THE BOOK--Playing The Percentages In Baseball

This is how I’ve been doing MLEs & projections.

Start with a fixed number of plate appearances. First ddjust the hbp, bb & so. Then find how many balls hit fair are left. How many are homeruns? That leaves balls in play. How many of those went for hits? How many of those went for extra bases? How many of those were triples?

I believe one point Pizza was making is that each of these should be regressed by different amounts. We discussed this here a couple months ago while I was working on my projections. I agree, it is true, but I also found that if I use 150 PAs of regression for all components it just didn’t make that much of a difference. For example, babip never found a minimum rms even after 1000 PAs, but the slope was so gradual that the difference in rms between 150 and 1000 PAs wasn’t really consequential (at least for batters).

Heads up - I will be discussing how each of the components age on Thursday.

I believe one point Pizza was making is that each of these should be regressed by different amounts.

I’m actually really surprised this idea hasn’t been fleshed out yet.  We’ve all been aware of its truth for years.

I believe the guys developing StatCorner.com (and tRA) have done some work on this (at least for pitchers, and they haven’t published it yet), but I’m really looking forward to seeing everyone’s results.

Four years ago, MGL did work here:
http://tangotiger.net/mgl/regression.pdf

And we had a thread here:
http://www.tangotiger.net/archives/stud0274.shtml

Post 6 gives you the summary:
http://www.tangotiger.net/archives/stud0274.shtml#1006

On HR rates, the pitcher gives up the flyball, but the batter makes it a home run.  That’s an over-simplification, but it gets the basic point across.  So, HR rates for pitchers will be about as consistent as FB rates over a long period of time.

And yeah, the point I’m making is that the regression coefficients are different from stat to stat.  In the background, I’ve been generating tables on exactly what those coefficients are on a PA-by-PA basis.  It’s slow to come, but it will eventually be out and available to all who are interested.

Tango/3—thanks for the links, I don’t remember seeing those before.  I was more thinking of regression in regards to batted ball data, though, taking BABIP to the next sub-level.  Regression of GB%, LD%, FG%, etc.  But also regression of run-values on those things, such as a player’s SLG on LDs, HR/FB, AVG on FB, etc.

We did those as well a long while ago.  Check under Batted_Ball here:
http://www.insidethebook.com/ee/index.php/site/categorylinks/

We did something along those lines anyway… don’t remember exactly what…

And of course, MGL’s DIPS piece has the information you need:
http://www.baseballthinkfactory.org/files/primate_studies/discussion/lichtman_2004-02-29_0/

(Note: that is a ground-breaking piece, and should be required reading for all newcomers.)

He reports both the correlation for the frequency of event types (GB, FB, LD), but also the correlation on the success for each event type.

He also points out that each data pair has around 500 BIP.

Those data should be enough to determine the regression components Sky is asking about.

I’ll get you started.

MGL reported a year-to-year correlation of .74 on GB per BIP.

r
= var(true)/var(observed)
= 1-var(random)/var(observed)

var(random) = .5*.5/500 = .022^2

With r=.74, this implies var(observed) = .044^2

In order to get var(random) = .044^2, we need BIP = 125

So, at 125 BIP, we regress the GB rate 50% toward the league mean.

r = BIP/(BIP+125)

regression amount = 1 - r

That simple.  You could also perform the same exercise using current one-year data, as I’ve done it before.

PC #4 - One of the things I have on my to do list is seeing how much HRs are the result of “mistake” or “fat” pitches. Data from hitracker shows that the variance of speed of bat for HRs is much lower for pitchers than it is for batters. I’m not so sure that for pitchers HRs are just a random outcome of a flyball. I think it may be that certain combinations of pitch type/location/count are more likely to be a HR. It’s up to the pitcher to not throw it, and up to the batter to recognize it and not let it go by. Eric Seidman has looked at some of this with his Johan Santana HR rate article, and it also gets into your own pitch recognition work. This is one part of that where I have a hypothesis, but it still needs rigorous testing (so getting my own pfx database finished in the offseason is a priority)