Lefties..righties....I'll face all of them...it doesn't matter to me.

I know someone will find something, but I can't see a way for this to be viewed as a bad move. Clubhouse guy or not, he can hit lefties. And $1 million/year is pretty cheap.

Oakland lineup?

Neither Chavez nor Keilty can hit lefties well at all, so I know where they were coming from with this signing. Plus Karros is reputed to be a pretty good defender, which seems to matter more and more to Beane.

At the same time, "Eric Karros starting at 1B for the A's" just sounds bizzare.

Right. Durazo doesn't hit lefties too well either, IIRC.

SG, he's only paying $300K above minimun for Karros. And Karros has a long track record in the majors, so he doesn't have to worry about an adjustment period that a minor leaguer would have or the uncertainty. I'd say that's worth $300K.

As for Karros' defense, from what I saw last year he's got decent hands but severely limited range. Past a diving Karros could be the A's version of past a diving Jeter.

Neither Chavez nor Keilty can hit lefties well at all, so I know where they were coming from with this signing.

Actually, Kielty is great against LHP, hitting .293/.401/.518 against them over the past 3 seasons. Karros can't play 3B, so he doesn't help with Chavez's weakness, although Chavez did have his best year against LHP in 2003: .220/.271/.403.

Plus Karros is reputed to be a pretty good defender, which seems to matter more and more to Beane.

UZR has Karros at 10 runs below average per 162 games from 2000-2003.

Karros was signed to platoon with Hatteberg, and possibly Durazo.

v LHP 2001-2003

So when the Tigers sign someone and say it's about chemistry, they're idiots, but if Billy Beane does it, then there's no way this could be a negative?

Instead of looking at what the GM says, why don't you evaluate the actual move? You also completely misunderstood Beane's point, which is: I think it will be a good clubhouse, but mostly because it's a team that will win.

Translation: Karros will help us win more, which will create better chemistry.

SG, TO has it as $600K. Is it $1M? Oops.

Snowboy wrote:

Dan Holmes wrote:

I figure the "ntr MGL" comment above was alluding to tr MGL's finding that the split stats of RHB v. LHP do not appear to predict future splits any better than a full regression to a league average split. So Karros' big split recently likely does not presage mashin' numbers this year.

One other thing. Who's the better first baseman? I list EqA and UZR at 1B, 2001-2003...

Player A: .243, .289, .259 / N/A, +13, -13

For what its worth, UZR does not include the ability of a 1B to scoop throws, something that appears to be a signficant portion of the position's defensive value. Whether Karros' "hands" are good enough to make up for an apparent rapid decline in range, I don't pretend to know. But I'll bet DePodesta has a stat that is a bit more complete for 1B defense.

I figure the "ntr MGL" comment above was alluding to tr MGL's finding that the split stats of RHB v. LHP do not appear to predict future splits any better than a full regression to a league average split. So Karros' big split recently likely does not presage mashin' numbers this year.

While I'm not sure I believe this theory, MGL has even said that platoons are still worthwhile if the LHB has a large split, as Hatteberg does.

That's Hatteberg (A) and Karros (B). Karros' defense looks to be most likely worse, and his 2003 EqA is somewhat inflated by his use as a platoon player.

Well, Karros will be a platoon player next year, too.

I would argue that Graham Koonce, with recent MLEqAs of .265 and .274 as a full-timer, deserves his shot at the full-time job if the competition is just Hatteberg and Karros.

While it's popular to champion Koonce's cause, he's really nothing special. Here's Hatteberg and Kooce's EqA the past 3 years:

Koonce: .260, 268, .274

Danny,

I generally agree. I didn't mean to say Karros will be useless as a platoon player, I just meant that he was highly unlikely to put up a 900+ OPS against lefties as his recent splits suggest he would. Something solidly in the 800-850 range would be more than useful.

My point about Karros' 2003 EqA being inflated had to do with the raw comparison between him and Hatteberg, not his usage pattern for next year.

And I agree that Koonce is nothing special, and PECOTA thinks he's made of mango poop. (MGL's projection has him at a 815 OPS, FWIW) My point was that neither Hatteberg nor Karros appears notably better than Koonce. They're nothing special either.

I don't think the A's are hurting themselves particularly badly by paying $3M for somewhat below average production. Koonce might be able to replicate that at 1/10th the price, but I can understand the decision not to take that risk with a non-prospect.

Hmph. Could sworn Keilty was sucking it against lefties. My bad, shoulda checked myself first.

As the original ntr MGL in this thread, yes I was alluding to his conclusion that lefty mashers are a myth. Surfer, I think MGL concluded that platoon splits did exist for righties such as Karros, but that they were not as pronounced as they sometimes appeared. So he can probably be expected to continue hitting well agaist lefties, just not monstrously so.

I agree with dlf on the defensive issues. Beane's defensive metrics seem to mirror MGL's work in many ways (pursuit of Cameron, acquiring Kotsay, dropping Grieve, etc). But he may have a way of measuring 1B that takes into account receiving throws, which as dlf notes, is a big part of the job.

1) Karros still believes that he's an everyday player (show me a quote otherwise)

Even if that's true, who cares? Beane is openly talking about a platoon, which I can only assume Karros was aware of.

2) Karros, even against lefties, still only has decent OBA's (.389) and he's completely useless against right handers.

Only decent? There were 12 players in the AL with an OBP above .389 last year. He won't be playing against RHP, so who cares?

