When a team wins the World Series (or even a game), the winning manager is typically forgiven of all his ‘sins.’ His mistakes, large and small, are relegated to the scrap heap marked, “Here lies the sins of our manager and all managers before him, dutifully forgotten or forgiven by elated and grateful fans and media pundits and critics alike.”

But should they be forgotten or forgiven simply because his team won the game or series? I’m not going to answer that. I suppose that’s up to those fans and the media. What I can say is this: As with many things in life that require a decision or a strategy, the outcome in sports rarely has anything to do with the efficacy of that decision. In baseball, when a manager has a choice between, say, strategy A or strategy B, how it turns out in terms of the immediate outcome of the play or that of the game, has virtually nothing to do with which strategy increased or decreased each team’s win expectancy (their theoretical chance of winning the game, or how often they would win the game if it were played from that point forward an infinite number of times).

Of course, regardless of how much information we have or how good our analysis is, we can’t know with pinpoint accuracy what those win expectancies are; however, with a decent analysis and reasonably accurate and reliable information, we can usually do a pretty good job.

It’s important to understand that the absolute magnitude of those win percentages is not what’s important, but their relative values. For example, if we’re going to evaluate the difference between, say, issuing an intentional walk to player A versus allowing him to hit, it doesn’t matter much how accurate our pitcher projections are or even those of the rest of the lineup, other than the batter who may be walked and the following batter or two. It won’t greatly affect the result we’re looking for – the difference in win expectancy between issuing the IBB or not.

The other thing to keep in mind – and this is particularly important – is that if we find that the win expectancy of one alternative is close to that of another, we can’t be even remotely certain that the strategy with the higher win expectancy is the “better one.” In fact, it is a custom of mine that when I find a small difference in WE I call it a toss-up.

The flip side of that is this: When we find a large difference in WE, even with incomplete information and an imperfect model, there is a very good chance that the alternative that our model says has the higher win expectancy does in fact yield a higher win percentage if we had perfect information and a perfect model.

How small is “close” and how big is “a large difference?” There is no cut-off point above which we can say with certainty that, “Strategy A is better,” or below which we have to conclude, “It’s a toss-up.” It’s not a binary thing. Basically the larger the difference, the more confident we are in our estimate (that one decision is “better” than the other from the standpoint of win expectancy). In addition, the larger the difference, the more confident we are that choosing the “wrong strategy” is a big mistake.

To answer the question of specifically what constitutes a toss-up and what magnitude of difference suggests a big mistake (if the wrong strategy is chosen), the only thing I can offer is this: I’ve been doing simulations and analyses of managerial decisions for over 20 years. I’ve looked at pinch hitting, base running, bunting, relievers, starters, IBB’s, you name it. As a very rough rule of thumb, any difference below .5% in win expectancy could be considered a toss-up, although it depends on the exact nature of the decisions – some have more uncertainty than others. From .5% to 1%, I would consider it a moderate difference with some degree of uncertainty. 1-2% I consider fairly large and I’m usually quite certain that the alternative with the larger WE is indeed the better strategy. Anything over 2% is pretty much a no-brainer – strategy A is much better than strategy B and we are 95% or more certain that that is true and that the true difference is large.

With all that in mind, I want to revisit Game 6 of the World Series. In the top of the 5th inning, the Astros were up 1-0 with runners on second and third, one out, and Justin Verlander, arguably their best starting pitcher (although Morton, McCullers and Keuchel are probably not too far behind, if at all) , due to bat. I’m pretty sure that the Astros manager, Hinch, or anyone else for that matter, didn’t even think twice about whether Verlander was going to bat or not. The “reasoning” I suppose was that he’s only pitched 4 innings, was pitching well, and the Astros were already up 1-0.

Of course, reasoning in “words” like that rarely gets you anywhere in terms of making the “right” decision. The question, at least as a starting point, is, “What is the Astros’ win expectancy with Verlander batting versus with a pinch hitter?” You can argue all you want about how much removing Verlander, burning a pinch hitter, using your bullpen in the 5th, and perhaps damaging Verlander’s ego or affecting the morale of the team, affects the outcome of the game and the one after that (if there is a 7th game) and perhaps even the following season; however, that argument can only be responsibly made in the context of how much win expectancy is lost by letting Verlander hit. As it turns out, that’s relatively easy to find out with a simple game simulator.  We know approximately how good or bad of a hitter Verlander is, or at least we can estimate it, and we know the same about a pinch hitter like Gattis, Fisher, or Maybin. It doesn’t even matter how good those estimates are. It’s not going to change the numbers much.

Even without using a simulator, we can get a pretty good idea as to the impact of a pinch hitter in that situation: The run expectancy with a typical hitter at the plate is around 1.39 runs. With an automatic out, the run expectancy decreases to .59 runs, a loss of .78 runs or 7.8% in win expectancy. That’s enormous. Now, Verlander is obviously not an automatic out, although he is apparently not a good hitting pitcher, having spent his entire career in the AL prior to a few months ago. If we assume a loss of only .6 runs, we still get a 6% difference in win expectancy between Verlander and a pinch hitter. These are only very rough estimates however, since translating run expectancy to win expectancy depends on the score and inning. The best thing we can do is to run a game simulator.

I did just that, using the approximate offensive line for a poor hitting pitcher, and that of Evan Gattis as pinch hitter. The difference after simulating 100,000 games for each alternative was 6.6%, not too far off from our basic estimate using run expectancies. This is a gigantic difference. I can’t emphasize how large a difference that is. Decisions such as whether to IBB a batter, bunt, replace a batter or pitcher to get a platoon advantage, remove a starter for a reliever, replace a reliever for a better reliever, etc. typically involve differences in win expectancy of 1% or less. As I said earlier, anything greater than 1% is considered significant and anything above 2% is considered large. 6.6% is almost unheard of. About the only time you’ll encounter that kind of difference is exactly in this situation – a pitcher batting versus a pinch hitter, in a close game with runners on base, and especially with 1 or 2 outs, when the consequences of an out are devastating.

To give you an idea of how large a 6.6% win expectancy advantage is, imagine that your manager decided to remove Mike Trout and Joey Votto, perhaps the two best hitters in baseball, from a lineup and replace them with two of the worst hitters in baseball for game 6 of the World Series. How much do you think that would be worth to the opposing team? Well, that’s worth about 6.6%, the same as letting Verlander hit in that spot rather than a pinch hitter. What would you think of a manager who did that?

Now, as I said, there are probably other countervailing reasons for allowing him to hit. At least I hope there were, for Hinch’s and the Astros’ sake. I’m not here to discuss or debate those though. I’m simply here to tell you that I am quite certain that the difference between strategy A and B was enormous – likely on the order of 6-7%. Could those other considerations argue towards giving up that 6.6% at the moment? Again, I won’t discuss that. I’ll leave that up to you to ponder. I will say this, however: If you think that leaving Verlander in the game for another 2-3 innings or so (he ended up pitching another 2 innings) was worth that 6.6%, it’s likely that you’re sadly mistaken.

Let’s say that Verlander is better than any bullpen alternative (or at least the net result, including the extra pressure on the pen for the rest of game 6 and a potential game 7, was that Verlander was the best choice) by ½ run a game. It’s really difficult to argue that it could be much more than that, and if it were up to me, I’d argue that taking him out doesn’t hurt the Astros’ pitching at all. What is the win impact of ½ run a game, for 2.5 innings? Let’s call the average leverage in the 5th-7th innings 1.5 since it was a close game in the 5th. That comes out to 2.1%. So, if letting Verlander pitch through the middle of the 7th inning on the average was better than an alternative reliever by ½ run a game, the impact of removing Verlander for a pinch hitter would be 4.5% rather than 6.6%. 4.5% is still enormous. It’s worth more than the impact of replacing George Springer with Derek Fisher for an entire game because Springer didn’t say, “Good morning” to you – a lot more. Again, I’ll leave it to you to mull the impact of any other countervailing reasons for not removing Verlander.

