THE BOOK--Playing The Percentages In Baseball

When you have kids, are you going to replace the growth chart on the wall with a regressed version that compares them to other children of similar ages?

Or, to stretch out the example, if your 6 year old goes from 4’0 to 4’1, are you going to explain to him that he didn’t actually get taller, because the growth chart says he should now be 4’3? Or would your kid look at you with a confused look when you tried to explain that 4’1 was actually not taller than 4’0?

Maybe I’m just hanging out with the wrong people, but to me, progress is defined at the specific individual level.  I understand what you’re saying, and from a projection standpoint, I don’t disagree, but I’m not sure that anyone I know defines progress as you do here.

That is an amusing example, but I am 100% serious and 100% correct, and doing it the way “everyone” does it is just plain wrong, and will lead to erroneous and dangerous conclusions.

David - when the child grows from 4’0 to 4’1, it is a direct measurement of an objective fact. When we look at how many homeruns someone hit this year, it is a sampling of his ability.

I toss a coin ten times and get six heads. You toss your coin ten times and get five heads. Do I have a better coin than you do?

It is a fact that Gonzalez hit 24 HRs in 2006 and 30 in 2008, but what can we infer from that sample about how good of a HR hitter he is? Is he better than Fielder of Howard?

That said, I look at things differently than Tango, and he has at times told me I was wrong.

When I look at the numbers from the article Tango cites, why did the author only use two seasons? Why did he not start at the beginning of the season? Even with the numbers that were presented, if you know the standard year to year variation, even for full time players, you realize that there’s little or no difference between the numbers. They are all within the range of sampling error.

I looked at Gonzalez’s numbers from 2004-2008, using MLE’s for 2004-2005 Oklahoma. I would have went back further, but didn’t have the minor league park factors handy.

Year _PA _BA/_OB/_SA BABIP ISO BB SO
2004 553 264/312/374 308 110 060 171
2005 535 274/318/428 302 154 059 169
2006 634 304/356/500 344 196 068 178
2007 729 282/339/502 315 220 077 192
2008 291 292/354/549 314 258 076 196

In 2007 & 2008, his BB & SO rates were both up a bit, and were virtually identical. The three years before that were virtually identical. These two rates need less than a full season to be reliable.

His BABIP popped up in 2006, but the other four years are basically identical. This takes the longest to be reliable, almost three seasons.

The one pattern I do see is a steady and consistent climb in his ISO. However, unlike global warming, I will not project that it will continue to rise forever. The 258 may well be an outlier that will not be reproduced. This is the number I will key on, as it is the only one to show real movement, but also the most likely candidate for regression. Can it continue to rise? (Players can gain strength in their early to middle twenties). Has it already passed the true level? We will have better answers at the end of 2009.

BTW, half a seaosn of 2008 is the first time he’s shown to be more than a league average 1B with the bat, and of course that’s a small sample size and may not last. I do not accept the author’s conclusion that Gonzalez fell back from 2006 to 2007. Except for a small rise in ISO, the two years were almost identical, which is much more common than seeing a player “improve”

One of the things the author was doing, for whatever reason, is comparing his actual age 24 to age 25 to age 26 stats - not by season, but by actual age.  So that is one reason for the “discrepancy” between his stats and yours, Brian.  Regardless, what I am taking about is not what you are talking about, I don’t think.

MGL - I was agreeing with you that the approach of the BP writer was inadequate, and that I didn’t share his conclusions either.

I offered another way of looking at the stats, which did not use regression, but does not rule it out (although I usually save regression for the totals line)

I wanted to point out that when comparing rate stats from one season to another you just need to keep in mind what the standard variance is for each stat, which I guess is saying the same thing. Anyway, he suffered from small and selective samples as well.

So even though Gonzalez hit .304 in 2006 and .282 in 2007, I can look at all his rates and see almost no difference from the one season to the other.

mgl: The article looked at actual performance at age 24 vs. actual performance at age 25 and concluded that the player got worse.  I agree with your point that it is better to look at the true talent estimate (regressed age 24 data) instead of actual performance for this purpose.  But should we be comparing to age 25 actual performance or age 25 true talent estimate (regressed ages 24 and 25 data)?  I think your example is comparing to age 25 actual, but isn’t the revised true talent estimate better?

Ahem.  That was a THT article.

Actually, the main conclusions I reached in my article at The Hardball Times (not Prospectus) were that if you look at things a little differently, you might find something unexpected, and also that the length of a single season is a somewhat arbitrary 162-game stretch.

I also don’t recall saying that Gonzalez slipped from 2006 to 2007. His overall production both seasons was roughly the same despite a 22-point drop in BA in ‘07, which I think was a good sign for future growth.

Anyway, I thought this was interesting way to look at the subject. And I also didn’t think I reached any firm conclusions about the progress of Gonzalez as a hitter, but I could be wrong.