3) Wasn't Mike Kinkade available?

No, he already signed to play in Japan next season.

Karros, even against lefties, still only has decent OBA's (.389) and he's completely useless against right handers.

Decent?

OK, even if we knew nothing about the supposed fact that all RHB's have the same true platoon splits, regardless of their observed (sample) splits, I don't think that an reasonably intelligent persom could advocate just ignoring a RHB's stats versus RHP if you want to project his stats versus LHP! Surely, a RHB's stats versus RHP tells you something about his talent versus LHP. If RH batter A has an OPS of .900 in 300 PA versus LHP and .600 versus RHP, surely no one is going to argue that his true OPS versus LHP is close to the .900 and we can just ignore the .600! Similarly, if RH batter B has an OPS of .870 versus LHP in 100 PA and .830 versus RHP in 300 PA, surely no one is going to choose batter A over batter B to face LHP! Yet, half of the posts here ar printing Karros' OPS versus LHP and ignoring his OPS versus RHP! Not to mention the fact that playres simply don't get a lot of historical PA' versus LHP, such that their observed OPS versus LHP is always suspect due to sample size issues.

Of course, as I have said in the past (and much to my joy, many people have read and understood), a RHB's observed platoon splits have little or no predictive value, no matter how large or small that platoon ratio is, and no matter how large or small the sample size!.

The important concept in baseball and in stats in general, is that if there is any signifciant "skill" associated with a measurement, then sample size is critical in determining the regression. For example, we know that a payer's BA has a large "skill" component. However, for 5 or 10 AB's, we would regress a player's observed BA almost 100% towards the league average to estimate his true BA or project his future BA. We all know that intuitively. If player A has a BA of .500 in AB's, we all know that that means virtually nothing and our best estimate of his true BA is league average. However, if a player has a .310 BA in 1000 AB's, we know intuitively that our best guess of his true BA is somewhere between league average and the .310. In fact, the proper regression for 1000 AB's is about 60%, so the best estimate of this player's true or future BA is around .290.

OTOH, if there is little or no skill in a partiucalr measurement, then the sample size makes no difference! Nor does the size of the observed "split" or deviation from the mean! The regression is always 100% and our best estimate of that player's true value for that measurement is always the leage average. For example, let's say that we measure a player's odd/even days OPS splits. Since there is no "skill" associated with such a split (I assume), any deviation from the league average ratio (which should be 1.00 in this case) in any number of PA's would still be regressed 100%! SOmeone can argue, "But wait a minute! So-and-so had an observed odd/even OPS ratio of 1.5 in 2000 PA's! Surely their true ratio must not be 1.0!" Too bad, so sad, it is!

Now, the important thing here is that we can easily determine the extent to which any measurement has "skill" associated with it. There are actually at least 2 related but separate methods, but I'll only describe one of them. One is to compute the correlation coefficient from one roughly equal time period to another of the measurement in question. Typically, we use y-t-y correlations, but we don't have to. If our sample size of players is large enough, and if that correlation is near zero (or minus in some cases), then we can be fairly certain that there is no effective "skill" implied in the measurement. Again, if there is no effective skill, then for any given player with any observed measurement (like a pltoon ratio), no matter how much that oberved measurement deviates from the norm (the league average) and no matter how large the sample, the only conclusion we are allowed to reach is that those deviations are random "noise" and we must regress that oberved measurement 100% towards the league average if we want to estimate the player's true talent or future performance with regard to that measurement.

That was a mouthful, but the regressions don't lie!

So what about a RHB's platoon splits? Is there any signficiant "skill" assoicated with it? Even if there is, how much should Karros's observed (career) splits be regressed to project his future splits. I've already explained that if you want to project a player's OPS versus one-side pitching you NEVER just ignore his OPS versus the other-side hitting. Whether there is "skill" or not with platoon rationm, that is the WRONG way to do it. The right way is to determine how much skill (if any) there is, then to take a player's observed platoon ratio and apply the appropriate regression based on the number of PA's that observed platoon ratio was computed from. Then you can take that estimated true platoon ratio and apply it to his OVERALL OPS to get his projected OPS versus same or oppposite side pitching.

Of course, all of that is moot if there is little or no "skill" in a RHB's platoon ratio. If that is the case, we simply ignore a RHB's observed ratio (again, no matter how many PA's it is based on), and instead substitute the league average OPS platoon raio for RHB's - which is 1.08, BTW). That is what and why DIPS does what it does.

Before I give you some y-t-y regressions for platoon ratios for batters and pitchers, I'll throw out some approximate (from memory) y-t-y correlations for players with 500 PA's for some common measurements that we intuitively know has plenty of skill assocuated with it:

OPS .590

MGL said a whole lot which I should analyze when I'm not at work, but let me make one comment, which is that a non-zero correlation could be broken down to a large one on a select group, and a small one for the majority. This is the problem with blindly applying statistics to everybody. For example, I don't think anyone would disagree that the following players are much much worse against lefties: Chavez, Giambi, Thome, Abreu, etc.

Okay, I actually have at least two more comments. First, I know that 300 PA is selected for sample size issues, but it misses players like Mike Kindade, whose 3-year splits are obscene.

Second, the correlations are for the OPS ratios (OPSvsL/OPSvsR) to themselves, right? Even if the correlation is zero, this just means that they go and up down randomly, not that they fluctuate around 1. I could be entirely wrong about what's being measured, however.

