the span of a milli-second, then we'd be talking about a static person. And while we wouldn't be 100% certain as to what that particular Barry Bonds at that point in time has in terms of true talent level, we'd be extreme close to that point.

And, when we talk about Bonds' career, we are talking about the average of Bonds over the time points where his talent was "reflected". Great word. I'll be using that.
   96. Slivers of Maranville descends into chaos (SdeB) Posted: July 27, 2009 at 04:43 PM (#3268546)

Presume someone else weighed them, and you didn't. That person told you that one is weighted, and the other 99 aren't.


I understand the question. If someone told me that he weighted them, I would accept that because I accept the concept of 'weight' as a real thing. If 'true talent' were a real thing, then an analogous question would also be appropriate. The question is, is true talent a real thing?

Perhaps this is another way of putting it. Imagine being asked the question "You are given two coins. You are told one is blessed, and one isn't. How do you determine which is which?" Doesn't this question assume the existence of a property known as 'blessedness'? And if such a property doesn't exist, doesn't the question become meaningless?
   97. PreservedFish Posted: July 27, 2009 at 04:48 PM (#3268549)
How certain are you that the coin that came out 600 heads was the weighted coin?


This question is so out of the blue. This is really an equivalent to Neifi v Bonds?

You could have made it a million tosses, with one coin at 600,000 and all of the others between 490,000 and 510,000
   98. Tango Posted: July 27, 2009 at 04:49 PM (#3268551)
I'm defining true talent as "the innate physical, emotional and mental skill that surfaces in some combination in the face of competition at a particular moment in time and space".

So, true talent "exists" because the definition forces its existence.
   99. Blackadder Posted: July 27, 2009 at 04:51 PM (#3268555)
About MGL supposedly being a d-i-c-k: doesn't he also spend $10,000 of his own money every year to purchase the data from STATS he uses to construct UZR, and then make the UZR calculations freely available? I think that says a lot more about the man than a few blog posts that are perhaps more curt than they need to be.
   100. Backlasher Posted: July 27, 2009 at 04:54 PM (#3268560)
That's not true. The hanging curve ball has an impact on the results, not the talent.

Of course its true. That is the whole point. If you reduce the time to a small enough interval, the potential is the same, primarily because the event space is so small. As you begin expanding the time of the event space so that there is a meaningful different in potential, the potential output of the actor changes incredibly.

If this truly was what would be attempted to be modeled, there are so many multivariate actors that the model would quickly be overcome with entropy.

That isn't what is attempted to be modeled. Instead, its a pure stochastic representation of expected output over an interval with a degree of confidence over that interal. It makes a lot of "assumptions" (not "approximations") about some of the causal actors, including the health of the player, the type of competetion being faced, and the type of environment being played. The more sophisticated the system, the less assumptions that are made; however, as shown before, there is so much entropy in accounting for these items that such sophistication is not worth its cost compared to the reliability of its output (Tango has stated this pretty eloquently and in plain langugae before in what I call his "Marcel Axiom").
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