The Scutaro Phenomenon: Progression to the Mean

by oaktoon on Aug 5, 2006 8:23 AM PDT Comment 44 comments

We had a heated debate a while back.

I argued for more playing time for Scutaro, since I contended that he was likely to exceed his career OPS for the rest of the year given the horrible start he endured for the first two months. Others disagreed, saying the rest of his season would be essentially random-- he had as much chance of having a lower OPS than his career mark as having a higher OPS.

Well, here are the facts. At his nadir on June 2nd, Marco's OPS was 495.

Since then he is 306-344-484 for an OPS of 828, and his seasonal total is now very close to his career mark.

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Sample size is puny

Flip a coin 20 times, get heads each time, is it more likely to be tails the next flip?

If you think so, don't go to vegas. This is no way to win at black jack.

by The Hypocrite on Aug 5, 2006 8:26 AM PDT reply actions 0 recs

in this case...

you are simply wrong. Human beings are different than coins.

oaktoon

by oaktoon on Aug 5, 2006 8:32 AM PDT up reply actions 0 recs

That is far from an accepted fact friend

Far from it. You can't just state that without backup.

by The Hypocrite on Aug 5, 2006 8:37 AM PDT up reply actions 0 recs

Poor analogy...

You're right on your coin flipping, but that's not an argument against 'Toon. In fact, if anything, it's an argument for him. If you look at Scoot's stats (based on what 'Toon is saying), you'd see that the "small sample" at the beginning of the year was your 20 heads in a row and that if you were betting, you'd see that that's only an aberation and that over the course of a larger sample, his numbers would even out. While I might not be sold on Scoot as a starter, 'Toon's argument certainly does have merit.

by DMOAS on Aug 5, 2006 8:38 AM PDT up reply actions 0 recs

Toons argument is that the next 20 are likely

To be better than 10/10. They aren't. Regression to the mean happens gradually not in some magical reversal of fortune.

by The Hypocrite on Aug 5, 2006 8:42 AM PDT up reply actions 0 recs

Then you're mis-reading the argument

The bare bones of his argument are...

Scoot sucked at the begining of the year.
Scoot's career numbers are overall better than then beginning of the year sample (small sample size).
By law of averages, if Scoot is given more playing time, his numbers will balance out to his career numbers (which by virtue of your coin flipping argument, statistics would should that to be true).
Ergo, given more playing time, Scoot will likely play a lot better than his career numbers (at least for for a period of time) which will in turn balance out his seasonal numbers towards his career numbers.

At no point does his 'Toon claim Scoot will become a God at the plate, just that he will most likely improve if he was played more. So far, since July/Aug, he's shown that to be true. Will his current pace continue? Probably not, but that's not what 'Toon is saying. That's what you're assuming he's saying or reading into.

by DMOAS on Aug 5, 2006 8:51 AM PDT up reply actions 0 recs

In fact....

pretty soon I start to get worried that he'll slip to below the mean.

oaktoon

by oaktoon on Aug 5, 2006 8:54 AM PDT up reply actions 0 recs

I don't misunderstand

I said the law of averages does not mean that scoot will have a streak that balances out the bad times.

That's not how the law of averages works. Look it up. Regression to the mean does not mean you have balancing "streaks". It means that the average that you would expect will slowly bring up the low times due to the fact that the sample size is small.

Toon knows what he is saying. He knows he is using this opportune moment to praise scoot and prove his "point" whatever the hell it is.

If it is that Scoot should play more, then his point is just wrong. He shouldn't. He should play as much as he has at most.

by The Hypocrite on Aug 5, 2006 10:16 AM PDT up reply actions 0 recs

Agree & Disagree

I think he understands it fine, perhaps over emphasizing it a bit, but speaking for myself, it still applies. The law of averages doesn't say you'll have a positive streak to balance out a negative streak. That much anyone can agree on. While looking at an individual flip of the coin following 20 heads in a row doesn't necessitate a higher probability of tails on the next one. But, examined within the frame of a 1000 coin flips, you'll likely (though not statistically proven) to hit on a streak of 20 tails in quick succession, maybe not in a row, but perhaps 60/100 or 120/200, 170/300. It does mean that in all statistical likelihood, you'll see the tails balance out in the end.

Relating back to Scoot:
A) There was a possibility that he'd "make up" for his poor performance, not a likelihood.

B) He's just as likely to play the rest of the season out by his statistical norm than he is to continue it OR even revert back to his poor performance.