For example, I don't think anyone would disagree that the following players are much much worse against lefties: Chavez, Giambi, Thome, Abreu, etc.

Okay, I actually have at least two more comments. First, I know that 300 PA is selected for sample size issues, but it misses players like Mike Kindade, whose 3-year splits are obscene.

No offense, Noffs, but you are clearly missing the whole point...

Correct me if I'm wrong, but it seems to me that your point is in evaluating what to expect from a specific right handed batter, a general manager should utterly and completely ignore that specific batter's platoon tendencies and instead use overall norms even when that batter's individual "sample" has over 7000 PAs.

As this position seems rather counter-intuitive, and your post above only states conclusions without any factual support, please link to a study that reaches this conclusion.

There are other issues besides those presented in my long post. For example, once we determine the regression amounts given a certain mumber of PA's, the "mean" that we regress towards is NOT necessarily the mean of the entire population of LH or RH pitchers or batters. This is esspecially true of pitchers. The "mean" that we regress each player's sample platoon ratios towards is the mean of the population from which the player comes. What this means is that if a LHP, for example, is a sidewinding fastball/slider type, then his population is all LHP who are fastball/slider sidewinders. That population probably has an OPS platoon ratio higher than the opulation of all LHP's. Same thing for a pitcher like Viola who threw over the top and had a screwball (I think). His population is LHP's who "throw over the top and have a scrrewball." Clealry the population mean platoon ratio for them is also different (smaller, if not "negative") than that of the entire population of LHP's.

And to edify Noff a little bit, yes all RHB's observed (sample) platoon ratios randomly fluctuate around the league average of 1.08 (not 1.00). And ALL fluctuation around that 1.08, no matter how large the sample of PA's, is in fact random - for RHB's.

And yes (a little more edification), it is possible that some classes of players have a higher positive correlation than the overall correlation. However, if the overall correlation is near zero, it is unlikely that any significant portion of the population has a much higher correlation, otherwise the overall correlation would NOT be near zero. Also, even if there were classes within the population that had signifciantly higher correlations than the opoulation as a whole, if we are not aware or have evidence (the evidence must be something OTHER than his observed extreme ratio) that a certain player like Karros belongs to such a class, we must apply the overall population correlation to him, which in the case of OPS platoon ratio for RHB's, is near zero.

As far as Giambi, Koskie, Chavez, et al. the entire point of my long post was that: a) yes, LHB's DO have unique true platoon ratios, but that, b) you still have to take their sample platoon ratios and regress them according to the number of PA's that sample platoon ratio is based on!

Let's take Chavez for example. The average OPS platoon ratio for LHB's is 1.17. The correlation for 300 total PA's is .224 (which is fairly high, BTW, considering that in 300 total PA's, only around 60 of them are versus LHP). Chavez' observed or sample OPS platoon ratio for his career is around 1.4 in around 3000 PA's. Using a regression of .776 (1-r) for 540 PA (players with a min 300 PA average 540 PA), we get a regression of 39% for 3000 PA. So Chavez' observed OPS platoon ratio of 1.4 gets regressed 39% towards the average of 1.17 for all LHB's, which yields an estimated true OPS platoon ratio of 1.31 for Chavex, which is quite a bit higher than that of the average LHB, but a little lower than his observed ratio of 1.40. So yes, our best guess is that Chavez indeed has more trouble with LHP than the average LHB.

Since RHB's like Karros have a near 100% regression for any number of PA's, we cannot say that about any RHB no matter what their sample ratios look like...

Correct me if I'm wrong, but it seems to me that your point is in evaluating what to expect from a specific right handed batter, a general manager should utterly and completely ignore that specific batter's platoon tendencies and instead use overall norms even when that batter's individual "sample" has over 7000 PAs.

Yes, yes, and yes!

Why is that counterintuitive? RHB's face mostly RHP's throughout their entire lives! None of them (at least those that make it to the majors) are going to be "scared" or intimidated by RH pitching! The primary reason why we see variability in LHB's platoon ratio is that some LHB's are more scared or intimidated than others by LH pitching.

I gave you all the "facts" and data you need to reach the same conclusion that I did! Did you not read my entire post? I specifically said that a correlation from one time period to another tells you everything you need to know about whether a certain measurement (like platoon ratio) is "skill" related - IOW, whether that measurement in any given time period has any predictive value.

The correlation for RHB's was -.07 with a 95% confidence interval of .26. Thus, based on that number alone, we are very confident that a RHB's sample platoon ratio over virtually any number of PA's, has little or no predictive value. If you want me write up a nice, formal study of 8-10 pages, which will bascially you the exact same thing and which will presetnt the exact same data, you'll have to pay me a lot of money. If someone wants to use more data to get more statistical "confidence" in the results, I have no objection to that. Given the potential sample error in the data I presented, there is some chance (less than .5%) that the true correlation for 540 PA's is at least .10, in which case I would have concluded that RHB's do indeed have some "unitque" platoon ratios, although not that much. Keep in mind that I am NOT saying that RHB's in general do not have slight true differences in platoon ratios, such that the proper regression for a decent number of PA's might be 90% rather than 100%, or that there are not a small percentage (it would have to be a very small percentage for the overall corr. to be near zero) of players who have true platoon ratios signficantly different than the average. There's just no way to identify such players, regardless of their sample ratios or number of PA's. We HAVE to use the overall regression rates for all players...

