Explaining Away Regression To The Mean
Odds are you’ve read a story lately about how Russell Branyan is struggling as he reaches the summer of his first season as a full-time player. After a monstrous first half, he’s not hitting as well lately, and the explanations are pouring in. He’s tired. His back hurts. Pitchers are figuring him out. Managers have figured out how to shift against him and he hasn’t adjusted. If you’re looking for a reason for Branyan’s struggles, you have a buffet of choices to blame them on.
Of course, there’s a simpler explanation – it’s just natural regression to the mean.
In April, Branyan posted a .405 batting average on balls in play. In May, it was .391. These are outrageously high totals that nobody in history has been able to sustain, much less a first baseman whose hardest hit balls end up in the seats. There was basically no chance that he’d be able to continue getting balls in play to find a hole 39% of the time. We talked about this quite a bit, warning that regression was coming. A guy who strikes out as much as Branyan does can’t hit .300. It’s almost impossible.
Indeed, regression did come. In June, his BABIP was a more normal .286, right around where we’d expect Branyan’s true talent level to be, based on his skillset. His monthly line was still a good .265/.376/.590, but the batting average didn’t get inflated by balls avoiding gloves in record numbers. July, though, has been uglier – .180/.288/.426, giving rise to all the various theories for the cause of the slump.
Branyan’s BABIP in July? .200. His other, more stable numbers?
13.6% BB% in July, 12.8% BB% for the season
33% K% in July, 28.5% K% for the season
.246 ISO in July, .292 ISO for the season
His walks and strikeouts are barely up and his power is very slightly down. Over 70 plate appearances, we’re talking about basically no difference at all. And, the extra strikeouts are actually just due to some coin flip calls by the home plate ump – his contact rate (69% in July) is higher than it was April-June (67%). There’s literally nothing to worry about here – Branyan’s slump is just normal BABIP variation. He got some good bounces in April and May and he’s got some bad bounces in July. He’s the exact same player he was, and reacting to the results will simply lead to making a bad assumption about what’s going on.
But this happens all the time. Not just with Branyan, but across the board. Remember Sean White’s struggles a few weeks ago? The local media decided it was because he was getting tired after being worked too hard for the first few months. White himself said he felt great, and had no problems, but that didn’t matter. He was giving up hits, and that meant he was running on fumes.
Sean White’s BABIP by month: .182, .182, .333 (he’s exhausted!), .125
White drastically overachieved the first two months of the season thanks to some good defense and good luck. The results started to match his talent level in June, and this was blamed on overwork. He’s been lucky again in July, but there’s no reason given to why he’s no longer tired. And remember, White claimed he felt great the entire time.
Players understand how this stuff works. Branyan was asked about why he’s slumping, and his response was basically “This stuff happens. The season is cyclical. Sometimes you run hot, sometimes you run cold.” (paraphrase because I can’t find the actual quote right now)
For whatever reason, though, people just can’t accept that there is not always a primary driving reason for a change in results. That’s why we get stuff like “so and so has changed his batting stance and is now hitting .500 for the last two weeks”, but you never hear about the new stance again after he goes back to hitting .260. Or, from a Mariner-centric point of view, you’ll hear a lot of talk about how the M’s need to keep their pitching rotation strong to keep the bullpen from regressing due to overwork.
Bad news – the bullpen is going to regress either way. Whether the M’s keep Bedard and Washburn or not, there a bunch of relievers on this team with numbers that are unsustainable. The M’s bullpen has an ERA that is 0.69 runs lower than their FIP, and while the defense is a decent chunk of that, there’s a luck component in there too. Sean White and Chris Jakubauskas are running crazy low BABIPs. 1.8% of Aardsma’s fly balls are leaving the park. These numbers are going to regress. They have to.
And when they do, you’re going to hear explanations for why. White will be tired again. Jakubauskas will have lost the command of his fastball. Aardsma will feeling the pressures of his first pennant race as a closer. We could write the stories right now. But, in the end, it’s just going to be simple regression to the mean, just like we saw with Branyan in June. He ran lucky for two months, had a normal Branyan month, and now is running unlucky. It doesn’t mean anything.
The sooner that we can get the world to embrace the concept of random variance, the better. Results fluctuate wildly in small samples due to uncontrollable factors. That’s just a fact of life, and when we’re forming our opinions, we need to realize just how powerful regression really is.
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63 Responses to “Explaining Away Regression To The Mean”
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Where I have a tough time with regression to the mean is when it is applied to an entire team.
For example: let us assume that the M’s have the talent of a .500 club. However, they start the season off with a 10 game win streak. Is it expected that over the course of an entire season they will regress and have enough losses that they end up at .500 or are those 10 games “in the bank” and it is expected that from that time forward they are a .500 club and thus will finish up at 10 games over .500?
Is that trying to use regression to the mean as a predictor of future success, which it shouldn’t be used for?
We’ve discussed this like a million times already. It’s the second. And no.
Regression to the mean doesn’t know anything about history. What happened in the past doesn’t matter.
If a .500 team wins their first 10 games of the season, but your opinion of their true talent level doesn’t change, then you now expect them to go 76-76 the rest of the way, and finish with an 86-76 record.
You do not expect them to go 71-81 so that they finish back at .500. That would be regression past the mean. It’s a logical fallacy.
