More pitching randomness than just DIPS

Last month, Nick Steiner discovered something interesting: pitchers don't actually seem to pitch any worse when getting shelled than when getting batters out. That is: if you were to look at the types of pitches thrown, their speed, and their break, the shutout pitches look the same as the "give up five runs in three innings" pitches.

If that's the case, the implication is that the differences are batters, umpires, or luck. I think it's mostly luck. Previously, I argued that simulation games like APBA serve as evidence of that. The same pitcher's APBA card, with the same batters, can result in a shutout or a blowout just based on dice rolls, and the pattern of performance looks fairly realistic. I don't know of any studies on this, but I bet if you played out a random pitcher's season on APBA, and then you put his APBA first innings side-by-side with the first innings of his actual starts, you'd have a tough time figuring out which was which.

Anyway, Nick expands on the topic today, over at Hardball Times. He found a bunch of pitches that looked almost exactly the same: 2-1 count, nobody on, fastball following a fastball, righty pitcher, righty hitter, similar location, similar speed, similar break. Although the pitches and situations were almost the same, the results were wildly different: sometimes a strike, sometimes a ball, sometimes a home run, sometimes an out, sometimes a double.

The idea is similar to DIPS, which posits that what happens after a batter puts the ball in play is mostly out of the control of the pitcher. Nick is saying that, outside of the actual characteristics of the pitch, what happens to a it is also out of the pitcher's control. All the pitcher can do is put the ball in a certain place at a certain speed with a certain movement, and then it's up to the batter and umpire and random chance.

So, suppose a certain pitch in a certain spot on a certain count usually results in 0.1 runs more than average. If a pitcher threw 50 of those, and it turned out the batters hit them hard, which resulted in 10 runs instead of 5, you could assume those extra five runs were random, and not the pitcher's "fault". That would allow you to better project his performance in future years -- as a GM, you might be able to find some underpriced pitchers, and trade away your overvalued ones. Just like a "DIPS ERA," which evaluates a pitcher based on factors other than his balls in play, you could create a "PitchF/X ERA" which evaluates a pitcher based only on the qualities of the pitches he threw, rather than what happened to them.

To do that, I think more work needs to be done. There probably aren't enough samples in each "bin" to get you good estimates of the value of a specific pitch. You might have to somehow smooth out the data, so you can extrapolate as to how much a 95 mph pitch is worth compared to a 93 mph pitch (Nick found the slower pitch actually led to better results for the pitcher, which is probably just a statistical anomaly you'd want to fix). You'd also have to think about other things that this analysis doesn't consider: patterns of pitch selection, tipping off pitches, understanding batters' weaknesses, and so on.

But even without those caveats, I think this is something that could work, with enough reliable data.

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What I find interesting about all this stuff is that it further formalizes the idea that most of what happens in a baseball game is luck. There is a tendency to treat a player's accomplishments as a direct manifestation of his skill, even in small sample sizes where it probably isn't. When Albert Pujols hits a home run, there's tendency to talk about how it was the pitcher's fault for giving him that pitch to hit, or why Pujols was able to recognize it and hit it out. Reality is probably different. I'd bet that a lot of Pujols home runs came on "good" pitches, in the sense that their expectation was zero or positive, but Pujols just happened to get good wood on them. And I bet you'd find more than the occasional weak ground ball on what was actually a juicy pitch to hit.

Because Pujols is random too. Given a certain pitch on a certain count in a certain place with a certain amount of break, Pujols is sometimes going to hit it out, sometimes he'll swing and miss, sometimes he'll ground out, and so on. It's all a matter of the probabilities coming together, like the dice rolls in an APBA game.

In "The Physics of Baseball," Robert Adair reports that the difference between hitting the ball to center field and hitting the ball foul is 1/100 of a second. No batter is so good that he can always time his swing to .01 seconds. Some batters may be closer to that than others: maybe one batter has an SD of 1/100 of a second, so that he hits the ball fair 2/3 of the time, and another has an SD of 2/100 of a second, so that he hits the ball fair only 38% of the time. Talent and practice and concentration can lower a player's SD, but not to zero. There's still a lot of luck involved even for Albert Pujols. Over a season, the luck will even out and he'll hit over .300, but in any given game, he could easily go 0-for-4, without there being anything wrong with his talent on that day.

The luck isn't just because hitting a baseball is hard. Think about foul shooting in basketball. Even the best players don't shoot free throws with much more than 90% accuracy. And free throws are shot under the exact same circumstances every time, with no opposition trying to stop you. Foul shooting is something every NBA player has been doing since childhood, over and over and over, and they still can't get much better than 9 times out of 10. Why is that? It's probably the same thing as hitting a baseball: you have to do a lot of things right, with your eyes and arms and hands, and if you're more than a certain bit off, the ball won't go. And humans just aren't biologically built to be perfect enough that we can be within those very narrow limits every time. If the trajectory of a successful shot has to be within 0.1 degree of perfect (I'm making these numbers up), and our bodies are good enough only to give us a standard deviation of 0.06 degrees, even after practicing for 15 years, then no matter what, we're still going to be missing 10% of shots. That's just the way it is.