The word is not "edify" as much as "clarify," on both our parts.

To quote myself, "First, I know that 300 PA is selected for sample size issues, but it misses players like Mike Kindade, whose 3-year splits are obscene." I realized as soon as I posted this that my wording would miss my intended meaning, and imply that I don't understand the concept of sample sizes.

What I was trying to say if a player had a deficiency in hitting one type of a pitcher (an actual lack of skill) then there's a good chance that he wouldn't be a full-time player, and wouldn't show up if you use the 300 PA cut-off. Most full-time major-league hitters, there being less than 300 of them in the world, you'd think would be pretty skillful at hitting both left- and right- handed pitchers, unless they're just obscene against righties (Giambi, Chavez, Thome, Abreu).

Moving onwards, I'm glad to you admit that there's your sidewinding LOOGY types likely have a more pronounced split. Prior to that, your stance was a tad hardline for me, though I find your data intriguing.

"it is possible that some classes of players have a higher positive correlation than the overall correlation. However, if the overall correlation is near zero, it is unlikely that any significant portion of the population has a much higher correlation"

As a counterexample (which may or may not work, since I'm at work and don't have time to really get into it properly), I will use knuckleballers and BABIP. Of course, it depends on how you're defining "significant," but if such a group exists, no matter how small, and you're talking about a player who's a part of it, I consider that significant.

Do you mean as in 'these regressions', or 'regressions don't lie'? Because they absolutely can if you're not doing a good job in managing your assumptions about the population. This, of course, potentially feeds directly into Noffs' comment (46).

It was a hyperbolic statement, but....

Yes, correlation coefficients (cc's) are only as good as the underlying data. For exmaple, if the relationship is not linear, the cc's can be misleading or worthless. If there are outliers, that can unfarily suppress the correlation. Etc.

The typical "problems" associated with "regressions" and "correlations" are not particularily relevant to this issue.

How does .776 become 39%?

Sorry about jumping from one step to another without "showing the work."

Regression amount is always 1-r (when you take two independent samples from the same population), where r is correlation coefficient of one set of sample data on the other (there are some other assumptions of course). Since the observed correlation for LHB's of one sample of 540 PA's on another (for the same players of course) was .224 (of course this is only an estimate of the true correlation, but that's all we have to work with), the regression amount for a player with 540 PA's is 1-r or .774, or 77.4%. The r and thus the regression amount is a direct function of the number of PA's. Tango's Q&D formula for computing the correct regression for any number of PA's (or BIP's or whatever the "opportunity" is) is X/(PA+X), where X is some constant based on the correlation you get from your original calculations. In the original calculations (running the regressions), the r was .224 and the regression was 1-r, or .776 (77.6%). That gives us a value for X of around 1900 (I rounded it off to the nearest 100), since 1900/(1900+540) is 77.9%. Now that we know X, we can interpolate the proper regression for 3000 PA's rather than 540 PA's. Using Tango's formula, we get 1900/(1900+3000), which is 38.7%!

Okay, one more post. First, switching back and forth mid-sentence is not recommended and leads to things like this "I'm glad to you admit that there's your sidewinding LOOGY types" which should read "I'm glad that you admit that..."

Second, "Keep in mind that I am NOT saying that RHB's in general do not have slight true differences in platoon ratios, such that the proper regression for a decent number of PA's might be 90% rather than 100%, or that there are not a small percentage (it would have to be a very small percentage for the overall corr. to be near zero) of players who have true platoon ratios signficantly different than the average. There's just no way to identify such players, regardless of their sample ratios or number of PA's. We HAVE to use the overall regression rates for all players..."

Here's where I think scouting reports comes in handy in specific player breakdowns. For example, Alfonso Soriano is a sucker for righties' sliders down and away. Now I'll check the splits: 1.12 last year. Fair. Actually, 1.12 to 1.08 doesn't seem like much, but we're talking about 102 OPS points instead of 67, which is significant, leading me to think that we may have a restricted range problem, though I haven't had the required math in years to comment fully.

Hee Shop Choi gets tied up by lefties' hard inside fastballs. Checking: He was 1/17 against lefties last year, so that's not enough to say. Wish I had minor league splits.

MGL,

I don't see how anything you've written has shown that the A's aren't that "smart."

You prject Karros for a .763 OPS against LHP. Hatteberg has had a .687 OPS against LHP over the past 3 years. I don't know how much you would regress Hatteberg's platoon split, but I think it's clear that Karros is better against LHP than Hattaberg.

You project Koonce for a .815 OPS, which would be better than Durazo had last year. Durazo had a .285 EqA last year, while Koonce has never had an EqA above .274 and has been above .260 just once. PECOTA projects Koonce to have a .729 OPS.

At worst, you can argue that the A's overpaid Karros as a mild improvement over Hatteberg vs LHP and insurance in case Koonce doesn't continue to improve at 28.

I don't have time to address all of these questions and concerns. I'll start with the comment about the A's not being "smart." What is it called when you do a detailed, thorough and accurate analysis, and someone criticizes an unimportant, hyperboic comment you make? Is that a "red herring?"

I guess for $600,000 it's not that big a deal what kind of player Karros is. I just thought (still do) that Koonce is a much better choice. I'm sure you are right that Karros has better projections than Hatty versus LHP. Maybe Oak is real smart. I don't really know. I just crunch the numbers.