C) Despite his hot "streak" (which I never mentioned that he'd streak), he should in no way, shape or form be starting for us. That much we totally agree on. Hot or not, he's not a starter. I'd rather see someone like Perez get the chance since his statistical norm is fairly solid and whether he goes off on a balance tear or not, the curve for him is far more favorable.

by DMOAS on Aug 5, 2006 10:59 AM PDT up reply actions 0 recs

You and I agree on the facts

But not on whether toon understands the facts, that's all.

;-)

by The Hypocrite on Aug 5, 2006 12:15 PM PDT up reply actions 0 recs

More than anything tho

I find it ridiculous that someone who wanted Beane to blow the team up because the OFFENSE sucks which has been Toon's primary position would then make a stink about Scutaro being an offensive solution.

Ugh. It's just absurd.

The Mean he is "progressing to" is:

.253 / .303 / .385 / .688 OPS Career

by The Hypocrite on Aug 5, 2006 8:46 AM PDT up reply actions 0 recs

hey...

he has been better than Crosby. And now he gets to play.

oaktoon

by oaktoon on Aug 5, 2006 8:49 AM PDT up reply actions 0 recs

He reallly hasn't been better than Crosby

I agree he has not been any worse though, that's for sure.

Very similar numbers in the OPS department. If I had to play one or the other I'd still play Crosby who will hit the ball out of the park more often when he does run into one.

But being anti - scoot, which I admit I am, doesn't mean I'm pro crosby.

I want Jimenez to get a real shot. He's no stud either, but it can't hurt with the nubmers scoot and crosby put up.

by The Hypocrite on Aug 5, 2006 8:54 AM PDT up reply actions 0 recs

But he has...

Last two months OPS of over 800-- Crosby's been much lower than that-- in fact, i believe he's been well under 700.

oaktoon

by oaktoon on Aug 5, 2006 8:56 AM PDT up reply actions 0 recs

Before you posted this diary

I had some pity for you and the way you are picked on around here, but this is merely picking a fight, dude.

Post this in two weeks please, if Scoot has "regressed to the mean" again.

I'm sure by then you will have moved on to some other convenient fact that makes you look smart by then, tho, and won't remind us of this particular battle.

by The Hypocrite on Aug 5, 2006 8:31 AM PDT reply actions 0 recs

well....

he won't in two weeks, dude.

And the other post you have attacked me for is a tacit admission that I was wrong, so like so many others on AN, I can't win no matter what I do.

oaktoon

by oaktoon on Aug 5, 2006 8:33 AM PDT up reply actions 0 recs

He won't?

You really think Scoot is the answer? Even if he DOES post his career OPS that is a sub .700 OPS. Gimme D'J Jimenez any day.

You can't win because you think it is about winning or losing, being right or wrong. You post in platitudes instead of in a way that explores the possibitlities with an understanding that NOONE has any fucking idea how things are going to turn out. With Scoot or the A's.

by The Hypocrite on Aug 5, 2006 8:41 AM PDT up reply actions 0 recs

wrong side of the bed, eh??

Never ran into you before. I ain't taking the bait. Can't we all just get along??

I'm really in a very mellow mood-- no part caused by the team's good play. Happy that some of my direst feelings seem not to be fulfilled. So flame all you want-- it's just going by right me.

oaktoon

by oaktoon on Aug 5, 2006 8:45 AM PDT up reply actions 0 recs

Fine, I'm done too then

And I'm sorry for the previous diary where you were trying to admit mistakes. Shouldn't have flamed there.

But this one is really just picking a fight and you must know that.

Mellow or not. Maybe it was a mistake.

by The Hypocrite on Aug 5, 2006 8:48 AM PDT up reply actions 0 recs

You've run into me briefly

I haven't been posting long. I have low tolerance for platitudes and would much rather see discussion that didn't try to one up each other, which this post seems to have as a primary goal.

by The Hypocrite on Aug 5, 2006 8:49 AM PDT up reply actions 0 recs

If that was true ...

...you would have moved on about 6 posts ago.

Foolin' yourself?

"-1 is our runs margin after 109 games"

by A s Eh on Aug 5, 2006 9:19 AM PDT up reply actions 0 recs

Start from the beginning

Why don't you provide a link to the diary, and restate EXACTLY what you predicted back then, what people disagreed with back then, and how Scutaro's performance proves you right?

by matthias on Aug 5, 2006 8:51 AM PDT reply actions 0 recs

I won't bother with the link

I simpy said that Scutaro--- after his low point-- would better his career OPS the rest of the season as he "progressed to the mean".. and thus wasn't a bad bet to play more often (Crosby had injury issues at the time as he does now again)

Others said it was akin to coin-flipping-- and that the Scutaros of the world who start a season terribly are no more or less likely to best their career marks.