Before we go, I want to also quickly address Roberts’ decision to walk Springer and pitch to Bregman after Verlander struck out. There were 2 outs, runners in second and third, and the Astros were still up 1-0. Of course Roberts brought in Morrow to pitch to the right-handed Bregman, although Morrow could have pitched to Springer, also a righty. What was the difference in win expectancies between walking and not walking Springer? That is also easy to simulate, although a basic simulator will undervalue the run and win expectancy when the bases are loaded because it’s difficult to pitch in that situation. In any case, the simulator says that not walking Springer is worth around 1.4% in win expectancy. That is considered a pretty large difference, and thus a pretty significant mistake by Roberts, although it was dwarfed by Hinch’s decision to let Verlander bat. It is interesting that one batter earlier Hinch gratuitously handed Roberts 6.6% in win expectancy and then Roberts’ promptly handed him back 1.4%! At least he returned the generosity!

Now, if you asked Hinch what his reasons were for not pinch hitting for Verlander, regardless of his answer – maybe it was a good one and maybe it wasn’t – you would expect that at the very least he must know what the ‘naked’ cost of that decision was. That’s critical to his decision-making process even if he had other good reasons for keeping Verlander in the game. The overall decision cannot be based on those reasons in isolation. It must be made with the knowledge that he has to “make up” the lost 6.6%. If he doesn’t know that, he’s stabbing in the dark. Did he have some idea as to the lost win expectancy in letting his pitcher bat, and how important and significant a number like 6.6% is? I have no idea. The fact that they won game 7 and “all is forgiven” has nothing to do with this discussion though. That I do know.


Last night in game 4 of the 2017 World Series, the Astros manager, A.J. Hinch, sort of a sabermetric wunderkind, at least as far as managers go (the Astros are one of the more, if not the most, analytically oriented teams), brought in their closer, Ken Giles, to pitch the 9th in a tie game. This is standard operating procedure for the sabemetrically inclined team – bring in your best pitcher in a tie game in the 9th inning or later, especially if you’re the home team, where you’ll never have the opportunity to protect a lead. The reasoning is simple: You want to guarantee that you’ll use your best pitcher in the 9th or later inning, in a high leverage situation (in the 9+ inning of a tie game, the LI is always at least 1.73 to start the inning).

So what’s the problem? Hinch did exactly what he was supposed to do. It is more or less the optimal move, although it depends a bit on the quality of that closer against the batters he’s going to face, as opposed to the alternative (as well as other bullpen considerations). In this case, it was Giles versus, say, Devenski. Let’s look at their (my) normalized (4.00 is average) runs allowed per 9 inning projections:

Devenski: 3.37

That’s a very good reliever. That’s closer quality although not elite closer quality.

Giles: 2.71

That is an elite closer. In fact, I have Giles as the 6th best closer in baseball. The gap between the two pitchers is pretty substantial, .66 runs per 9 innings. For one inning with a leverage index (LI) of 2.0, that translates to a 1.5% win expectancy (WE) advantage for Giles over Devenski. As one-decision “swings” (the difference between the optimal and a sub-optimal move) go, that’s considered huge. Of course, if you are going to use Giles later in the game anyway if you stay with Devenski for another inning or two, if the game goes that long, you get some of that WE back. Not all of it (because he may not get to pitch), but some of it. Anyway, that’s not really the issue I want to discuss.

Why were many of the so-called sabermetric writers (they often know just enough about sabermetrics or mathematical/logical thinking in general to be “dangerous,” although that’s a bit unfair on my part – let’s just say they know enough to be “right” much of the time, but “wrong” some of the time) aghast, or at least critical, of this seemingly correct move?

First, it was due to the result of course, which belies the fact that these are sabermetric writers. The first thing they teach you in sabermetrics 101 is not to be results oriented. For the most part, the results of a decision have virtually no correlation with the “correctness” of the decision itself. Sure, some of them will claim that they thought or even publicly said beforehand that it was the wrong move, and some of them are not lying – but it doesn’t really matter. That’s only one reason why lots of people were complaining of this move – maybe even the secondary reason (or not the reason at all), especially for the saber-writers.

The primary reason (again, at least stated – I’m 100% certain that the result strongly influenced nearly all of the detractors) was that these naysayers had little or no confidence in Giles going into this game. He must have had a bad season, right, despite my stellar projection? After all, good projection systems use 3, 4 or more years of data along with a healthy dose of regression, especially with relievers who never have a large sample size of innings pitched or batters faced. Occasionally you can have a great projection for a player who had a mediocre or poor season, and that projection will be just as reliable as any other (because the projection model accurately includes the current season, but doesn’t give it as much weight as nearly all fans and media do). So what were Giles’ 2017 numbers?

Only a 2.30 ERA and 2.39 FIP in a league where the average ERA was 4.37! His career ERA and FIP are 2.43 and 2.25, and he throws 98 mph. He’s a great pitcher. One of the best. There’s little doubt that’s true. But….

He’s thrown terribly thus far in the post-season. That is, his results have been poor. In 7.2 IP his ERA is 11.74. Of course he’s also struck out 10 and has a BABIP of .409. But he “looked terrible” these naysayers keep saying. Well, no shit. When you give up 10 runs in 7.2 innings on the biggest stage in sports, you’re pretty much going to “look bad.” Is there any indication, other than having poor results, that there’s “something wrong with Giles?” Given that his velocity is fine (97.9 so far) and that Hinch saw fit to remove Devenski who was “pitching well” and insert Giles in a critical situation, I think we can say with some certainty that there is no indication that anything is wrong with him. In fact, the data, such as his 12 K/9 rate, normal velocity, and an “unlucky” .409 BABIP, all suggest that there is nothing “wrong with him.” But honestly, I’m not here to discuss that kind of thing. I think it’s a futile and silly discussion. I’ve written many times how the notion that you can just tell (or that a manager can tell – which is not the case here, since Hinch was the one who decided to use him!) when a player is hot or cold by observing him is one of the more silly myths in sports, at least in baseball, and I have reams of data-driven evidence to support that assertion.

What I’m interested in discussing right now, is, “What do the data say?” How do we expect a reliever to pitch after 6 or 7 innings or appearances in which he’s gotten shelled? It doesn’t have to be 7 IP of course, but for research like this, it doesn’t matter. Whatever you find in 7 IP you’re going to find in 5 IP or in 12 IP, assuming you have large enough sample sizes and you don’t get really unlucky with a Type I or II error. The same goes for what constitutes getting shelled compared to how you perceive or define “getting shelled.” With research like this, it doesn’t matter. Again, you’re going to get the same answer whether you define getting shelled (or pitching brilliantly) by wOBA against, runs allowed, hard hit balls, FIP, etc. It also doesn’t matter what thresholds you set – you’ll also likely get the same answer.

Here’s what I did to answer this question – or at least to shed some light on it. I looked at all relievers over the last 10 years and split them up into three groups, depending on how they pitched in all 6-game sequences. Group I pitched brilliantly over a 6-game span. The criteria I set was a wOBA against less than .175. Group III were pitchers who got hammered over a 6-game stretch, at least as far as wOBA was concerned (of course in large samples you will get equivalent RA for these wOBA). They allowed a wOBA of at least .450.  Group II was all the rest. Here are what the groups looked like:

Group Average wOBA against Equivalent RA9
I .130 Around 0
II .308 Around 3
III .496 Around 10


Then I looked at their very next appearance. Again, I could have looked at their next 2 or 3 appearances but it wouldn’t make any difference (other than increasing the sample size – at the risk of the “hot” or “cold” state wearing off).


