THE BOOK--Playing The Percentages In Baseball

Tom, it’s not the size of the beta coefficient that determines the strength of the relationship.  It’s the r-squared value of the regression equation.

Do you lurk in The Lounge?  We were just discussing this yesterday.  And now I look like an idiot.  Thanks.

Tom, it’s not the size of the beta coefficient that determines the strength of the relationship.  It’s the r-squared value of the regression equation.

I wish I was smart.

Colin, I feel the exact same way reading this blog. I’m going to suggest a Tango 101 class for next school year.

There was actually someone who was teaching a Sabermetrics class at a college at some point.  There’s also Jim Albert, a professor who wrote a stats textbook using baseball examples.  Whenever I teach stats, I always seem to fall back on baseball examples.

Also, Tom, did you use the 13*HR + 3*BB - 2*K formula or another?

Pizza, I don’t think I said anything about that.  The correlation equation gave me this, as I posted:

ERA (year 2) = 0.49*FIP + 0.10*ERA + 1.79

So, that’s all I said: take 50% FIP, 10% ERA and 40% league average.

I included HBP as well with the BB.  I think the constant I used to convert FIP to ERA was to add +3.10.

David Tybor taught a sabermetrics class at Tufts.  Not sure if he still does.

Andy Andres is now teaching the Tufts class.

Gotta disagree on r-squared.

The coefficient of determination can be useful, and probably is here, where the chances of your being overfit are slender.  But r-squared speaks to the explained variation of the entire regression, and is silent about the contributions of the constituent variables.

If you’d dropped the acronym ‘anova’, maybe.  Here, absent all other data, I’ll take beta over r-squared, thanks.

Pizza, what do you use to determine the relative weights of the indy variables in predicting the dependent variable, in this case, next year’s ERA, which I think is what Tom meant, not the strength of the whole regression equation itself? It seems like the coefficients give you the right answer.  I also wish I knew a lot more about statistics than I do, and fear that I am too old to learn much more.

just out of curiosity… having already graduated college and wanting to learn more about statistics, does anyone know of any programs online or perhaps a tutorial book??? i don’t really have a set enough schedule to take any physical classes.

I was wondering the same thing, Roy. I can’t vouch for the validity of it, but I’ve found something that looks promising at:

http://stattrek.com/Lesson1/Intro.aspx

Also, UC Berkley seems to make their Stats 2 course available for free as a set of video/podcasts:

http://webcast.berkeley.edu/course_details.php?seriesid=1906978362

I’ve also found an (older) set of course notes for the same course:

http://www.stat.berkeley.edu/users/rice/Stat2/lectures.html

No idea if this will be of use to anyone, including myself.

You’re never too old!  Sign up for an intro stats class at the local community college.  If not, pick up a used stats textbook from a used book store off Amazon.

The word that I was reacting to in the original post was “stronger.” The coefficients give an equation that best predicts next year’s ERA, which is fine if all you want is an equation that will predict next year’s ERA.

However, to say that FIP is four times (ratio comparison) stronger of a predictor than ERA requires that both variables be on (about) the same scale.  In this case FIP and ERA are roughly on the same scale (that is a 3.50 on both scales refers to about roughly the same thing), so the comparison will fly.  But to keep things clean, you need to compare the standardized coefficients in the model to start making ratio statements.

The other problem is that multiple regression simply tries to create the best fit equation to the data, which is great for uncorrelated variables.  FIP and ERA are probably correlated (and thus share variance).  To fix that, add an interaction term into your model (FIP * ERA) and see what shakes out with the coefficients.

I suppose the r-squared thing is more my bias toward variance decomposition methods.

I re-duplicated the original analyses, again min 60 IP in both years:

ERA1 and FIP1 are correlated at .774 (no surprise, that’s what FIP is supposed to do, more or less).  ERA has a slightly lower mean (4.17 vs. 4.27) and a bigger SD (1.09 vs .82), meaning that we’re not exactly on the same scale, but close enough.

Standardized coefficients in the two variable model are .097 (ERA) and .341 (FIP) so it’s more accurate to say that FIP is 3.5 times stronger than ERA in that model, once you account for the scale issue.