As far as those players who have "real extreme splits," I should say "Enter Cartman or McEnroe," but I won't. The whole point of the regression analysis in this contect is to tell you "what to expect" from ALL players, from the ones near to the means to the ones that are furthest away from the mean. The regression answers your question "at what point do you not assume that an extreme split is NOT due to chance." Besides the fact that that is a stupid, unanserable question, if the regression is zero, and you have no reason to think that any partiucalr player is nt part of your population (the "reason" cannot include the sample splits), then the answer is "there is no point!" All players, regardless of how extreme their sample splits are, get regressed 100%. If that were not the case, the regression would not have come out zero! If the regression were not xero, as with pitchers and LHB's, then the answer is "there is no magic 'point,'" it's just that every sample split gets regressed a certain amount (based on PA's), such that the ones with extreme splits will end up with estimated true splits more exteme than ones with less extreme sample splits. If a LHB, like Chavez, has a sample ratio of 1.5 (that is extreme) in 3000 PA's, then his estimated true ratio might be 1.4, still extreme. If another player had a sample ratio of 1.2 in 3000 PA's, then his estimated true ratio would be 1.8 (there league average is 1.7). That's the way it works. If there is no r, 100% regression, no "skill," etc. then even if the sample split were 10.0 in 3000 PA's, the estimated true tatio is still 1.7! Given enough players, chance alone will give us any extreme split you can possible come up with. That is why when we pre-determine that the regression is 100%, that a player's sample splits have no predictive value, we simply chalk up an extreme split to luck! Becuase we get to look at lots and lots of players, it is very likley that we will indeed find players that have all kinds of extreme splits simply die to luck!

Here's an experiment I am going to do right now on my computer. I am going to look at the RHB's in 1998-2002 who had THE most extreme splits for that year and then see how they did the next year inthe platoon department. If Ross and the others are right, surely this group would have to have higher than average splits in the next year! Here goes:

OK, there were 27 such players who had at least 300 PA in back to back years. They had an average extreme platoon ratio of 1.36 in year X. In year x+1, they all had a combined platoon ratio of 1.09, right around league average (1.08). IF I sample playres who were even more extreme than that in year X, I get only 8 players. In year X, they had an average platoon ratio of 1.49 and in year x+1, they had 1.02. I could go on and on and increase my sample sizes, but the results are always fouing to be the same. No matter how extreme the paltoon ratios are in any given time period (for RHB's), they will always return to league average in another time period, because those variations are due to luck alone (hecne an overall r of near z

I think there's a continuum of readers here, from the most mathematically sophisticated to those who, well, aren't. I don't have any problem with MGL using whatever data/arguments he thinks necessary to drive home a point. I'd hate to see him (or anyone) "dumb down" a post by trying to predict the least knowledgeable likely reader. After all, essentially the same logic would eliminate obscure TV show references, music lyrics, etc.

Is it a trap?

If you want to get a clear idea of whether there is a skill to the split - take all the at bats of every player with a positive platoon split and those with a negative platoon split and compare the plate appearances of those same groups the next year. Or just take all those with a positive platoon split and compare them to the average of next year. Do that over a couple decades and if there is no correlation between the groups numbers you might have something.

I doubt you will find that.

Done deal.

I took all RH batters with any number of PA's in 1998-2003. For every even year, I looked at only those players with a platoon ratio of greater than 1.09 (there averafge platoon ratio is 1.09). In the next year (the odd years) I looked at those same players, again, regardless of how many PA's they had.

375 players total

So how many players with extreme "THE" most extreme splits (i.e. who have the worst hitting against right-handers among those who "mash" left handers) are going to be given 300 plate appearances the following season if they continue to struggle mightily against any and all right handed pitchers when given the opportunity? Not surprisingly, the answer is almost none.

Well, since this is an argument about Eric Karros it's worth pointing out that he's had more than 300 AB's for each of the last 12 years. His platoon splits for the last 3 year's are 1.44, 1.29, 1.27 (1.35 for the 2 year period) so in no year was his split more extreme than the average of the 8 "extreme" players tested. Basically it looks like the pool of players MGL tested fits Karros very well. You say it's "not surprising" that MGL's pool of players like Karros show no real platoon split but it was just a few hours ago when you said that Karros hit lefties particularly well. I thought you'd be at least a little surprised.

You might be right that there are righties who could only hit lefties and that those players never get the chance to show it. Maybe they never even made the major leagues. As far as I can tell MGL's study isn't about the players without data. It's about whether to take anything from the extreme platoon splits we see in the data.

Some good posts actually exploded into cyberspace.

Ross, in case you are still not satisfied (that's like asking my dog after I feed him if he wants some more food0 that for all intendive purposes ALL RH MAJOR LEAGUE HITTERS HAVE THE SAME TRUE PLATOON RATIO, send me your address and I'll mail you a vial of my blood...

Someone obvious got too excited about post #69.

MGL, I've always been impressed by how aggressively you believe in your theories.

I still find it really hard to believe that Shane Spencer, for example, "should" have a 1.08 ratio. But there's nothing in your methodology that is arguable. A lot of things (DIPS comes to mind) just sound mind-boggingly weird the first time you hear them, but they make sense in time. Heck, I remember thinking Rob Neyer was crazy when he said Paul O'Neill was an offensively liability in 2000.

I'm still not 100% convinced, but bravo.