Group Average wOBA against wOBA next appearance
I .130 .307
II .308 .312
III .496 .317


While we certainly don’t see a large carryover effect, we do appear to see some effect. The relievers who have been throwing brilliantly continue to pitch 10 points better than the ones who have been getting hammered. 10 points in wOBA is equivalent to about .3 runs per 9 innings, so that would make a pitcher like Giles closer to Devenski, but still not quite there. But wait! Are these groups of pitchers of the same quality? No. The ones who were pitching brilliantly belong to a much better pool of pitchers than the ones who were getting hammered. Much better. This should not be surprising. I already assumed that when doing the research. How much better? Let’s look at their seasonal numbers (those will be a little biased because we already established that these groups pitched brilliantly or terribly for some period of time in the same season).

Group Average wOBA against wOBA next appearance Season wOBA
I .130 .307 .295
II .308 .312 .313
III .496 .317 .330


As you can see our brilliant pitchers are much better than our terrible ones. Even if we were able to back out the bias (say, by looking at last year’s wOBA), we still get .305 for the brilliant relievers and .315 for the hammered ones, based on the previous season’s numbers. In fact, we’ll use those instead.

Group Average wOBA against wOBA next appearance Prior season wOBA
I .130 .307 .305
II .308 .312 .314
III .496 .317 .315


Now that’s brilliant. We do have some sample error. The number of PA in the “next appearance” for group’s I and III are around 40,000 each (SD of wOBA = 2 points). However, look at the “expected” wOBA against, which is essentially the pitcher talent (Giles’ and Devenski’s projections) compared to their actual. They are almost identical. Regardless of how a reliever has pitched in his last 6 appearances, he pitches exactly as his normal projection would suggest on that 7th appearance. The last 6 IP has virtually no predictive value even at the extremes. I don’t want to hear, “Well he really (really, really) been getting hammered – what about that big shot?”.  Allowing a .496 wOBA is getting really, really, really hammered, and .130 is throwing almost no-hit baseball, so we’ve already looked at the extremes!

So, as you can clearly see, and exactly what you should have expected, if you really knew about sabermetrics (unlike some of these so-called saber-oriented writers and pundits who like to cherry pick the sabermetric principles that suit their narratives and biases), is that 7 IP of pitching compared to 150 or more, is almost worthless information. The data don’t lie.

But you just know that something is wrong with Giles, right? You can just tell. You are absolutely certain that he’ll continue to pitch badly. You just knew that he was going to implode again last night (and you haven’t been wrong about that 90% of the time in your previous feelings). It’s all bullshit folks. But if it makes you feel smart or happy, it’s fine by me. I have nothing invested in all of this. I’m just trying to find the truth. It’s the nature of my personality. That makes me happy.

There’s an article up on Fangraphs by Eno Saris that talks about whether the pitch to Justin Turner in the bottom of the 9th inning in Game 2 of the 2017 NLCS was the “wrong” pitch to throw in that count (1-0) and situation (tie game, runners on 1 and 2, 2 outs) given Turner’s proclivities at that count. I won’t go into the details of the article – you can read it yourself – but I do want to talk about what it means or doesn’t mean to criticize a pitcher’s pitch selection – on one particular pitch, and how pitch selection even works, in general.

Let’s start with this – the basic tenet of pitching and pitch selection: Every single situation calls for a pitch frequency matrix. One pitch is chosen randomly from that matrix according to the “correct” frequencies. The “correct” frequencies are those which result in the exact same “result” (where result is measured by the win expectancy impact of all the possible outcomes combined).

Now, obviously, most pitchers “think” they’re choosing one specific pitch for some specific reason, but in reality since the batter doesn’t know the pitcher’s reasoning, it is essentially a random selection as far as he is concerned. For example, a pitcher throws an inside fastball to go 0-1 on the batter. He might think to himself, “OK, I just threw the inside fastball so I’ll throw a low and away off-speed to give him a ‘different look.’ But wait, he might be expecting that. I’ll double up with the fastball! Nah, he’s a pretty good fastball hitter. I’ll throw the off-speed! But I really don’t want to hang one on an 0-1 count. I’m not feeling that confident in my curve ball yet. OK, I’ll throw the fastball, but I’ll throw it low and away. He’ll probably think it’s an off-speed and lay off of it and I’ll get a called strike, or he’ll be late if he swings.”

As you can imagine, there are an infinite number of permutations of ‘reasoning’ that a pitcher can use to make his selection. The backdrop to his thinking is that he knows what tends to be effective at 0-1 counts in that situation (score, inning, runners, outs, etc.) given his repertoire, and he knows the batter’s strengths and weaknesses. The result is a roughly game theory optimal (GTO) approach which cannot be exploited by the batter and is maximally effective against a batter who is thinking roughly GTO too.

The optimal pitch selection frequency matrix is dependent on the pitcher, the batter, the count and the game situation. In that situation with Lackey on the mound and Turner at the plate, it might be something like 50% 4-seam, 20% sinker, 20% slider, and 10% cutter. The numbers are irrelevant. Then a random pitch is selected according to those frequencies, where, for example, the 4-seamer is chosen twice as often as the sinker and slider, the sinker and slider twice as often as the cutter, etc.

Obviously doing that even close to accurately is impossible, but that’s essentially what happens and what is supposed to happen. Miraculously, pitchers and catchers do a pretty good job (really you just have to have a pretty good idea as to what pitches to throw, adjusted a little for the batter). At least I presume they do. It is likely that some pitchers and batters are better than others at employing these GTO strategies as well as exploiting opponents who don’t.

The more a batter likes (or dislikes) a certain pitch (in that count or overall), the less that pitch will be thrown. In order to understand why, you must understand that the result of a pitch is directly proportional to the frequency at which it is thrown in a particular situation. For example, if Taylor is particularly good against a sinker in that situation or in general, it might be thrown 10% rather than 20% of the time. The same is true for locations of course, which makes everything quite complex.

Remember that you cannot tell what types and locations of pitches a batter likes or dislikes in a certain count and game situation from his results! This is a very important concept to understand. The results of every pitch type and location in each count, game situation, and versus each pitcher (you would have to do a “delta method” to figure this) are and should be exactly the same! Any differences you see are noise – random differences (or the result of wholesale exploitative play or externalities as I explain below). We can easily prove this with an example.

Imagine that in all 1-0 counts, early in a game with no runners on base and 0 outs (we’re just choosing a ‘particular situation’ – which situation doesn’t matter), we see that Turner gets a FB 80% of the time and a slider 20% of the time (again, the actual numbers are irrelevant). And we see that Turner’s results (we have to add up the run or win value of all the results – strike, ball, batted ball out, single, double, etc.) are much better against those 80% FB than the 20% SL. Can we conclude that Turner is better against the FB in that situation?

No! Why is that? Because if we did, we would HAVE TO also conclude that the pitchers were throwing him too many FB, right? They would then reduce the frequency of the fastball. Why throw a certain pitch 80% of the time (or at all, for that matter) when you know that another pitch is better?

You would obviously throw it less often than 80% of the time. How much less? Well, say you throw it 79% and the slider 21%. You must be better off with that ratio (rather than 80/20) since the slider is the better pitch, as we just said for this thought exercise. Now what if the FB still yields better results for Turner (and it’s not just noise – he’s still better versus the FB when he knows it’s coming 79% of the time)? Well, again obviously, you should throw the FB even less often and the slider more often.