Well, unless I'm mistaken, since their low points:

scutaro
Payton
Bradley
Johnson (despite being sent down)

all have bested their career marks. Thomas hasn't, but that's only because he's on the decline from some pretty ridiculous OPS numbers in his 20s and early 30s. Chavez hasn't because of some crippling injuries.

Ellis, OTOH, has not. Nor crosby-- but he's battling injury issues, too.

oaktoon

by oaktoon on Aug 5, 2006 9:17 AM PDT up reply actions 0 recs

You aren't mistaken, they have improved

But they were not more likely to do so because they did poorly.

It just so happened to have happened.

Proximity does not prove causality.

by The Hypocrite on Aug 5, 2006 10:19 AM PDT up reply actions 0 recs

re

You weren't right. If you were right, Crosby and Ellis would be crushing the ball. You still don't understand the principle of regression to mean.

by 31Boots on Aug 5, 2006 9:09 AM PDT reply actions 0 recs

Believe me...

I understand the principle.

And you want to have a wager on Ellis from here on out? I bet he's over his career OPS-- and probably by a significant amount. Crosby is hurt (as is Chavez) and I think that puts him into a different category.

Thomas and Bradley and payton and Johnson are all arguments on my side, of course... so I can match your tit with plenty of my tat.

oaktoon

by oaktoon on Aug 5, 2006 9:12 AM PDT up reply actions 0 recs

ARRRRGHH!

You need to read up on statistics and probability dude.

http://en.wikipedia.org/wiki/Regression_toward_the_mean

http://en.wikipedia.org/wiki/Law_of_averages

http://en.wikipedia.org/wiki/Probability

You can't claim you understand the principle and then use anecdotal evidence to prove your point. If you use anecdotal evidence (like Scoots better hitting) you prove you DON'T understand the principle.

by The Hypocrite on Aug 5, 2006 10:22 AM PDT up reply actions 0 recs

but oaktoon is all about anecdotal evidence

the guy changes his mind every other day!

A's v Giants "is kind of like the difference between going to see the Ramones and going to see the Bee Gees. A's fans will go see the Ramones." -BB 07/27/05

by xbhaskarx on Aug 5, 2006 10:25 AM PDT up reply actions 0 recs

OK I'll post it

http://athleticsnation.com/story/2006/6/5/9360/86429

In a comment titled "This is a Classic 'Regression to Mean'" you said "Scutaro... over the next 4-6 weeks, he could easily be a 750-800 guy as he is "progressing" to the mean;".

Your prediction, as it happens, was spot on.

But if you bothered to read the replies you would see that nobody said your prediction was wrong. What a couple of us said was that your prediction was not a valid deduction from the principle of regrssion to the mean. And how Scutaro performed has no bearing on that discussion.

Like all of us you have opinions about baseball. Like all of us, but more than most, you enjoy sharing those opinions in public. I have no problem with that. I don't even have a problem with you being utterly ignorant of the most basic principles of statistics. But to the extent that you might be miselading others into false opinions about statistics I'm going to point that out.

Your opinion in this case was a perfectly reasonable guess that happened to be right. It just didn't have anything to do with regression to the mean or any other statistical principle.

by matthias on Aug 5, 2006 9:38 AM PDT reply actions 0 recs

Amen

by elcroata on Aug 5, 2006 10:22 AM PDT up reply actions 0 recs

bingo

smart guy, matthias. if only more people like him would write two diaries a day, instead of oaktoon...

A's v Giants "is kind of like the difference between going to see the Ramones and going to see the Bee Gees. A's fans will go see the Ramones." -BB 07/27/05

by xbhaskarx on Aug 5, 2006 10:23 AM PDT up reply actions 0 recs

Precisely

Thank you!

by The Hypocrite on Aug 5, 2006 10:23 AM PDT up reply actions 0 recs

what about Baysian statistics?

Since we have no idea what the 'true' mean that Scutaro would regress to, how do we know that the higher value is the actual mean he's regressing to? It could be that his Platonic mean is low, and he's been above it by chance.

by MobiusKlein on Aug 5, 2006 11:06 AM PDT up reply actions 0 recs

it's "Bayesian"

and that's pretty much all in know about the whole bayesian vs frequentist thing.
this discussion is now officially too statnerdy for me...

