From "Hey, Bill".
Since hitting a baseball requires such coordination of many moving body parts, and it is easy for a piece (and therefore the whole mechanism) to get out of whack, do you think the clusters of hits we take to be hot streaks are just the player executing at a maximum level?
--johnkzufall
Yeah, that’s actually a good argument in the way you stated it, and there is a kernel of truth in it. I relate this to a sport which is more at my athletic level, which is pool. I have a pool table in my basement, and I run the table several times a day, and count how many shots it takes me to knock down 15 balls. Sometimes, once in a while, it is 15 shots—I have done it in as few as 11—and sometimes it takes 40 shots. Or even more.
I am 100% certain that not ALL of this variance is random. I am 100% certain that I fall into unproductive habits, as I am playing, that make me less effective—three of them specifically. I start "sawing" the stroke, pushing the back end of the cue down instead of sending it straight forward into the cue ball. I start "jerking" the shots, rather than shooting smoothly. There are some shots for which it is the best approach to flick the cue quickly forward and then jerk it quickly back, but that’s about 15% of the shots, and I find myself doing it repeatedly when it is not appropriate. Third, I start rushing from shot to shot without taking the time to think through, before each shot, how I want to approach the shot, how I want to spin the ball, where I want to leave the cue ball to set up the following shot, etc. I know that I do these three things (and have some lesser included offenses); I have known it for years, but I still fall into these bad habits, and find myself missing shots.
Shouldn’t I believe, then, that baseball players fall into similar bad habits from swing to swing, and that this makes them less effective sometimes than at other times?
Yes, I should believe that, and I do believe it. I also believe, for what it is worth, that a batter’s level of effectiveness can vary, to an extent, because of "petty confidence", petty confidence being the transient, unreliable type of confidence that may be here today and totally gone by Sunday. I don’t question but that these are real variables, and also, players are often playing with manageable injuries that don’t prevent them from competing, but may prevent them from performing at the level at which they might otherwise reach. I don’t doubt that there are additional performance variables that I have not mentioned, but which some master of the obvious will find it necessary to point out to us.
At the same time, there is also the tendency of hits (and all other performance elements), to form random clusters, so then the performance variation has both real and artificial elements. The question is, to what extent, in watching the games, are we seeing what is real, and to what extent are we seeing an illusion created by random clusters?
Suppose that you take a player’s statistics, and re-organize his at bats at random. . . .or suppose that you take his Start-a-Madic, ASPC or Ethan Allen’s magic spinning wheel game card and recreate a thousand at bats for him. You will find, absolutely and without question, that there is just as much up and down variation in the random performance as in the player’s actual record. This has been studied hundreds of times. There is a very good web site devoted to the issue, the Hot Hand Web Site (http://thehothand.blogspot.com, maintained by Texas Tech professor Alan Reifman.) I don’t want to overstate the study; the Hot Hand phenomenon has been studied hundreds of times by dozens of different researchers, and occasionally, one of us thinks we possibly have found some tiny and elusive difference between the "actual" and simulated data. But for the most part, those studies always show that the variance in the real-life performance is identical to the variance that would be expected if nothing was operating except the normal randomization.
This is not an absolutely convincing argument that nothing is going on here except random variation. It is certainly possible for other effects to mimic the patterns of random variation closely enough that it might be difficult to distinguish between the two, and it is certainly more than possible that might be difficult to distinguish between pure random variation and some mix of random and causal variation. But the question becomes, then, how much causal variation is it reasonable to think might be completely hidden in a mix of causal and random variation?
Well, if it was 50-50, it would be extremely easy for us to distinguish between the patterns in the two sets of data. We know how much random variation can be found in any data set; that’s a pretty basic and easy thing to calculate or at least estimate. If you add a second level of variation equal to the first, it will create obviously non-random patterns.
If it 70-30—in other words, if the causal variation was roughly half the size of the random variation—that, again, would be easy to distinguish from pure random variation. Even if it was 90-10, we should be able to distinguish between that and pure random variation. If it was 99-1, maybe we would have a hard time telling one from the other.
So when you see the variations in performance, what is it that you are seeing? You’re seeing randomness. . ..not pure and absolute randomness, perhaps, but largely randomness. 95% or 99% of what you are seeing is just random variations in performance.
There is another way to approach the issue. How much variation in performance is it reasonable to think might occur due to things like petty confidence and a hitter falling into bad habits?
Well, I don’t know, exactly, but .270 hitters have months in which they hit .400. Marquis Grissom in June of 1994 hit .385 (47 for 122). Johnny Damon in 2000 hit almost .500 for a solid month. It is not reasonable to think that players actually reach that level of performance ability. If a player could become a .400 hitter for a month, somebody would hit .400 every month. Somebody would hit .400 in his career.
Johnny Damon was essentially the same hitter in 2011 that he was in 1996, and every year in between. It is not reasonable to think to that he suddenly, for a few weeks in his career, became something radically and totally different, and then somehow, time after time, returned to exactly what he always had been. He is not a shape shifter. It is much more reasonable to believe that he was the same player or essentially the same player throughout, but that he simply had a cluster of superlative games that made him look different for a short period of time.
We know that the standard deviation of batting average in a season, for players who bat 500 or more times, is 27 points. It is not reasonable to suppose that hitters go from being 3 standard deviations above the norm in one month to 3 standard deviations below the norm the next month. It is even less reasonable to suppose that a hitter flips from standard deviations above to standard deviations below from week to week (in terms of his true underlying ability), but somehow finds himself more or less in the same position time after time, given 600 plate appearances.
Let’s go back to the issue of the variation that occurs in my pool playing from game to game, which might be analogous to the variation that occurs in your golf game if you are one of them golfer types. How long does it take you to fix a glitch in your putting style, given that you have a certain level of ability as a putterer? I do fall into bad habits, as a pool player, and this does cost me a few shots now and then, but I also spot these problems and fix them on a pretty short schedule. 30, 40 shots; I’m going to figure out what I am doing wrong, and get it right.
If we assume that players spot the flaws in their swings and fix them on a similar schedule in terms of the number of swings, what is that going to take? A couple of games, maybe?
Look, Yasiel Puig
a) is not a .400 hitter, and
b) is not temporarily a .400 hitter, either.
He’s a .280 hitter, probably, maybe a little less. He doesn’t temporarily become something other than what he is, just because a string of ground balls scoot through the infield and a bunch of Dodger fans are not strong enough to blow away the smoke. I don’t actually become a good enough pool player to run the table in 15 shots; it’s just something that happens once in a while. Hot streaks and slumps are smoke and mirrors. It’s not that there is nothing there; it is more like random variance is New York City and the actual up and down changes in ability are Immokalee, Florida. When you talk about the people who live in New York City and Immokalee, you’re mostly talking about the Big Apple.