Where does this end? Every time we decrease the frequency of the FB, the batter gets worse at it since it’s more of a surprise. Remember the relationship between the frequency of a pitch and its effectiveness. At the same time, he gets better and better at the slider since we throw it more and more frequently. It ends at the point in which the results of both pitches are exactly equal. It HAS to. If it “ends” anywhere else, the pitcher will continue to make adjustments until an equilibrium point is reached. This is called a Nash equilibrium in game theory parlance, at which point the batter can look for either pitch (or any pitch if the GTO mixed strategy includes more than two pitches) and it won’t make any difference in terms of the results. (If the batter doesn’t employ his own GTO strategy, then the pitcher can exploit him by throwing one particular pitch – in which case he then becomes exploitable, which is why it behooves both players to always employ a GTO strategy or risk being exploited.) As neutral observers, unless we see evidence otherwise, we must assume that all actors (batters and pitchers) are indeed using a roughly GTO strategy and that we are always in equilibrium. Whether they are or they aren’t, to whatever degree and in whichever situations, it certainly is instructive for us and for them to understand these concepts.

Assuming an equilibrium, this is what you MUST understand: Any differences you see in either a batter’s results across different pitches, or as a pitcher’s, MUST be noise – an artifact of random chance. Keep in mind that it’s only true for each subset of identical circumstances – the same opponent, count, and game situation (even umpire, weather, park, etc.). If you look at the results across all situations you will see legitimate differences across pitch types. That’s because they are thrown with different frequencies in different situations. For example, you will likely see better results for a pitcher with his secondary pitches overall simply because he throws them more frequently in pitcher’s counts (although this is somewhat offset by the fact that he throws them more often against better batters).

Is it possible that there are some externalities that throws this Nash equilibrium out of whack? Sure. Perhaps a pitcher must throw more FB than off-speed in order to prevent injury. That might cause his numbers for the FB to be slightly worse than for other pitches. Or the slider may be particularly risky, injury-wise, such that pitchers throw it less than GTO (game theory optimally) which results in a result better (from the pitcher’s standpoint) than the other pitches.

Any other deviations you see among pitch types and locations, by definition, must be random noise, or, perhaps exploitative strategies by either batters or pitchers (one is making a mistake and the other is capitalizing on it). It would be difficult to distinguish the two without some statistical analysis of large samples of pitches (and then we would still only have limited certainty with respect to our conclusions).

So, given all that is true, which it is (more or less), how can we criticize a particular pitch that a pitcher throws in one particular situation? We can’t. We can’t say that one pitch is “wrong” and one pitch is “right” in ANY particular situation. That’s impossible to do. We cannot evaluate the “correctness” of a single pitch. Maybe the pitch that we observe is the one that is only supposed to be thrown 5 or 10% of the time, and the pitcher knew that (and the batter was presumably surprised by it whether he hit it well or not)! The only way to evaluate a pitcher’s pitch selection strategy is by knowing the frequency at which he throws his various pitches against the various batters in the various counts and game situations. And that requires an enormous sample size of course.

There is an exception.

The one time we can say that a particular pitch is “wrong” is when that pitch is not part of the correct frequency matrix at all – i.e., the GTO solution says that it should never be thrown. That rarely occurs. About the only time that occurs is on 3-0 counts where a fastball might be the only pitch thrown (for example, 3-0 count with a 5 run lead, or even a 3-1 or 2-0 count with any big lead, late in the game – or a 3-0 count on an opposing pitcher who is taking 100% of the time).

Now that being said, let’s say that Lackey is supposed to throw his cutter away only 5% of the time against Turner. If we observe only that one pitch and it is a cutter, Bayes tells is that there is an inference that Lackey was intending to throw that pitch MORE than 5% of the time and we can indeed say with some small level of certainty that he “threw the wrong pitch.” We don’t really mean he “threw the wrong pitch.” We mean that we think (with some low degree of certainty) he had the wrong frequency matrix in his head to some significant degree (maybe he intended to throw that pitch 10% or 20% rather than 5%).*

So, the next time you hear anyone say what a pitcher should be throwing on any particular pitch or that the pitch he threw was “right” or “wrong,” it’s a good bet that he doesn’t really know what he’s talking about, even if they are or were a successful major league pitcher.

* Technically, we can only say something like, “We are 10% sure he was thinking 5%, 12% sure he was thinking 7%, 13% sure he was thinking 8%, etc.” – numbers for illustration purposes only.

It’s quite simple actually.

Apropos to the myriad articles and discussions about the run scoring and HR surge starting in late 2015 and continuing through 2017 to date, I want to go over what can cause league run scoring to increase or decrease from one year to the next:

  1. Changes in equipment, such as the ball or bat.
  2. Changes to the strike zone, either the overall size or the shape.
  3. Rule changes.
  4. Changes in batter strength, conditioning, etc.
  5. Changes in batter or pitcher approaches.
  6. Random variation.
  7. Weather and park changes.
  8. Natural variation in player talent.

I’m going to focus on the last one, variation in player talent from year to year. How does the league “replenish” it’s talent from one year to the next? Poorer players get less playing time, including those who get no playing time at all (retired, injured, or switch to another league). Better players get more playing time and new players enter the league. Much of that is because of the aging curve. Younger players generally get better and thus amass more playing time and older players get worse, playing less – eventually retiring or released.  All these moves can lead to each league having a little more or less overall talent and run scoring than in the previous year. How can we measure that change in talent/scoring?

One good method is to look at how a player’s league normalized stats change from year X to year X+1. First we have to establish a base line. To do that, we track the average change in some league normalized stat like Linear Weights, RC+ or wOBA+ over many years. It is best to confine it to players in a narrow age range, like 25 to 29, so that we minimize the problem of average league age being different from one year to the next, and thus the amount of decline with age also being different.

We’ll start with batting. The stat I’m using is linear weights, which is generally zeroed out at the league level. In other words, the average player in each league, NL and AL separately, has a linear weights of exactly zero. If we look at the average change from 2000 to 2017 for all batters from 25 to 29 years old, we get -.12 runs per team per game in the NL and -.10 in the AL. That means that either these players decline with age and/or every year the quality of the league’s batting gets better. We’ll assume that most of that -.12 runs is due to aging (and that peak age is close to 25 or 26, which it probably is in the modern era), but it doesn’t matter for our purposes.

So, for example, if in year X to X+1 in the NL, all batters age 25-29 lost -.2 runs per game per team, what would that tell us? It would tell us that league batting in year X+1 was better than in year X by .1 runs per team per game. Why is that? If players should lose only -.1 runs but they lost -.2 runs, and thus they look worse than they should relative to the league as a whole, that means that the league got better.

Keep in mind that the quality of the pitching has no effect on this method. Whether the overall pitching talent changes from year 1 to year 2 has no bearing on these calculations. Nor do changes in parks, differences in weather, or any other variable that might change from year to year and affect run scoring and raw offensive stats. We’re using linear weights, which is always relative to other batters in the league. The sum of everyone’s offensive linear weights in any given year and league is always zero.

Using this method, here is the change in batting talent from year to year, in the NL and AL, from 2000 to 2017. Plus means the league got better in batting talent. Minus means it got worse. In other words, a plus value means that run scoring should increase, everything else being the same. Notice the decline in offense in both leagues from 2016 to 2017 even though we see increased run scoring. Either pitching got much worse or something else is going on. We’ll see about the pitching.

Table I

Change in batting linear weights, in runs per game per team

Years NL AL
00-01 .09 -.07
01-02 -.12 -.23
02-03 -.15 -.11
03-04 .09 -.11
04-05 -.10 -.14
05-06 .15 .05
06-07 .09 .08
07-08 -.05 .08
08-09 -.13 .08
09-10 .17 -.12
10-11 -.18 .04
11-12 .12 0
12-13 -.03 -.05
13-14 .01 .07
14-15 .06 .09
15-16 .01 .05
16-17 -.03 -.12


Here is the same chart for league pitching. The stat I am using is ERC, or component ERA. Component ERA takes a pitcher’s raw rate stats, singles, doubles, triples, home runs, walks, and outs, per PA, park and defense adjusted, and converts them into a theoretical runs per 9 inning, using a BaseRuns formula. Like linear weights, it is scaled to league average. A plus number means that league pitching got worse, and hence run scoring should go up.

