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Defensive Independent Hitting, Or ShH

Posted By Bradley Woodrum On August 4, 2011 @ 3:00 pm In Rangers,Rays,Red Sox,Research,Yankees | 101 Comments

Maybe there’s is a better way to predict how well a hitter is doing? Rather than glancing at his OBP and SLG and OPS or his wOBA and wRC+ and then mentally calibrating that number according to an inflated or deflated BABIP, maybe we can find a simple means of combining the key elements into a single formula.

Well, I believe I have stumbled onto just such a formula.

Th’other day, when I was trying to solve the mystery of the Tampa Bay Rays and their utterly broken run expectancy chart, I began ruminating about the relationship between walks, strikeouts, and an ability to create runs. You see, the Rays tend towards true outcomes: lotsa walks, lotsa strikeouts. So, for some strange reason — be it bad luck or bad hitter-type chemistry — the Rays seem to have an inability of reaching a standard run expectancy with the bases loaded.

Anyway, I began to investigate this trifle and produced an interesting comparison:



The greener area (less walks, more Ks) is obviously worse, just as the white area is obviously better. In between, however, is the tenuous white-greenish area of mixed results.

What particularly piqued my interest was not really a new finding of any sort, but merely the visual represent of the different means of success among MLB offenses.

For instance, the Rangers put a lot of balls in play. They walk very little and strike out very little, but are still a successful offense (116 wRC+ or 16% above average). Meanwhile, the Yankees and Red Sox have a lot less defensive dependence, taking bases on walks and striking out much more often. These teams have similar results, but lay on different points on the spectrum.

So I axed myself: “What does the relationship of plate discipline look like with respect to run scoring?”

Not a profound or unanswered question by any means, but a fun exercise. The relationship is neither surprising nor overwhelmingly strong:

What surprised me with this dandy little regression — and what made me wander down the rabbit hole — was the high R-squared and minuscule P values (not shown). I did not expect that the BB/K ratio would represent ~47% of the variation of wRC+. When I think of great hitters, I usually do not immediately think about their balance of walks and strikeouts.

I then pondered: “How deep does this relationship go? Could there be a defensive independent means of evaluating a hitter?”

If half of a team’s offensive variation comes from walks and strikeouts, then maybe homers could make up the rest of that variation? Well, a half dozen regressions later, I concluded two thangs:

1) Defensive independent events — walks, strikeouts, and homers — have a very strong correlation with park-adjusted run scoring (wRC+).

2) And BABIP fills any and all remaining gaps.

The beauty of BABIP is that it encapsulates basically the junk drawer of remaining elements. BABIP has luck, speed, and defensive dependence in it, so the resulting R-squared is basically infinity.

I took these two little, unsurprising yet key, facts and slung them at a decade’s worth of hitters. Then, I looked at the more recent era — let’s call it the Dying Ball Era please! — and produced this:

I call it Should Hit, as in: Yuniesky Betancourt should hit 80 wRC+ with a normal (career) BABIP. Of course, if you put in a players present BABIP instead of their career, then you should get something like above, where there’s a nearly one-to-one relationship.

The formula is simple, which is why I love it. Regressing K%, BB%, HR%, and BABIP on wRC+ (from 2009 through 2011), we get (approximately) this:

Should Hit = -60 + 277(BB%) + -184(K%) + 1133(HR%) + 465(BABIP or xBABIP)

Walks and strikeouts and home runs normalize way more quickly than BABIP, which can go crazy for whole seasons. Should Hit — or ShH (pronounced shh, as in shut up) for those who love acronyms* — allows us to use the three more stable (and more adjustable) elements of hitting to our advantage.

Not only do walk, strikeout, and homer rates stabilize quickly, they also have some of the highest variations through a player’s career as individuals are constantly changing their approach or dealing with pitchers adapting to them. Whereas BABIP is a slow swinging pendulum — constantly based around a consistent point, but never quite there — BB%, K%,and HR% are small needles quickly finding exact points which change slightly almost every season.

So, using Should Hit, I can predict how any player would perform given an array of BABIPs. Take this year’s anomaly, Casey Kotchman. After getting off-season surgery on his eyeballs, Kotchman has instantly gone from a worse-than-league-average hitter to a 134 wRC+ hitting machine. Most non-Rays fans (and myself) look at Kotchman’s crazy .360ish BABIP and say: “I know what comes next. Pride goes before destruction, a haughty spirit before a fall, and a high BABIP before a nasty regression — or something like that.”

Anyway, given the peculiar Best Shape of My Life story preceding his resurgence, Kotchman has earned a slew of devotees committed to believing he will keep his pace up. If we put his numbers in Should Hit, we get this:

So, if we think Kotchman’s new vision can really sustain his ultra-high BABIP, then he can legitimately be a 120 to 130 wRC+ hitter. But, the truth is he’s not walking much and striking out more than usual. Should Hit does not like that and says, t’were his BABIP to revert to career norms, he’d be having maybe the second-worst season of his career.

Now, ShH is not an xBABIP tool. If you want an xBABIP calculator, then go here. For ShH, I prefer to just use a little common sense and career BABIPs, assuming a player has more than one season of data.

Because I luv crowd-sourcing, here’s a Google Doc with the Should Hit formula. Feel free to download or save a copy and play with it to your heart’s darkest desires.

For the Google Doc, just input the walk and strikeout rates of a player’s current season. Then add their present home run total (or career totals work well enough too) and the present (or career) plate appearances — this calculates the home run rate.

Then, input their present BABIP. You will notice the resulting wRC+ is not as high as it is in their present 2011 season. I believe this comes from a calibration issue due to the Dying Ball Era’s lowered expectations.

Modern “plus” metrics having lower standards right now because of the league-wide depression in offenses. Originally — as noted above — I used a whole decade of data to form Should Hit’s slopes. Unfortunately, the distance between 45-degrees and the regression narrowed each time I sliced off a season of the Steroid Era.

So, the present rendition has a bit of a calibration issue. All that means is you will want to put in their present BABIP first, then your predicted BABIP (or and xBABIP) for comparison’s sake. Or, you can just use my Should Hit (Advanced!) which adds this layer for you:

In closing:

1) Play around with Should Hit and ShHA! and let me know what you think.

2) Are there problems in my reasoning? Let me know. I’ve used what I hoped was the simplest reasonings and the simplest methods (linear regressions), but maybe it’s more complicated than it appears to me.

3) Let me know what you think about the external validity of this little tool. As I mentioned, the Steroid and Dying Ball Eras have thrown significant monkey wrenches into league averages, but I would like to think I avoided those problems. Also, has anyone else done something similar to ShH in the past? I imagine others more brilliant have long-explored defensive independent hitting already, but I could not recall of such a thing.

Finally, have fun!

*I do not like acronyms in sabermetrics. They make otherwise simple concepts seem complex and alien to the un-inundated. Initially, I wanted to avoid an acronym altogether, but in the name of reasonable spreadsheet column widths, I decided to go with ShH. And in the name of younger audiences, I decided against ess-hit (written “SHit”) for more obvious reasons. If you must, though, just think of it as expected weighted runs created plus, xwRC+ — which looks like a virus in your registry.


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