As a player, your goal can't be to make 100% of your shots. I think that's impossible, based on the limitations of the human brain and body. What you *can* do is practice enough, and the right way, that you reduce your slight errors, your standard deviation from the "ideal" shot, as much as possible. You can also work to make sure that you're always at your best. If you're normally a 90% shooter, but in clutch situations your hands shake and you hit only 80% -- well, getting your clutch performance from 80 to the 90 percent you're capable of will be a lot easier, I think, than raising your non-clutch 90 percent to 91 percent.

But no matter what, whether you're a pitcher, batter, basketball player, goalie, or whatever -- there is a limit to how perfect or predictable you can get. The best you can do is to work hard enough that your practice and talent gives you the best possible APBA card you can get. After that, you're at the mercy of the dice rolls.



Glove slap: Tango

Can steroids increase HRs by 50%? (Update)

This is a follow-up to my previous post on the Tobin steroids paper. Thanks to Joe P. and John Matthew for letting me know that R. G. Tobin's steroids paper is now available online, at Alan Nathan's site, here.

Tobin starts by quoting a study that found that weightlifters given steroids showed a 9.3% increase in muscle mass (compared to 2.7% for non-users following the same training regimen). He therefore assumes a steroid-induced 10% increase in muscle mass. This corresponds to a 10% increase in *cross-sectional* muscle mass (I presume this is because muscles don't grow in length, just width). It is "well established" that a 10% increase in cross-sectional mass leads to a 10% increase in the force the muscles can exert. A 10% increase in force means a 10% increase in energy. And a 10% increase in energy leads to a 5% increase in bat speed (Tobin doesn't say, but I assume this is because energy is proportional to the square of velocity).

Then, after making some assumptions about the physics of the collision and the ball's travel, Tobin calculates that after a 5% increase in bat speed, the percentage of home runs per ball in play would increase from 10% to 16.6%, a 66% increase.

All this seems perfectly plausible to me, except that I'm not sure it matches the empirical home run data. Tobin shows a historical chart of home runs (as a percentage of balls in play) by top sluggers over the years. There is a significant increase starting in 1995. But Tobin argues that there is a significant *decrease* starting in 2003, the year MLB steroid testing was introduced. And, yes, there is a drop between 2002 and 2003, but an increase in the following years, so that 2005 is the fifth highest ever (and one of the top four is 1961!). So it would seem there's something happening other than steroids – and if steroids have indeed increased users' HR rates by 50%, we should have expected to see a much larger drop.

My feeling is that there must be other reasons than steroids -- or at least *additional* reasons -- for the recent power increase. Tobin argues against that:

"Such dramatic changes in performance over a short period of time are rare in well-established sports."

I'm not so sure that's true. NHL offense was at its highest level ever in the early 1980s, but close to its lowest ever only 15 years later. Fifty-goal scorers were rare until about the mid-1960s, when suddenly they became commonplace. I don't know enough about other sports, but I'd bet that there were similar changes in football and basketball, too.

Tobin notes, correctly, that a small change in the distance a ball travels can lead to a large change in the number of home runs hit. But even if the change resulted from something other than steroids, players would notice the change, and hit more fly balls in order to take advantage. (Power-hitting players would also become more valuable, and therefore there would be more of them signed to contracts – but since Tobin concentrates mostly on the leagues' top sluggers, this doesn't affect his conclusions.) So if physics suggested a 50% increase in home runs, you'd expect empirical results to be even higher: maybe, say 75% higher, 50% from physics, multiplied by another 17% increase from players trying to hit more fly balls than usual.

I guess my bottom line is that I'm willing to accept that 10% more muscle mass means 50% more home runs. But I'm skeptical that we're actually seeing the effects of a 50% increase. If we're not, that means that players on steroids are gaining less than 10% muscle mass.

An alternative is that *some* players are gaining 50% more home runs, but not *all* of the top sluggers. But, in that case, where are those other top sluggers getting their power? It must be from something other than steroids.

Finally, Tobin gives a little bit of attention to pitching. Just as a 10% increase in muscle leads to 5% more bat speed, it would also lead to 5% more velocity on the pitch. That correlates to an ERA improvement of 0.5 runs per game. As Tobin points out, that's not much compared to the effect on home runs. But it's still huge from a baseball standpoint. You'd expect extra velocity to lead to an increase in strikeouts (given that the range of ability in terms of DIPS is small). And that's what we've seen in recent years. But, again, couldn't the change have also been caused by other factors?

So this study points out that steroids can increase performance substantially. And, recently, we have indeed seen substantial performance increases. But does that mean that steroids caused them? The empirical record fails to convince me.

Can steroids increase HRs by 50%?

This press release from Tufts University promotes a forthcoming paper from a physicist that claims that steroids can increase the frequency of home runs by 50 percent.

"A change of only a few percent in the average speed of the batted ball, which can reasonably be expected from steroid use, is enough to increase home run production by at least 50 percent," [Roger Tobin] says.

My impression is that there are two parts to the paper: first, figuring out how much bat speed steroids can add; and, second, figuring out how those extra miles per hour can increase home run levels.

But 50% sounds like an overestimate. If the number were that high, wouldn't we have seen a very substantial drop in home run rates (if only among certain players) once MLB started steroid tests? Or maybe we have, and I didn't notice.

And maybe there are more qualifications in the actual paper than in the press release. We'll have to wait for the paper, I guess.

(Thanks to John Matthew for the link.)