Table II

Change in pitching, in runs per game per team

Years NL AL
00-01 .02 .21
01-02 .03 .00
02-03 -.04 -.23
03-04 .07 .11
04-05 .00 .07
05-06 -.14 -.12
06-07 .10 .06
07-08 -.15 -.10
08-09 -.13 -.17
09-10 .01 .04
10-11 .03 .16
11-12 .03 -.06
12-13 -.02 .26
13-14 -.02 -.04
14-15 .06 -.02
15-16 .03 .04
16-17 .04 -.01


Notice that pitching in the NL got a little worse. Overall, when you combine pitching and batting, the NL has worse talent in 2017 compared to 2016, by .07 runs per team per game. NL teams should score .01 runs per game more than in 2016, again, all other things being equal (they usually are not).

In the AL, while we’ve seen a decrease in batting of -.12 runs per team per game (which is a lot), we’ve also seen a slight increase in pitching talent, .01 runs per game per team. We would expect the AL to score .13 runs per team per game less in 2017 than in 2016, assuming nothing else has changed. The overall talent in the AL, pitching plus batting, decreased by .11 runs.

The gap in talent between the NL and AL, at least with respect to pitching and batting only (not including base running and defense, which can also vary from year to year) has presumably moved in favor of the NL by .04 runs a game per team, despite the AL’s .600 record in inter-league play so far this year compared to .550 last year (one standard deviation of the difference between this year’s and last year’s inter-league w/l record is over .05, so the difference is not even close to being statistically significant – less than one SD).

Let’s complete the analysis by doing the same thing for UZR (defense) and UBR (base running). A plus defensive change means that the defense got worse (thus more runs scored). For base running, plus means better (more runs) and minus means worse.

Table III

Change in defense (UZR), in runs per game per team

Years NL AL
00-01 .01 -.07
01-02 -.01 .05
02-03 .18 -.07
03-04 .10 .03
04-05 .12 .00
05-06 -.08 -.07
06-07 .02 .03
07-08 .04 .01
08-09 -.02 -.02
09-10 -.01 -.02
10-11 .15 -.04
11-12 -.10 -.07
12-13 -.02 .03
13-14 -.10 .03
14-15 -.02 -.02
15-16 -.07 -.05
16-17 -.06 .05


From last year to this year, defense in the NL got better by .06 runs per team per game, signifying a decrease in run scoring. In the AL, the defense appears to have gotten worse, by .05 runs a game. By the way, since 2012, you’ll notice that teams have gotten much better on defense in general, likely due to an increased awareness of the value of defense, and the move away from the slow, defensively-challenged power hitter.

Let’s finish by looking at base running and then we can add everything up.

Table IV

Change in base running (UBR), in runs per game per team

Years NL AL
00-01 -.02 -.01
01-02 -.02 -.01
02-03 -.01 .00
03-04 .00 -.04
04-05 .02 .02
05-06 .00 -.01
06-07 -.01 -.01
07-08 .00 .00
08-09 .02 .02
09-10 -.02 -.02
10-11 .04 -.01
11-12 .00 -.02
12-13 -.01 -.01
13-14 .01 -.01
14-15 .01 .05
15-16 .01 -.03
16-17 .01 .01


Remember that the batting and pitching talent in the AL presumably decreased by .11 runs per team per game and they were expected to score .13 fewer runs per game per team, in 2017, as compared to 2016. Adding in defense and base running, those numbers are a decrease in AL talent by .15 runs and a decrease in run scoring of only .07 runs per team per game.

In the NL, when we add defense and base running to batting and pitching, we get no overall change in talent, from 2016 to 2017, and a decrease in run scoring of -.04.

We also see a slight trend towards better base running since 2011, which should naturally occur with better defense.

Here is everything combined into one table.

Table V

Change in talent and run scoring, in runs per game per team. Plus means gain in talent and score more runs.

Years NL Talent AL Talent NL Runs AL Runs
00-01 .04 -.22 .09 .06
01-02 -.16 -.29 -.12 -.19
02-03 -.30 .19 -.02 -.41
03-04 -.08 -.29 .26 -.01
04-05 -.20 -.19 .04 -.05
05-06 .37 .23 -.07 -.15
06-07 -.02 -.02 .23 .16
07-08 .06 .17 -.16 -.01
08-09 .04 .29 -.26 -.09
09-10 .15 -.16 .05 -.12
10-11 -.31 -.09 .04 .15
11-12 .19 .11 .05 -.15
12-13 0 -.35 -.08 .23
13-14 .14 .07 -.10 .05
14-15 .03 .18 .11 .10
15-16 .06 .03 -.02 .03
16-17 0 -.15 -.04 -.07

If you haven’t read it, here’s the link.

For MY ball tests, the difference I found in COR was 2.6 standard deviations, as indicated in the article. The difference in seam height is around 1.5 SD. The difference in circumference is around 1.8 SD.

For those of you a little rusty on your statistics, the SD of the difference between two sample means is the square root of the sum of their respective variances.

The use of statistical significance is one of the most misunderstood and abused concepts in science. You can read about this on the internet if you want to know why. It has a bit to do with frequentist versus Bayesian statistics/inference.

For example, when you have a non-null hypothesis going into an experiment, such as, “The data suggest an altered baseball,” then ANY positive result supports that hypothesis and increases the probability of it being true, regardless of the “statistical significance of those results.”

Of course the more significant the result, the more we increase the prior probability. However, the classic case of using 2 or 2.5 SD to define “statistical significance” really only applies when you start out with the null hypothesis. In this case, for example, that would be if you had no reason to suspect a juiced ball, and you merely tested balls just to see if perhaps there were differences. In reality, you almost always have a prior P which is why the traditional concept of accepting or rejecting the null hypothesis based on the statistical significance of the results of your experiment is an obsolete concept.

In any case, from the results of MLB’s own tests, in which they tested something like 180 balls a year, the seam height reduction we found was something like 6 or 7 SD and the COR increase was something like 3 or 4 SD. We also can add to the mix, Ben’s original test whereby he found an increase in COR of .003 or around 60% of what I found.

So yes, the combined results of all three tests are almost unequivocal evidence that the ball was altered. There’s not much else you can do other than to test balls. Of course the ball testing would mean almost nothing if we didn’t have the batted ball data to back it up. We do.

I don’t think this “ball change” was intentional by MLB, although it could be.

In my extensive research for this project, I have uncovered two things:

One, there is quite a large actual year to year difference in the construction of the ball which can and does have a significant impact on HR and offensive rates in general. The concept of a “juiced” (or “de-juiced”) ball doesn’t really mean anything unless it is compared to some other ball – for example, in our case, 2014 to 2016/2017.

Two, we now know because of Statcast and lots of great work and insight by Alan Nathan and others, that very small changes in things like COR, seam height, and size can have a dramatic impact on offense. My (wild) guess is that we probably have something like a 2 or 3 feet (in batted ball distance for a typical HR trajectory) variation (one SD) from year to year based on the (random) fluctuating composition and construction of the ball.  And from 2014 to 2106 (and so far this year), we just happened to have seen a 2 or 3 standard deviation variation.

We’ve seen it before, most notably in 1987, and we’ll probably see it again. I have also altered my thinking about the “steroid era.” Now that I know that balls can fluctuate from year to year, sometimes greatly, it is entirely possible that balls were constructed differently starting in 1993 or so – perhaps in combination with burgeoning and rampant PED use.

Finally, it is true that there are many things that can influence run scoring and HR rates, some more than others. Weather and parks are very minor. Even a big change in one park or two or a very hot or cold year will have very small effects overall. And of course we can easily test or account for these things.