A's v Giants "is kind of like the difference between going to see the Ramones and going to see the Bee Gees. A's fans will go see the Ramones." -BB 07/27/05

by xbhaskarx on Aug 5, 2006 11:09 AM PDT up reply actions 0 recs

Thanks for the correction.

And I'm not sure either model is the best model for statistics with humans. How do you model a great player with a minor injury? The Bayesien expectation do not cut it, since there is additional information not included. But if you narrow the history window, you run into small sample size issues. Oh well.

by MobiusKlein on Aug 6, 2006 1:02 PM PDT up reply actions 0 recs

that depends

on whether we're talking about Jason Bay or Danys Báez.

A's v Giants "is kind of like the difference between going to see the Ramones and going to see the Bee Gees. A's fans will go see the Ramones." -BB 07/27/05

by xbhaskarx on Aug 6, 2006 6:09 PM PDT up reply actions 0 recs

Who gives a $hi7

we should have gotten Soriano.

Two-thirds of the earth is covered by water, the other third is covered by Kotsay.

by carp on Aug 5, 2006 11:10 AM PDT reply actions 0 recs

HA!

by rubin sierra on Aug 5, 2006 1:06 PM PDT up reply actions 0 recs

Not to belabor the point

But I think the "holier than thou" pseudoscientific folks are missing a fundamental point here.

This are human beings playing a game involving other humans.

Coin flipping or some other totally random event is absolutely ruled by the principles of statistics.

But a human endeavor-- which by definition is affected by the strengths and weaknesses of individul human beings is very different.

Thus you say if Scutaro does poorly for 100 ABS, there is no statistical basis to think he'll do anything but his career norm in the next 100.

whereas i say that any set of outcomes involving humans, as well as involving certain random factors, which they do, are partly governed by the condition of the humans themselves. In other words, scutaro's norm is not necessarily the product of the same behavior which is then subject to certain random effects; but in fact the product of differing levels of behavior, which are at least in part-- and I think large part, determined by the realitve quality of behavior.

In other words if Scutaro badly "slumps", chances are he will get us act together and do better than his norm in the next set of results.

That is what I predicted; that is what happened.

oaktoon

by oaktoon on Aug 5, 2006 1:40 PM PDT reply actions 0 recs

ROTFLMAO at Holier than thou pseudoscience

This is actually exactly what you are engaging in.

F&*^%ng hysterical.

Holier than thou because you think you are some sort of genius for guessing that a hitter might do well at some point in the season (duh, he's a major league hitter, he'll hit sometimes right?) and pseudoscientific because YOU USED the the scientific terminology of regression toward the mean INCORRECTLY.

YOU DID IT!! YOU ACCUSE US BUT IT IS YOU WHO IS GUILTY OF JUST THAT!! YOU ARE CLEARLY UNWILLING TO LOOK IN A MIRROR!! Just admit you are wrong for once for chrissakes. JUST ONCE!!

by The Hypocrite on Aug 5, 2006 2:51 PM PDT up reply actions 0 recs

Hate to disagree...

I really do. I honestly want to agree with you, but it's been shown time again that the same statistics that govern coin flipping can be applied to human's and their "unpredictability". But, having been dealing with a job that deals closely with stats of people's opinions, I've seen first hand how we can be seen in a very strict statistical sense. Look at every poll taken, the bigger the sample size, the easier it is to predict expected outcome. Keep in mind there's always that margin of error, but again, the margin goes down the greater sample size. While you can make the case that injuries, emotional state, age, weather, etc. can have an effect on a person, that tends to only account for separation from the norm, not shift of the norm. Nor does it effect the measurement.

There's very little that's truly random. Case in point, Fox's broadcasters nearly always suck. Sometimes they have someone who might be on the dull side of average, but you can pretty much count on them being bad. Likewise, you can pretty much count on Joe Morgan never reading Money Ball.

by DMOAS on Aug 5, 2006 4:09 PM PDT up reply actions 0 recs

Pass.

Can intangibles exist? Only the ones you can touch.

by salb918 on Aug 5, 2006 5:18 PM PDT reply actions 0 recs

What is KenDoll's mean?

Anyone? Anyone?

4 8 15 16 23 42

by LowcountryJoe on Aug 5, 2006 5:58 PM PDT reply actions 0 recs

kendall's mean

when the slack-jawed opposing pitcher tells him to "stick that f'ing thing out there."

A's v Giants "is kind of like the difference between going to see the Ramones and going to see the Bee Gees. A's fans will go see the Ramones." -BB 07/27/05

by xbhaskarx on Aug 6, 2006 9:20 AM PDT up reply actions 0 recs