FWIW, I too just assumed that platoon splits for RHB's were "real" (of course, like anything else, I knew that sample splits had to be regressed according to the number of PA's they were based on). I then read in the book Curve Ball that that was not true. I was somewhat skeptical, so I did my own research and sure enough, they were right!

Hank, honestly, off the top of my head, I don't know what the standard error is on platoon ratios for X number of PA's, but for 100,000 or so total PA's in the above study, it's not going to be much. IOW, if I included more years (larger samples), it's not going to change the results...

But how does the group with the smaller group of at bats have a ratio of 1.23 and the larger group and average of .90 (.899 rounded up) and the overall average come out at 1.09? If the two groups had equal at bats the average ratio would be 1.065. I don't see how those calculations can be consistent.

You are right. The two groups should average 1.09 or so, rather than 1.065. Let me check and I'll get back....

I don't know if anybody has bothered to look at this yet, but Karros's career ratio is only 1.10 or so (.841-.763), well within the boundaries of chance variation.

Of course, that doesn't mean this is a horrible move for the A's, because (a) Karros can still be expected to hit 8% better if used primarily against lefties rather than righties and (b) he should hit lefties better than Hatteberg. But more fuel for MGL's fire.

I don't know if anybody has bothered to look at this yet, but Karros's career ratio is only 1.10 or so (.841-.763), well within the boundaries of chance variation.

That is ironic....

You are right. The two groups should average 1.09 or so, rather than 1.065. Let me check and I'll get back....

The average platoon ratio for all RHB's in 98,00, and 02 was 1.064524, so the numbers are fine...

Oops, you guys have be going bonkers! All those last numbers were for OBA platoon ratio and not OPS. At least we know that OBA ratio for RHB's regresses all the way as well! I was doing some OBA and SA platoon ratios for Walt D., and forgot to change it back. Anyway, the average OBA and SA platoon ratios for RHB, LHB, and switch hitters are:

> 299 PA per year

OBA

RHB 1.072

Hopefully this doesn't get triple posted and if it was answered in the portion of the thread that went kablooey, I apologize.

I think MGL's study looking at all players above the median and all the players below potentially tosses the baby out with the bath water. If there are RHBs with unique splits, we shouldn't look for them in the great mass of players near the norm, but rather in the 5-10% of the most extreme in either direction. I don't know if that would show any, but it would be more meaningful when comparing populations to Eric Karros, whose observed OPS split in the last 3 years ~1.35. More germaine to the specific question of how Karros would perform would be a study limited to players with 700-1200 PA, at least 200 and no more than 400 against LHB who have a platoon ratio of 1.25 to 1.45, or similar boundaries.

Also, I don't buy the argument that its inherent because of the number of LHP in youth leagues. There are hundreds of major leaguers coming from hundreds of different backgrounds. No way, no how do their little league, high school, American Legion, or sandlot opponents all have roughly the same percentage of left handed throwers with the same ratio of different arm angles and pitch varieties.

I also came here because of Neyer's article. I'm definitely not mathematically inclined and, frankly, my eyes glazed over at MGL's otherwise fine and well-thought explanation of correlation coefficients, z scores, etc.

As I understand it, though, the essential points were that (a) RHBs do have platoon splits *but* (b) they aren't terribly predictive and can be written off to sample size, etc. as much as anything else. Put another way, there is no demonstrative "lefty-mashing" skill -- RHBs should expect to have a platoon advantage to the same degree as the league generally.

Is this close to the point?

Big Del,

I think that to some extent you are right and to some extent you are wrong, but I do not know nearly enough about statistics to adequately comment in your thesis. I'll leave that to the experts on Primer (like Hsu, Jordan, AED) if they are lurking and want to chime in.

I took some ideas that I recently learned on Primer and in some private discussions with some of the brilliant minds on Primer and ran with them. I think that what I presented was more or less accurate, but the readers can come to whatever conclusions they want, as really all I did was to provide some interesting data (it's all here, BTW).

As to our best estimate of Karros' or any other RHB's platoon ratio for this year or any other year, I stand by the mean of all RHB's, which is around 1.09. I could be wrong. As I said, I am no statistician.

We can perhaps be comforted in the fact that it is hardly important, one way or another, as compared to other things in our lives and in the world.

Thanks for all the feedback and comments. Funny, I didn't even post an article or study. Just made a few posts and toyed with the numbers a little. And it was Bill James, and then again Benett and Albert in the book Curve Ball (there may be more of course), who originally posited the notion that RHB's all have around the same true platoon ratios. That caught my attention about 2 years ago.

I also want to thank Tango, and all the statistical experts on Primer, for teaching me about how correlations, regression, and a comparison of observed and expected variance all relate to one another and to ascertaining whether a certain measurement, like platoon ratio, is based on a true "skill" (spread of talent in a population) or not.

I highly recommend 2 sites for further general reading in this area:

http://www.baseballstuff.com/tangotiger/solvingdips.pdf

http://stat-www.berkeley.edu/users/stark/SticiGui/Text/ch4.2.htm

I'll lurk on this thread for a while to learn some more, but I don't feel I can adequately or responsibly address or answer any of the statistical questions or concerns...

Big Del:

You have not demonstrated the likelihood that the 6-consecutive runs could have been by chance. In fact, you could have had 1.04,1.05,1.06,1.07,1.08,1.09, and you would have made the same conclusion. Furthermore, you have not demonstrated the effect that the simple size in each year has on the "runs".