Change in talent can surprisingly have a large effect on overall offense. For example, this year, the AL lost a lot of offensive talent which is one reason why the NL and the AL have almost equal scoring despite the AL having the DH.

The only other thing that can fairly drastically change offense is the strike zone. Obviously it depends on the magnitude of the change. In the pitch f/x era we can measure that, as Joe Roegele and others do every year. It has not changed much the last few years until this year. It is smaller now, which is causing an uptick in offense from last year. I also believe, as others have said, that the uptick since last year is due to batters realizing that they are playing with a livelier ball and thus are hitting more air balls. They may be hitting more air balls even without thinking that the ball is juiced -they may be just jumping on the “fly-ball bandwagon.” Either way, hitting more fly balls compounds the effect of a juiced ball because it is correct to hit more fly balls.

Then there is the bat, which I know nothing about. I have not heard anything about the bats being different or what you can do to a bat to increase or decrease offense, within allowable MLB limits.

Do I think that the “juiced ball” (in combination with players taking advantage of it) is the only reason for the HR/scoring surge? I think it’s the primary driver, by far.

There’s been some discussion lately on Twitter about the sacrifice bunt. Of course it is used very little anymore in MLB other than with pitchers at the plate. I’ll spare you the numbers. If you want to verify that, you can look it up on the interweb. The reason it’s not used anymore is not because it was or is a bad strategy. It’s simply because there is no point in sac bunting in most cases. I’ve written about why before on this blog and on other sabermetric sites. It has to do with game theory. I’ll briefly explain it again along with some other things. This is mostly a copy and paste from my recent tweets on the subject.

First, the notion that you can analyze the efficacy (or anything really) about a sac bunt attempt by looking at what happens (say, the RE or WE) after an out and a runner advance is ridiculous. For some reason sabermetricians did that reflexively for a long time ever since Palmer and Thorn wrote The Hidden Game and concluded (wrongly) that the sac bunt was a terrible strategy in most cases. What they meant was that advancing the runner in exchange for an out is a terrible strategy in most cases, which it is. But again, EVERYONE knows that that isn’t the only thing that happens when a batter attempts to bunt. That’s not a shock. We all know that the batter can reach base on a single or an error, he can strike out, hit into a force or DP, pop out, or even walk. We obviously have to know  how often those things occur on a bunt attempt to have any chance to figure out whether a bunt might increase, decrease or not change the RE or WE, compared to hitting away. Why Palmer and Thorn or anyone else ever thought that looking at the RE or WE after something that occurs less than half the time on a bunt attempt (yeah, on the average an out and runner advance occurs around 47% of the time) could answer the question of whether a sac bunt might be a good play or not, is a mystery to me. Then again, there are probably plenty of stupid things we’re saying and doing now with respect to baseball analysis that we’ll be laughing or crying about in the future, so I don’t mean that literally.

What I am truly in disbelief about is that there are STILL saber-oriented writers and pundits who talk about the sac bunt attempt as if all that ever happens is an out and a runner advance. That’s indefensible. For cripes sake I wrote all about this in The Book 12 years ago. I have thoroughly debunked the idea that “bunts are bad because they considerably reduce the RE or WE.” They don’t. This is not controversial. It never was. It was kind of a, “Shit I don’t know why I didn’t realize that,” moment. If you still look at bunt attempts as an out and a runner advance instead of as an amalgam of all kinds of different results, you have no excuse. You are either profoundly ignorant, stubborn, or both. (I’ll give the casual fan a pass).

Anyway, without further ado, here is a summary of some of what I wrote in The Book 12 years ago about the sac bunt, and what I just obnoxiously tweeted in 36 or so separate tweets:

Someone asked me to post my 2017 W/L projections for each team. I basically added up the run values of my individual projections, using Fangraphs projected playing time for every player, as of around March 15.

I did use the actual schedule for a “strength of opponent” adjustment. I didn’t add anything additional for injuries, chances of each team making roster adjustments at trade deadline or otherwise, managerial skill, etc. I didn’t try and simulate lineups or anything like that. Plus, these are based on my preliminary projections without incorporating any Statcast or pitch F/X data. Also, these kinds of projections tend to regress toward a mean of .500 for all teams. That’s because bad teams tend to weed out bad players and otherwise improve, and injuries don’t hurt them much – in some cases improving them. And good teams tend to be hurt more by injuries (and I don’t think the depth charts I use account enough for chance of injury). As well, if good teams are not contending at the deadline, they tend to trade their good players.

So take these for what they are worth.

team wins div wc div+wc ds lcs ws


was 89 0.499 0.097 0.597 0.257 0.117 0.048
nyn 88 0.437 0.114 0.55 0.239 0.106 0.044
mia 78 0.046 0.02 0.066 0.024 0.01 0.004
phi 72 0.007 0.002 0.009 0.003 0.001 0
atl 72 0.011 0.004 0.014 0.006 0.002 0.001

NL Central

chn 100 0.934 0.044 0.978 0.56 0.303 0.146
sln 86 0.049 0.273 0.322 0.137 0.059 0.022
pit 82 0.017 0.129 0.146 0.056 0.023 0.008
cin 67 0 0.001 0.001 0 0 0
mil 61 0 0 0 0 0 0


lan 102 0.961 0.025 0.987 0.591 0.327 0.164
sfn 85 0.03 0.214 0.245 0.098 0.041 0.016
col 78 0.005 0.047 0.052 0.018 0.007 0.003
ari 77 0.003 0.03 0.033 0.011 0.004 0.002
sdn 66 0 0 0 0 0 0


tor 87 0.34 0.114 0.455 0.229 0.118 0.061
bos 87 0.359 0.129 0.487 0.238 0.117 0.064
tba 83 0.15 0.077 0.227 0.105 0.051 0.027
bal 81 0.099 0.056 0.155 0.071 0.032 0.014
nya 79 0.053 0.035 0.088 0.038 0.018 0.008


cle 93 0.861 0.027 0.888 0.471 0.254 0.146
det 82 0.097 0.077 0.174 0.076 0.033 0.016
min 76 0.021 0.015 0.036 0.014 0.005 0.002
kca 75 0.02 0.014 0.033 0.014 0.005 0.003
cha 68 0.001 0.001 0.002 0 0 0


hou 91 0.541 0.13 0.671 0.362 0.188 0.11
sea 86 0.228 0.155 0.383 0.192 0.09 0.047
ala 84 0.181 0.12 0.301 0.146 0.071 0.036
tex 80 0.044 0.042 0.086 0.038 0.017 0.008
oak 73 0.006 0.007 0.014 0.006 0.002 0.001




The most important thing, bar none, that your government can do – must do – is to be truthful and transparent regardless of party, policy, or ideology. Your government works for you. It is your servant. As Lincoln famously said, in America we have a government, “of the people, by the people and for the people.” That is the bedrock of our Democracy.

A government that withholds, obfuscates, misrepresents or tells falsehoods should never be tolerated in a democracy. Raw, naked honesty is the first thing you must demand from your government. They. Work. For. You. Regardless of what you think of their promises and policies, if they are not honest with you, they cannot govern effectively because you can never trust that they have your best interests in mind.

Demand that your politicians are honest with you. If not, you must vote them out. It is every American’s responsibility to do so. It doesn’t matter what their party is or what you think they may accomplish. A dishonest government is like a dishonest employee. They will eventually sink your company. Anything but a transparent and forthright government is a cancer in a Democracy. It is self-serving by definition. You should demand honesty first and foremost from your public servants or our Democracy will crumble.


