THE BOOK--Playing The Percentages In Baseball

I think Pizza uses intraclass correlation to get an r or r^2 for more than two columns.

For example, instead of comparing babip for 2004 and 2005 and then for 2005 to 2006, he gets one result for 2004 to 2005 to 2006...and add more years if you like.

I don’t think it can be done in excel but I think he’s got more advanced statistical tools than that.

I’m sure Mr. Cutter will let me know if I’ve got that wrong.

I think what it does is something like the following:

Say you have one season’s worth of player stats, divided by game. You could find the correlation between each player’s first half stats and his second half stats (in some particular metric). You could also find the correlation between each player’s odd-numbered game stats and his even-numbered game stats. These are two ways of dividing the 162 games in half. But obviously there are a lot of other ways you could group them into two 81-game subsets. If you tried every possible division and found the correlation for each one, and then averaged all those correlations, I think you’d get something like the intraclass correlation. Actually, you’d really get Cronbach’s alpha, according to this:

(click name)

But the following suggests that Cronbach’s alpha is equivalent to the “stepped-up consistency version” of intraclass correlation, whatever that is:

http://en.wikipedia.org/wiki/Cronbach’s_alpha#Cronbach.27s_alpha_and_the_intra-class_correlation

I really don’t think that’s what he’s doing, but I’m very confused so I don’t know.

It’s possible that what he’s doing is taking a random set of half the PAs in one season and doing a correlation to the other half, and then repeating for another random set, such that he gets a virtual infinite set of PA to correlate to the other half. Maybe that’s why he said not to add too many years.

Like I said, I’m super confused and invest alot of time in what Pizza writes.  (Then again, I’m sure others might feel the same way about what I do!)

It’s possible that what he’s doing is taking a random set of half the PAs in one season and doing a correlation to the other half, and then repeating for another random set,

Without reading his description or poking around on the net, that sounds like a reasonable way of doing it.  More than reasonable.

Tom, check your spam filter… I think that my epic novel on the subject of ICC may have been stopped for further questioning.

Pizza, nothing there.  I hope that you made a copy of your treatise before posting here.

The short version is “it’s kinda like a year-to-year correlation, only it uses more than two years.” In theory, it could expand to an infinite number of years.

ICC is part of a technique known as hierarchical linear modeling (HLM, acronym soup!) HLM was originally designed for educational psychologists and analysts to look at what factors influence performance on standardized tests.  Scores will certainly measure something about the kids innate talent.  However, suppose the kid has a good (or awful) teacher.  You’d expect see some increase (or decrease) in performance across all 30 kids in that classroom.  We might also see that all the kids at this particular school tend to do well, or that kids in this district.  In political-speak, it’s a good way for assigning blame and credit for test scores.

ICC is just the lowest level of HLM.  It’s a measure of how much variance is explainable by individual variation in talent.  The specific ICC stat that I use is called AR(1) rho.  It’s designed to handle longitudinal data/multiple measures (like multiple years of data).

What happens is that you put in 3 or 4 or 1200 years worth of data.  The computer then creates a covariance matrix around these data.  For AR(1) specifically, the matrix incorporates an auto-regressive component.  The idea is that if I’ve hit 18 HR two years ago, and 20 last year, then a good bet on me, mathematically, is 22, knowing absolutely nothing else.  (I’m sure the actual algorithim is more sophisticated, but my mathematical knowledge ends there.) The idea though is that consistency isn’t based on hitting 20-20-20-20 HR a season, but staying true to a trend line.

What results is a number that looks and reads like a correlation, but is more than just your simple year-to-year.  It can be interpreted in much the way that a y-t-y can be (if you take the R-squared, you can say things like X% of the variance is consistent from year to year.)

The advantage of ICC is that it’s more stable than year to year based on the fact that it has more data available.  In the comments section of what you link to, I ran the y-t-y for different combinations of years for BABIP.  They ranged from .095 to .281.  Actually, had Voros done his study a year later, he might have seen .281 and saw that it was in the ballpark of HR rate and Sabermetric history might have been different.

What level of data do you need?  For example, could you simply have 1 seasonal line per player, one season only?  Or, do you need to have at least 2 lines per player?  For example, if you look only at 2007 data, do you need at least to have some set of 300 PA for your player and a second set of 300 PA?  And, would more granular information, say one record per PA per player be better?

In SPSS, you need one line per player per amount of time that you want to measure.  Since the player-season is the most common unit of analysis, I use that.  So, I have a line for David Wright 2005, David Wright 2006, David Wright 2007.  If you wanted to do Wright first half then Wright second half, those would be two separate lines, but equally as valid.

You can get an ICC for one time point only, although it would not be AR(1).  You’d probably have to use a diagonal covariance matrix structure (I only sorta know what that means too...)

I really haven’t been paying much attention, but I can say one thing more-or-less objectively: spss is the devil.  Fire it and use R, or if you somehow are memory-constrained, Sas, or if you are both memory- and pocketbook-constrained (though this seems impossible, since you can afford spss), buggy-but-basically-functional-now pspp.

Please.  Ugh, spss.  It’s a network-effect catastrophe that rivals mysql.  I don’t know which I hate more—though I lean to spss.  And that speaks volumes for anyone who knows how terrible mysql is.

I’ve never used R, but SAS is a programmer’s program, and I am not a programmer by any stretch of the imagination.  (In other words, SAS confuses me to no end.) And for what it’s worth, I can’t afford SPSS.  I’m a poor grad student.  I got a copy in exchange for doing some beta testing for them.

Aha.  Well, if you need menus and you’re a poor student, try R with R Commander.  And while spss’s scripting syntax probably is slightly more-parseable than sas’s, R code is to my mind much more readable and intuitive than either one.

R does have a learning curve, even with the gui helper library, but it’s a hundred times better than spss unless you need the few things spss does well: metadata, working on disk and not in memory, and pretty crosstabs.