While it is true that what we are looking at is group-level, and we are trying to infer, as our best guess, on the individual, I don't think that your look at the individual shows anything beyond random variation.

I should have said "they way you looked at it".

Karros may in fact have a true split, and it may be large enough to not ignore, and it may in fact get wider as he ages (or as he gets different shares of PAs?). But, I don't think the way you looked at it answers that with any statistical significance.

This may be very flattering for the "brilliant minds" here - but there is an old adage about "a little knowledge is a dangerous thing".

Ross,

I said I wasn't going to be posting on this thread, and I think I've always been cordial to you, but...

That statement is so out of line it is outrageous. To put me in the category of "a little knowledge can be a dangerous thing," is so over the top, it seriously makes me wonder about your sanity...

I lurk more than I participate here, Ross, and I can't give you a good reason why you should give a whit about what I think, but statements like:

This may be very flattering for the "brilliant minds" here - but there is an old adage about "a little knowledge is a dangerous thing".

Are a textbook illustration of how to go from "contrarian and valuable member who elevates discourse on this board" to "troll" in a few short keystrokes.

I specifically said that a correlation from one time period to another tells you everything you need to know about whether a certain measurement (like platoon ratio) is "skill" related"

While that above statement I made is not techincally 100% accurate, it is basically true. Any significant "skill" will result in a singificant correlation for any nubmer of sample elements (in this case, the number of sample elements was around 400 PAvRHP and 100 PAvLHP) above a deminimus amount.

A couple of the caveats (qualifications or limitations of "correlations" derived from linear regressions), which a few people mentioned are: It is assumed that we are looking for a linear relationship, and outliers (don't confuse that with extreme values, like the ones in the list above) can affect or obscure a linear relationship by "screwing" up the value of the "r".

I mentioned that in the case of platoon ratios, these should not be much of a problem, which is also pretty much true.

Now matter how you look at this problem - even if we had NASA and the NSA combined looking at it - you can't get away from the basic conclusion, which is that there is little predictive value in a player's RHB's platoon ratio. You don't have to be a statistical expert to conclude that. When the correlation between two samples is near zero, it is highly likely that the above statement is true. That should be obvious I think. As well, if I show you that all players who had platoon ratios above 1.09 in one year revert to platoon ratios of exactly 1.09 in the next, and the same is true for all players who have platoon ratios of less than 1.09 in one year, unless I am lying about the numbers, or I made a mistake inthe calculations (anyone is welcome to duplicate it), the basic conclusion should also be obvious.

Again, that doesn't mean that EVERY RH batter who ever played or is playing major league baseball has the same true platoon ratio. It just means that MOST of them do and/or that any differences among a large percetnage of players is very small. There may be 1% of the population of RH batters who have true platoon ratios quite a bit higher or lower than 1.09. It could be .5% or .1% or 0% or even 2%. It can't be 10% or 20% though. You can't tell the exact number from the linear regressions that I did. Yes, there are aparrently more complex statistical analyses you can do to tell, but doing the simple regressions tells you 99% of what you need to know.

Ross has tried to turn this very good discussion into something like "MGL presented some data and made some remarks about that data which turned out to be wrong and that is why 'a little knowledge can be a dangerous thing.'" Nothing could be further from the truth.

The data was very telling and the conclusions were more or less accurate and true ("very little perdictive value in a RHB's sample platoon ratio....")

Unfortunately, this discussion got split up into 2 different threads. Ont he other thread, AED, or Andy Dolphim, who is one of the "brilliant" statistical minds I was referring to, did some complex statistical analyses on platoon data for RHB and came up with the following regression equation for taking a RHB's sample platoon ratio in any numbe of PA's and "estimating" or projecting his true platoon ratio.

2500/(2500+1/(1/LHPA+1/RHPA))

If you plug in 400/100 or 395/105, whatever the splits were for my 500 PA (or so) samples were, that comes out to a regression of 96.9%, or a correlation of .032. That's pretty darn close to zero (the .032 correlation) and that is certainly consistent with "little or no predictive value..." As an example, if a RHB had a platoon ratio of 1.25 for a full year (say 600 PA or 450/150), his projected platoon ratio for the next year would be 1.097 (where the average ratio is 1.090). If anyone wants to argue with that, please address your arguments to AED and not to me (sorry Andy!).

Funny thing is, I stated in one of my posts that if I had to guess, I would guess that the true correlation for 500 total PA's was .02. AED comes up with .032. That's not a bad guess. I also showed that with a correlation of .02 (or AED's .032), if a player had lots of PA's and a very high or very low paltoon ratio (compared to the average), we might start to see a projected ratio a fair amount higher or lower than the mean. Of course, such players would be and are few and far between.

Here is AED's post from the other thread:

<i>...the regression amount seems to be approximately:

Mark,

You are correct, but if you read the whole thread (which will take about 3 days), you will see that the amount of correlation from one sample (season in this case) to another is a direct function of the size of the data (in this case, the PA's) in each of the elements in each of the time periods. Yes, the larger the PA's, the higher the correlation, but the correlation for the year to year samples tells you exactly what the correlation is for any number of years (or PA's). Re-read post #134. AED's equation expresses that relationship.