In this article, Tuffy Gosewisch, the new backup catcher for the Braves, talks catching with Fangraphs David Laurilia. He says about what you would expect from a catcher. Nothing groundbreaking or earth-shattering – nothing blatantly silly or wrong either. In fact, catchers almost always sound like baseball geniuses. They do have to be one of the smarter ones on the field. But…

Note: This is almost verbatim from my comment on that web page:

I have to wonder how much better a catcher could be if he understood what he was actually doing (of course they do, they get paid millions, they’ve been doing it all their lives, and are presumably the best in the world at what they do. Who the hell are you, you’ve never put on the gear in your life?).

All catchers talk about how they determine the “right” pitch. I’m waiting for a catcher to say, “There is no ‘right’ pitch – there can’t be! There’s a matrix of pitches and we choose one randomly. Because you see, if there were a ‘right” pitch and that was the one we called, the batter would know or at least have a pretty good idea of that same pitch and it would be a terrible pitch, especially if the batter were a catcher!”

If different catchers and pitchers have different “right” pitches and that’s why batters can’t guess them then there certainly isn’t a “right” pitch – it must be a (somewhat) random one.

When I say “random” I mean from a distribution of pitches, each with a pre-determined (optimal) frequency, based on the batter and the game situation. Rather than it be the catcher and pitcher’s job to come up with the “right” pitch – and I explained why that concept cannot be correct – it is their responsibility to come up with the “right” distribution matrix, for example, 20% FB away, 10% FB inside, 30% curve ball, 15% change up, etc. In fact, once you do that, you can tell the batter your matrix and it won’t make any difference! He can’t exploit that information and you will maximize your success as a pitcher, assuming that the batter will exploit you if you use any other strategy.

If a catcher could come up with the “right” single pitch that the batter is not likely to figure out, without randomly choosing one from a pre-determined matrix, well….that can’t be right, again, because whatever the catcher can figure, so can (and will) the batter.

We also know that catchers don’t hit well. If there were “right” pitches, catchers would be the best hitters in baseball!

Tuffy also said this:

“You also do your best to not be predictable with pitch-calling. You remember what you’ve done to guys in previous at-bats, and you try not to stay in those patterns. Certain guys — veteran guys — will look for patterns. They’ll recognize them, and will sit on pitches.”

Another piece of bad advice! Changing your patterns is being predictable! If you have to change your patterns to fool batters your patterns were not correct in the first place! As I said, the “pattern” you choose is the only optimal one. By “pattern” I mean a certain matrix of pitches thrown a certain percentage of time given the game situation and participants involved. Any other definition of “pattern” implies predictability so for a catcher to be talking about “patterns” at all is not a good thing. There should never be an identifiable pattern in pitching unless it is a random one which looks like a pattern. (As it turns out, researchers have shown that when people are shown random sequences of coin flips and ones that are chosen to look random but are not, people more often choose the non-random ones as being random.)

Say I throw lots of FB to a batter the first 2 times through order and he rakes (hits a HR and double) on them. If those two FB were part of the correct matrix I would be an idiot to throw him fewer FB in the next PA. Because if that were part of my plan, once again, he could (and would) guess that and have a huge advantage. How many times have you heard Darling, Smoltz or some other ex-pitcher announcer say something like, “After that blast last AB (on a fastball) the last thing he’ll do here is throw him another fastball in this AB?” Thankfully, for the pitcher, the announcer will invariably be wrong, and the pitcher will throw his normal percentage of fastballs to that batter – as he should.

What if I am mixing up my pitches randomly each PA but I change my mixture from time to time? Is that a good plan? No! The fact that I am choosing randomly from a matrix of pitches (each with a different fixed frequency for that exact situation) on each and every pitch means that I am “somewhat” unpredictable by definition (“somewhat” is in quotes because sometimes the correct matrix is 90% FB and 10% off-speed – is that “unpredictable?”) but the important thing is that those frequencies are optimal. If I constantly change those frequencies, even randomly, then they often will not be correct (optimal). That means that I am sometimes pitching optimally and other times not. That is not the overall optimal way to pitch of course.

The optimal way to pitch is to pitch optimally all the time (duh)! So my matrix should always be the same as long as the game situation is the same. In reality of course, the game situation changes all the time. So I should be changing my matrices all the time. But it’s not in order to “mix things up” and keep the batters guessing. That happens naturally (and in fact optimally) on each and every pitch as long as I am using the optimal frequencies in my matrix.

Once again, all of this assumes a “smart” batter. For a “dumb” batter, my strategy changes and things get complicated, but I am still using a matrix and then randomizing from it. Always. Unless I am facing the dumbest batter in the universe who is incapable of ever learning anything or perhaps if it’s the last pitch I am going to throw in my career.

There are only two correct things that a pitcher/catcher have to do – their pitch-calling jobs are actually quite easy. This is a mathematical certainty. (Again, it assumes that the batter is acting optimally – if he isn’t that requires a whole other analysis and we have to figure out how to exploit a “dumb” batter without causing him to play too much more optimally):

One, establish the game theory optimal matrix of pitches and frequencies given the game situation, personnel, and environment.

Two, choose one pitch randomly around those frequencies (for example, if the correct matrix is 90% FB and 10% off-speed, you flip a 10-side mental coin).

Finally, it may be that catchers and pitchers do nearly the right thing (i.e. they can’t be much better even if I explain to them the correct way to think about pitching – who the hell do you think you are?) even though they don’t realize what it is they’re doing right. However, that’s possible only to an extent.

Many people are successful at what they do without understanding what it is they do that makes them successful. I’ve said before that I think catchers and pitchers do randomize their pitches to a large extent. They have to. Otherwise batters would guess what they are throwing with a high degree of certainty and Ron Darling and John Smoltz wouldn’t be wrong as often as they are when they tell us what the pitcher is going to throw (or should throw).

So how is that catchers and pitchers can think their job is to figure out the “right” pitch (no one ever says they “flip a mental coin”) yet those pitches appear to be random? It is because they go through so many chaotic decision in their brain that for all intents and purposes the pitch selection often ends up being random. For example, “I threw him a fastball twice in a row so maybe I should throw him an off-speed now. But wait, he might be thinking that, so I’ll throw another fastball. But wait, he might be thinking that too, so…” Where they stop in that train of thought might be random!

Even if pitchers and catchers are essentially randomizing their pitches, two things are certain. They can’t possibly be coming up with the exact game theory optimal (GTO) matrices, and trust me there IS an optimal one (although it may be impossible for anyone to determine it, but I guarantee that someone can do a better job overall – it’s like man versus machine). Two, some pitchers and catchers will be better at pseudo-randomizing than others. In both cases there is a great deal of room for improvement on calling games and pitches.

Note: This post was edited to include some new data which leads us in the direction of a different conclusion. The addendum is at the end of the original post .

This is another one of my attempts at looking at “conventional wisdoms” that you hear and read about all the time without anyone stopping for a second to catch their breath and ask themselves, “Is this really true?” Or more appropriately, “To what extent is this true?” Bill James used those very questions to pioneer a whole new field called sabermetrics.

As usual in science, we can rarely if ever answer questions with, “Yes it is true,” or “No, it is not true.” We can only look at the evidence and try and draw some inferences with some degree of certainty between 0 and 100%. This is especially true in sports when we are dealing with empirical data and limited sample sizes.

You often read something like, “So-and-so pitcher had a poor season (say, in ERA) but he had a few really bad outings so it wasn’t really that bad.” Let’s see if we can figure out to what extent that may or may not be true.

First I looked at all starting pitcher outings over the last 40 years, 1977-2016. I created a group of starters who had at least 4 very bad outings and at least 100 IP in one season. A “bad outing” was defined as 5 IP or less and at least 6 runs allowed, so a minimum RA9 of almost 11 in at least 4 games in a season. Had those starts been typical starts, each of these pitchers’ ERA’s or RA9 would have been at least a run less or so.