Why are you regressing his age 24 performance but not his age 25 performance?

Let’s say that OPS gets regressed around 50% after that many AB’s (I forgot what the actual regression equation is).  So, his true talent at that point is the average of .919 and .750 (a league average non-pitcher in the NL - of course, Gonzalez is a big left-handed hitting first baseman, so his population mean is probably quite a bit higher than that, but let’s pretend for a moment that the .750 is correct), or .835.  At age 25, he hit .842, which is a progression of 7 points!

If you regress 50% to the population mean for first basemen (.793), then his age 24 season true talent estimate becomes .856, so it would appear to me that even on the basis of the methodology MGL outlined that Geoff’s statement that Gonzalez did not progress from age 24 to age 25 is still correct.

Mike F (#10), I was just using those (fake) numbers as an example (I said in my post that you probably don’t want to regress Gonzalez to .750).

The height thing is actually a good example!  What if we measured a child’s height with a technique or a “ruler” that had a lot of measurement error, such that we were not confident that we got a very good measurement at all?

Let’s say that he is 10 years old, and we measure him with a stick with carvings on it to represent inches (and they are distributed really badly on the stick), and we get 4’ 0”, but we know that that measurement is really unreliable.  And let’s say that the average 10 yo is 4’ 6”.  (And of course, we can’t see the kid to “know” how tall he probably is - maybe we are blind.) We would have to estimate that he is probably somewhere between 4’ and 4’6”.

Now let’s say that we measure him next month with a real ruler, and he is 4’ 1”.

Now, is our best estimate that he grew or did not grow?  NOT!  Of course.  This is exactly the same as the player whose performance ay a certain age is an imperfect estimate of his true talent.

Now, whether we have to regress his performance at age 25 again (like measuring the kid in one month with the same imperfect stick) in order to determine whether he “improved”, I have to think about.  We probably do.  That is a good point, Mike #9.

Geoff/8 - This is meant as a constructive criticism.

I read both articles on Adrian Gonzalez, I thought the first was a little better, but in both I had a problem with looking at a snapshot of one 365 day period compared to another, of the same or another player. It is hard to draw meaningful conclusions when limiting your view to small portions of the player’s entire record.

In your 2007 article, you were looking to see if Gonzalez has improved his power. I believe my post #3 in this thread proves your point. He has shown a consistent increase in ISO for 6 consecutive seasons. The comparison to Rafael Palmeiro is worth pursuing.

In looking for trends in several years worth of records, you can see that Gonzalez’s 2007 looked no better if not worse than his 2006. His BA dropped from .304 to .282, but that is mainly because his BABIP was abnormally high at .344 in 2006, then returned to the “true” range shown in his other four most recent seasons. He did improve his BB% a little and his ISO a lot. The BABIP abd BB% are basically unchanged in 2008, but the ISO is even higher (in a smaller sample).

You state that the beginning of the season is an arbitrary place to start counting, which is true to a degree, but I feel it is more important than any arbitrary date because all players share coming from the off season in which they weren’t playing (except maybe in winter ball). The past 365 or 730 etc days is useful to counteract the small sample size of early season stats.

BTW, the comment about being able to hit lefties quoting a .600+ SA was based on 5 weeks worth of data, career to date he is 257/312/445 vs LHP in 522 PA, 285/349/498 vs RHP in 1893 PA. Not terrible, but less than he hits righties

Looking at “trends” or comparing chunks of performance is rarely fruitful and will usually lead you astray.  It is not like height, or even fastball speed, because of the enormous random variance within each sample of performance.

In this case of Adrian Gonzalez, Geoff compared on year with another and concluded that Gonzalez did nor progress as expected.

This is how I looked at it - examining 5 years worth of data, 4 out of 5 his BABIP was essentially the same (within normal range of variance). It was his .344 in 2006 that was the outlier that wasn’t repeated. Not that Gonzalez failed to “progress”, because the 2006 number was not representative of his true value to begin with.

His ISO has increased 5 consecutive seasons, so this is where a regression analysis is needed to try to determine the true value. It’s a fact that each year has been higher than the one before. What’s not known is if he is already peforming above his “true” value, and will regress over the rest of this season or next, or if his “true” value is actually changing and the numbers will continue to rise.

I’m not trying to compare chunks of data, I think that’s what Geoff was doing. I am trying to see as complete a record as possible. I have no disagreement with regression, but I think that many times I can draw the same conclusions without going through the regression.

I would appreciate if you could tell me specifically where you think my technique might lead me astray.

Brian, I wasn’t referring to you or even to Geoff.  Just the general obsession with “trends” and comparing one artificial and arbitrary chunk of performance with another.

Given the “technology” we currently have, all we can do is take a player’s performance in total, weight literally each day differently for recency if we want to construct a projection, and regress towards some mean. That’s pretty much all we can do, at least with the knowledge we have now.

Everything else is just yapping.