However, given the correlation between FIP and ERA, let’s add in the interaction term so that the shared variance will be more properly handled by multiple regression:

ERA2 = .657 * ERA1 + .962 * FIP1 - .122 * FIP1 * ERA1. (those are raw/unstandardized coefficients; this equation is 1.5% better on R-squared than the original)

If you look at the standardized coefficients on that one, they come out to .673 for FIP and .607 for ERA.  FIP is still the better predictor when you control for the differences in scaling and for the shared variance between the measures, although the difference isn’t as big as it looked on the original.

In Tango’s first set of equations, Year One FIP and ERA measured separately against Year Two ERA, I don’t see how the coefficients are helpful at all.  I’d rather have the R squared.  And Cutter has done a great job of articulating and analyzing the problems with multivariable regression (which I can only fumble over).

I bought the Complete Idiot’s Guide to Statistics a couple of years ago and have found it very helpful for the basics.

Actually, the coefficients are very helpful, for the exact reason that Pizza was mentioning: ERA and FIP are on the same scale.

(Pizza: as far as I proceed, it doesn’t matter that the spread of ERA1 and FIP1 are not the same.  What matters is if y=mx+b has m=1 when correlating ERA1 and FIP1.  If m=1, and b=0, then we’ve got the exact same scale.)

I’ll have to think about your equation in post 16.

Pizza, in #16 the intercept is zero?

Tango,

These equations would be good baselines to compare the pitcher projections to.

Just ran a correlation of FIP to ERA, same year:

ERA = 1.01 * FIP - 0.15

As you can see by the slope, FIP has the same basic scale: it’s a 1:1 relationship.  If the FIP drops down by 1 run, the ERA will drop down by 1 run.

The -0.15 simply aligns FIP to ERA… for that sample.  If you simply look at the population mean of FIP and ERA, they are identical.  (They’d have to be, since I have that +3.1 fudge in the FIP equation.)

There are 2 reasons that in this sample data, we have -0.15 as a further intercept:
1. The regression I ran didn’t attempt to give different weight to the 60IP pitcher from the 180IP pitcher
2. It’s possible that the guys that dropped out of the sample is biased (guys with disproportionately higher ERA than their corresponding FIP, didn’t get a chance to reach the 60 IP threshhold).

So, in terms of “weight”, you give 100% to FIP and 0% to league average, when trying to scale FIP to the same year ERA, even though the r-squared between the two was 58%.  FIP is ERA, for all intents and purposes.

The r-squared could have been 1%, and it still wouldn’t change that relationship.

Actually, the coefficients are very helpful, for the exact reason that Pizza was mentioning: ERA and FIP are on the same scale.

Unless I’m missing something, I don’t agree.  The constants are substantially different.  You could have a tighter R squared with a smaller coefficient, then the answer between the two would not be clear cut at all.  In that case, I’d go with the better R squared, unless the difference is minimal.

I don’t see how you could have a tighter r-squared *and* a smaller coefficient, if ERA1 and FIP1 were both of the same scale.

Okay, I need to think about that.

The intercept on that equation was actually -.282

Tom, if you run it the other way with ERA1 predicting FIP1, you get .577 * ERA + 1.873.  The problem isn’t going to be at the mean.  It’s going to be at the edges.

But FIP is a causal agent to ERA, not the other way around.

If you take the top 10% in FIP, their mean will match the mean of ERA.  If you take the bottom 10% in FIP, their mean will match the mean of ERA.

***

Here, I just did it… I took the top 240 in FIP, and I got this:
FIP, 2.77, 4.28
The first number is the FIP of the top 240, the second one is the mean of the group.  So, the top 240 was 1.51 runs better.

The ERA of those 240 pitchers was 2.62, compared to the sample mean of 4.17, or 1.55 runs better.

On the flip side:
FIP, 5.71, 4.28
The 240 worst FIP pitchers had a FIP that was 1.43 runs worse than the sample mean.

The ERA of those pitchers was 1.48 runs worse.

It seems to me that 1 FIP run leads to 1 ERA run.

***

Of course you can’t do the reverse (Pizza/25), since the top10% of ERA is a product of FIP, hits, and random variation.

The top 240 in ERA had an ERA of 2.31, compared to a FIP of 3.07.

You just can’t do the equation with ERA as an independent variable and FIP as the dependent one.  It’s the other way around.