So it doesn't matter how many PA's you look at when you compute the correlations. You can take that correlation and extrapolate it for any number of PA's. Yes, the larger the number of PA's, the larger the correlation will be and the smaller the regression. So for 400/100 PA's, we get a correlation of around .032, and for 4000/1000 PA's (around 8 years full-time), we get a correlation of almost .25. That's really about it. IOW, you don't have to do the correlations for lots of PA's (3 or 5 years of data, as you suggest). You can interploate that from the correlation from one year. The only caveat is that your confidence intervals on those correlation coeffcients will get slightly smaller as you have more PA's (confidence intervals for "r"'s are a function of the number of elements in the regression, or N, and the size of the correlation itself, which in this case reflects the number of "trials" or PA's in each data element)...

Mark, the confidence intervals don't go up that much with the correlation. Remember, with correlations, the "sample size" is N, the number of players. If you want to do 3 or 5 year correlations on players who have say a min of 1500 or 2000 total PA's, rather than 500 total PA's in one year, your "sample size" will actually be smaller! The number of PA's in each sample element in the regression is not the "sample size." It is simply the number of trials in the "experiment" or "test" and defines the standard error for the result of each experiment. IOW, we do an "experiment" or "test" on 100 players in year x. All those players have around 500 total PA's each in year x. Each player's platoon ratio is the "test". The number of PA's in that "test" gives us the standard error of that test. In year x+1 (or any other year), we "re-test" each player doing the same "test" (taking their platoon ratio in around 500 PA's). We do this for a hundred (or whatever) players and we regress year x on year x+1 which gives us the correlation coefficient (among other things). The sample size of the regression is the number of players (100 or whatever). That is the primary factor in the confidence interval around the correlation coefficient. The number of PA's in the "test" does not determine the confidence interval directly. In directly it does, becuase the more the PA's, the higher the correlation. For correlations (unlike means of normal curves), the correlation coefficient itself also determines to a small extent the confidence interval around that correlation coefficient. I'll give you an example, and then you will see why it is not that important how many years (or PA's) we use for out regression. If the true correlation for 500 PA's is indeed around .03, and we regress 100 players, the standard deviation of the correlation coefficient is around .0975 (it's not exactly symmetical around the "mean" for correlation coefficients, BTW). That means, of course, that if the true "r" is .03 when we do that regression, we expect that 95% of the time we will get a sample "r" between -.17 and +.23. I am taking this right off of a statistics table. Now let's say that we use 3 years worth of data, rather than one. We regress 3 years on 3 years. Let's say we still have 100 players (this is a stretch, since the more years we use, the harder it will be to find players who meet our requirements). The true correlation for 3 years should now be .09 (You can interpolate that from the .03 using AED's formula somewhere above). Now, if we look at that table again, for an "r" of .09 and N=100 again, the SD is still .0975. I guess that perhaps the SD stays the same as long as the N is still the same. So actually there is zero benefit in using "tests" with more PA's. Actually there is. Even though the SD is the same, the "standrdized" SD is lower with more PA's in the "test". IOW, the SD divided by the correlation is lower, such that a sample correlation of .09 with a SD of .0975 is "better" than a sample correlation of .03 with a SD of .0975. So yes, you are right, but the benefit is not that great, plus as I said, you are going to have a harder and harder time finding players the more PA's you want to use.

Honestly, I know that sabermeticians and statisticians harp about sample size all the time, but one must understand why. When looking for "granular distinctions," sample size can be important. When looking for generalized statements, like the answer to "Do RHB's sample platoon ratios during some reasonable reasonable period of time have much predictive value," sample size for the correlations is not that critical. Whether the true correlation for 500 PA's is .02, .02, or .05 doesn't change the answer to the question. If someone tells me that they ran a regression and the correlation came out .02 with the 99% confidence interval between -.13 and plus .15, it really doesn't interest me to spend the time looking for and at a larger sample, when all I wanted to know was whether there was a signficiant predictive value in the thing we were measuring (given some number of PA's of course). If I get that kind of result, I'm satisifed that there is a 90% chance that there is almost no predictive value, a 99% chance that there is very little, a .5% chance that there is a fair amount (corr>.15), etc. There is always a limitation in analyzingf sample data, and there is nothing we can do about it. We have to arbitrarily make deicisions as to at what point we are satisfied with a particular conclusion, and because it is based on sample data, any an all "conclusions" have a finite chance of being dead wrong.

Make sense?

Mark, you make a good point, but to tell you the truth, I never did a formal study in the first place. Another ironic thing about this thread, which has become like the game "telephone." I started out by making some comments about platoon ratio, ran some tests, presented the data and some "conclsuions," ran some more tests, and here we are. I have neither the interest nor the time to do any more research in this area....

My statistics classes are very rusty, and I know I'm treading on very thin ice, but what the hell. I dusted off an old statistics analysis program to try to generate some random data, just to demonstrate how an Erik Karros might not be such an outlier after all. I used a Bernoulli random number generator to simulate times on base for 6 seasons, with a base OBP of .33 for PA against RHP (450 of them) and .3597 for PA against LHP (110 of them) - the second number is 1.09 times .330. My hypothetical "Random Karros" has no particular skill at getting on base against LHP - "he" is a column of 1s and 0s. However, according to the data, "Random Karros" has Bonds-like skill against lefties!

"In 1974, George Brett was hitting .220 or so at the break. He hit over .400 after the break and finished at .282."

Not exactly. Courtesy of Retrosheet, George's PA and pre- and post- All-Star numbers.

Pre - 228, 242/284/308