Have you guys seen any research examining differences in the standard deviation of baseball stats? I think I’ve read before that speedy baseball players tend to have higher career BABIP numbers than others.
Have you seen any examination of the skillset that might result in a more consistent (lower SD) result? It seems that would be a desirable item to examine, although I’d guess we simply do not have the data to come to a reasonable conclusion.
Regression to the mean may not be the explanation for a lower BABIP if an infield shift is going to permanently lower that number.
We then may be talking about an entirely different kind of regression. But still out of Branyan’s control (or is it?) and eliminating the “he’s tired” argument.
As for the bullpen’s eventual regression, I still see that as an argument for having a strong rotation to give the bullpen fewer innings with which to regress and lose games with its true talent level.
Almost nothing in the universe is actually random (speaking with a ridiculous amount of background in mathematics and physics). There is always a reason governed by the laws of the universe. The problem is that at times it is impossible to determine the real “why” because (sometimes) we don’t have the technology and other times because there is too much “noise” to make an accurate determination as to what is truly causing something. So it’s a matter of us through time and experimentation, weeding out the noise from the variables that actually matter.
A case in point in something we use every day, a computer. Pretty much all languages have a “random” number generator (and most programs use a “random” number somewhere). However, in every single case this “random” number generator is completley deterministic. It’s impossible on anything but a quantum computer (which for now is impossible to make) to actually generate a random number. However, the mathematical functions developed to produce these “random” numbers are such that they make a nice scatter plot on a chart given various inputs (usually the time). So the results appear very random, but in fact are deterministic, same input = same output. But, good luck trying to find the “why” (the function that governs the input/output pairs). If it’s a good mathematical model, it will be impossible with current technology to figure out. (note: not all are good; many in fact are not. The C language, for instance, is crap and it’s very easy to determine their “random” number generator function).
This was just a simple example with computers, but this type of thing is reflected in nature all over the place. Almost nothing is random (and I only say “almost” instead of just “nothing” because of various things in quantum mechanics that we don’t yet fully understand). But these types of things don’t show up in baseball, so nothing in baseball is random. There is always a reason. It’s just that the reasons are often much to complicated for us to be able to tell. Most baseball “experts” then will say “it was because he changed his stance”, even though that has nothing to do with the actual reason. Often the actual reason might be that he happened to hit the ball 1/8th of an inch higher on the barrel and it allowed the ball to hang up just enough for the outfielder to catch it or “random” things like this that players have almost zero control over. Which of course in turn gives rise to us calling it “random” for all practical purposes. But in the end there is a always a reason, even if it’s not within our grasp to see in every case.
I would think the shift would decrease BABIP only if the batter doesn’t adjust to it.
If the batter adjusts to it by going the other way some of the time, he should be able to increase his BABIP at the expense of his power. Which would seem to be one of the purposes of the shift — to invite the batter to make an adjustment that will decrease his likelihood of hitting a home run.
It would be interesting to look at Branyan’s hit distribution over the course of the season to see if he’s going the other way any more than he was earlier in the season. That would be an indication that he’s adjusting to the shift.
In my limited observation, I’ve seen Branyan lose several hits to the short right fielder but I’ve only seen him go the other way once. To his credit, Griffey did poke a ground ball through the vacant shortstop hole the other night against the shift for an RBI.
Given the relative skillsets of Branyan and Griffey at this point in their respective careers, it might make more sense for Griffey to adjust to the shift that way while Branyan should keep doing what he is doing, even if he loses some singles.
wow bilbo27, that’s deep.
However, in the context of baseball performance and what baseball players can reasonably control, I think we can call certain variances random.
When you put randomness (or the lack thereof) in those mathematical terms you are taking them out of human context (as we are not god-like creatures who are going to understand all the universal forces that lead to “non random” events). Language that occurs between humans carries lots of implications. So, for sake of argument with other humans, let’s just imply that events are perceivably random when we use the word “random”.
Which you already said. I’m an idiot for writing that last post. 🙂
Some nice explanations of regression to the mean and randomness here. A decent book for further reading (non-technical, no statistics background required) is Nassim Taleb’s “Fooled By Randomness”, which goes over these and the many other ways in which people in everday life mis-use or mis-perceive probability and statistics. He’s become more famous for his “Black Swan” book, which is also good but gets a little more into grand metaphysical speculation (almost inevitable, since that book is about major events which cannot be predicted).
Almost nothing in the universe is actually random (speaking with a ridiculous amount of background in mathematics and physics). There is always a reason governed by the laws of the universe.
You’re discounting quantum physics? Because (as I understand most of it) there is a huge element of randomness and pure probability in the universe. I’m not criticizing, my degree is in biochem and I can’t help but believe that the clockwork theory wasn’t invalidated by Heisenberg…he just stated that we aren’t ever going to be able to read the clock without blindly feeling the hands. I personally subscribe to the modified clockwork theory many above have described.
I find it strange that people can’t understand randomness. Almost everyone has played a sport, or a game, or a video game, or tossed rocks at a stump. I know you want to justify running three racks in pool, or winning five times in a row when you had 60/40 hand odds, or whatever. But when you accept random it really does help once you come back down.
And I did see the commentary below about quantum physics, but the way it’s being treated now seems to lead to randomness on a much larger scale than electrons just deciding to appear on the other side of the galaxy.