Next I only looked at those pitchers who had an overall RA9 of at least 5.00 in the seasons in question. The average RA9 for these pitchers with some really bad starts was 5.51 where 4.00 is the average starting pitcher’s RA9 in every season regardless of the run environment or league. Basically I normalized all pitchers to the average of his league and year and set the average at 4.00. I also park adjusted everything.

OK, what were these pitchers projected to do the following season? I used basic Marcel-type projections for all pitchers. The projections treated all RA9 equally. In other words a 5.51 RA with a few really bad starts was equivalent to a 5.51 RA with consistently below-average starts. The projections only used full season data (RA9).

So basically these 5.51 RA9 pitchers pitched near average for most of the their starts but had 4-6 really bad (and short) starts that upped their overall RA9 for the season by more than a run. Which was more indicative of their true talent? The vast majority of the games where they pitched around average, the few games where they blew up, or their overall runs allowed per 9 innings? Or, their overall RA9 for that season (regardless of how it was created) plus their RA9 from previous seasons and then some regression thrown in for good measure – in other words, a regular, old-fashioned projection?

Our average projection for these pitchers for the next season (which is an estimate of their true talent that season) was 4.46. How did they pitch the next season – which is an unbiased sample of their true talent (I didn’t set an innings requirement for this season so there is no survivorship bias)? It was 4.48 in 10,998 TBF! So the projection which had no idea that these were pitchers who pitched OK for most of the season but had a terrible seasonal result (5.51 RA9) because of a few terrible starts, was right on the money. All the projection model knew was that these pitchers had very bad RA9 for the season – in fact, their average RA was 138% of league average.

Of course since we sampled these pitchers based on some bad outings and an overall bad ERA (over 5.00) we know that in prior seasons their RA9 would be much lower, similar to their projection (4.46) – actually better. In fact, you should know that a projection can apply just as well to previous years as it can to subsequent years. There is almost no difference. You just have to make sure you apply the proper age adjustments.

Somewhat interestingly, if we look at all pitchers with a RA9 above 5 (an average of 5.43) who did not have the requisite very bad outings, i.e. they pitched consistently bad but with few disastrous starts, their projected RA9 was 4.45 and their actual was 4.25, in 25,479 TBF.

While we have significant sample error in these limited samples, not only is there no suggestion that you should ignore or even discount bad ERA or RA that are the result of a few horrific starts, there is a (admittedly weak) suggestion that pitchers who pitch badly but more consistently may be able to outperform their projections for some reason.

The next time you read that, “So-and-so pitcher has bad numbers but it was only because of a few really bad outings,” remember that there is no evidence  that an ERA or RA which includes a “few bad outings” should be treated any differently than a similar ERA or RA without that qualification, at least as far as projections are concerned.

Addendum: I was concerned about the way I defined pitchers who had “a few disastrous starts.” I included all starters who gave up at least 6 runs in 5 innings or less at least 5 times in a season. The average number of bad starts was 5.5. So basically these were mostly pitchers who had 5 or 6 really bad starts in a season, occasionally more.

I thought that most of the time when we hear the “A few bad starts” refrain, we’re talking literally about “a few bad starts,” as in 2 or 3. So I changed the criteria to include only those pitchers with 2 or 3 awful starts. I also upped the ante on those terrible starts. Before it was > 5 runs in 5 IP or less.  Now it is >7 runs in 5 IP or less – truly a blowup of epic proportions. We still had 508 pitcher seasons that fit the bill which gives us a decent sample size.

These pitchers overall had a normalized (4.00 is average) RA9 of 4.19 in the seasons in question, so 2 or 3 awful starts didn’t produce such a bad overall RA. Remember I am using a 100 IP minimum so all of these pitchers pitched at least fairly well for the season whether they had a few awful starts or not. (This is selective sampling and survivorship bias at work. Any time you set a minimum IP or PA, you select players who had above average performance, through luck and talent.)

Their next year’s projection was 3.99 and the actual was 3.89 so there is a slight inference that indeed you can discount the bad starts a little. This is in around 12,000 IP. A difference of .1 RA9 is only around 1 SD so it’s not nearly statistically significant. I also don’t know that we have any Bayesian prior to work with.

The control group – all other starters, namely those without 2 or 3 awful outings – had a RA9 in the season in question of 3.72 (compare to 4.19 for the pitchers with 2 or 3 bad starts). Their projection for the next season was 3.85 and actual was 3.86. This was in around 130,000 IP so 1 SD is now around .025 runs so we can be pretty confident that the 3.86 actual RA9 reflects their true talent within around .05 runs (2 SD) or so.

What about starters who not only had 2 or 3 disastrous starts but also had an overall poor RA9? In the original post I looked at those pitchers in our experimental group who also had a seasonal RA9 of > 5.00. I’ll do the same thing with this new experimental group – starters with only 2 or 3 very awful starts.

Their average RA9 for the experimental season was 5.52. Their projection was 4.45 and actual was 4.17, so now we have an even stronger inference that a bad season caused by a few bad starts creates a projection that is too pessimistic; thus maybe we should  discount those few bad starts. We only have around 1600 IP (in the projected season) for these pitchers so 1 SD is around .25 runs. A difference between projected and actual of .28 runs is once again not nearly statistically significant. There is, nonetheless, a suggestion that we are on to something. (Don’t ever ignore – assume it’s random – an observed effect just because it isn’t statistically significant – that’s poor science.)

What about the control group? Last time we noticed that the control group’s actual RA was less than its projection for some reason. I’ll look at pitchers who had > 5 RA9 in one season but were not part of the group that had 2 or 3 disastrous starts.

Their average RA9 was 5.44 – similar to the 5.52 of the experimental group. Their projected was 4.45 and actual was 4.35, so we see the same “too high” projection in this group as well. (In fact, in testing my RA projections based on RA only – as opposed to say FIP or ERC – I find an overall bias such that pitchers with a one-season high RA have projections that are too high, not a surprising result actually.) This is in around 7,000 IP which gives us a SD of around .1 runs per 9.

So, the “a few bad starts” group outperformed their projections by around .1 runs. This same group, limiting it to starters with an overall RA or over 5.00, outperformed their projections by .28 runs. The control group with an overall RA also > 5.00 outperformed their projections by .1 runs. None of these differences are even close to statistically significant.

Let’s increase the sample size a little of our experimental group who also had particularly bad RA overall by expanding it to starters with an overall RA of > 4.50 rather than > 5.00. We now have 3,500 IP, 2x as many IP, reducing our error by around 50%. The average RA9 of this group was 5.13. Their projected RA was 4.33 and actual was 4.05 – exactly the same difference as before. Keep in mind that the more samples we look at the more we are “data mining,” which is a bit dangerous in this kind of research.

A control group of starters with > 4.50 RA had an overall RA9 of 4.99. Their projection was exactly the same as the experimental group, 4.33, but their actual was 4.30 – almost exactly the same as their projection.

In conclusion, while we initially found no evidence that discounting a bad ERA or RA caused by “several very poor starts” is warranted when doing a projection for starters with at least 100 IP, once we change the criteria for “a few bad starts” from “at least 5 starts with 6 runs or more allowed in 5 IP or less” to “exactly 2 or 3 starts with 8 runs or more in 5 IP or less” we do find evidence that some kind of discount may be necessary. In other words, for starters whose runs allowed are inflated due to 2 or 3 really bad starts, if we simply use overall season RA or ERA for our projections we will understate their subsequent season’s RA or ERA by maybe .2 or .3 runs per 9.

Our certainty of this conclusion, especially with regard to the size of the effect – if it exists at all – is pretty weak given the magnitude of the differences we found and the sample sizes we had to work with. However, as I said before, it would be a mistake to ignore any inference – even a weak one – that is not contradicted by some Bayesian prior (or common sense).