Archive for December, 2016

Richard Nichols (@RNicholsLV on Twitter) sent me this link. These are notes that the author, Lee Judge, a Royals blogger for the K.C. Star, took during the season. They reflect thoughts and comments from players, coaches, etc. I thought I’d briefly comment on each one. Hope you enjoy!

Random, but interesting, things about baseball – Lee Judge

▪ If a pitcher does not have a history of doubling up on pickoff throws (two in a row) take a big lead, draw a throw and then steal on the next pitch.

Of course you can do that. But how many times can you get away with it? Once? If the pitcher or one of his teammates or coaches notices it, he’ll pick you off the next time by “doubling up.” Basically by exploiting the pitcher’s non-random and thus exploitable strategy, the runner becomes exploitable himself. A pitcher, of course, should be picking a certain percentage of the time each time he goes into the set position, based on the likelihood of the runner stealing and the value of the steal attempt. That “percentage” must be randomized by the pitcher and it “resets” each time he throws a pitch or attempts a pickoff.

By “randomize” I mean the prior action, pick or no pick, cannot affect the percentage chance of a pick. If a pitcher is supposed to pick 50% prior to the next pitch he must do so whether he’s just attempted a pickoff 0, 1, 2, or 10 times in a row. The runner can’t know that a pickoff is more or less likely based on how many picks were just attempted. In fact you can tell him, “Hey every time I come set, there’s a 50% (or 20%, or whatever) chance I will attempt to pick you off,” and there’s nothing he can do to exploit that information.

For example, if he decides that he must throw over 50% of the time he comes set (in reality the optimal % changes with the count), then he flips a mental coin (or uses something – unknown to the other team – to randomize his decision, with a .5 mean). What will happen on the average is that he won’t pick half the time, 25% of the time he’ll pick once only, 12.5% of the time he’ll pick exactly twice, 25% of the time he’ll pick at least twice, etc.

Now, the tidbit from the player or coach says, “does not have a history of doubling up.” I’m not sure what that means. Surely most pitchers when they do pick, will pick once sometimes and twice sometimes, etc. Do any pitchers really never pick more than once per pitch? If they do, I would guess that it’s because the runner is not really a threat and the one-time pick is really a pick with a low percentage. If a runner is not much of a threat to run, then maybe the correct pick percentage is 10%. If that’s the case, then they will not double-up 99% of the time and correctly so. That cannot be exploited, again, assuming that a 10% rate is optimal for that runner in that situation. So while it may look like they never double up, they do in fact double up 1% of the time, which is correct and cannot be exploited (assuming the 10% is correct for that runner and in that situation).

Basically what I’m saying is that this person’s comment is way to simple and doesn’t really mean anything without putting it into context as I explain above.

▪ Foul balls with two strikes can indicate a lack of swing-and-miss stuff; the pitcher can get the batters to two strikes, but then can’t finish them off.

Not much to say here. Some pitchers have swing-and-miss stuff and others don’t, and everything in-between. You can find that out by looking at…uh…their swing-and-miss percentages (presuming a large enough sample size to give you some minimum level of certainty). Foul balls with two strikes? That’s just silly. A pitcher without swing-and-miss stuff will get more foul balls and balls in play with two strikes. That’s a tautology. He’ll also get more foul balls and balls in play with no strikes, one strike, etc.

▪ Royals third-base coach Mike Jirschele will walk around the outfield every once in a while just to remind himself how far it is to home plate and what a great throw it takes to nail a runner trying to score.

If my coach has to do that I’m not sure I want him coaching for me. That being said, whatever little quirks he has or needs to send or hold runners the correct percentage of time is fine by me. I don’t know that I would be teaching or recommending that to my coaches – again, not that there’s anything necessarily wrong with it.

Bottom line is that he better know the minimum percentages that runners need to be safe in any given situation (mostly # of outs) – i.e. the break-even points – and apply them correctly to the situation (arm strength and accuracy etc.) in order to make optimal decisions. I would surely be going over those numbers with my coaches from time to time and then evaluating his sends and holds to make sure he’s not making systematic errors or too many errors in general.

▪ For the most part, the cutter is considered a weak contact pitch; the slider is considered a swing-and-miss pitch.

If that’s confirmed by pitch f/x, fine. If it’s not, then I guess it’s not true. Swing-and-miss is really just a subset of weak contact and weak contact is a subset of contact which is a subset of a swing. The result of a swing depends on the naked quality of the pitch, where it is thrown, and the count. So while for the most part (however you want to define that – words are important!) it may be true, surely it depends on the quality of each of the pitches, on what counts they tend to be thrown, how often they are thrown at those counts, and the location they are thrown to. Pitches away from the heart of the plate tend to be balls and swing-and-miss pitches. Pitches nearer the heart tend to be contacted more often, everything else being equal.

▪ With the game on the line and behind in the count, walk the big-money guys; put your ego aside and make someone else beat you.

Stupid. Just. Plain. Stupid. Probably the dumbest thing a pitcher or manager can think/do in a game. I don’t even know what it means and neither do they. So tie game in the 9th, no one on base, 0 outs, count is 1-0. Walk the batter? That’s what he said! I can think of a hundred stupid examples like that. A pitcher’s approach changes with every batter and every score, inning, outs, runners, etc. A blanket statement like that, even as a rule of thumb, is Just. Plain. Dumb. Any interpretation of that by players and coaches can only lead to sub-optimal decisions – and does. All the time. Did I say that one is stupid?

▪ A pitcher should not let a hitter know what he’s thinking; if he hits a batter accidentally he shouldn’t pat his chest to say “my bad.” Make the hitter think you might have drilled him intentionally and that you just might do it again.

O.K. To each his own.

▪ Opposition teams are definitely trying to get into Yordano Ventura’s head by stepping out and jawing with him; anything to make him lose focus.

If he says so. I doubt much of that goes on in baseball. Not that kind of game. Some, but not much.

▪ In the big leagues, the runner decides when he’s going first-to-third; he might need a coach’s help on a ball to right field — it’s behind him — but if the play’s in front of him, the runner makes the decision.

Right, we teach that in Little League (a good manager that is). You teach your players that they are responsible for all base running decisions until they get to third. Then it’s up to the third base coach. It’s true that the third base coach can and should help the runner on a ball hit to RF, but ultimately the decision is on the runner whether to try and take third.

Speaking of taking third, while the old adage “don’t make the first or third out at third base” is a good rule of thumb, players should know that it doesn’t mean, “Never take a risk on trying to advance to third.” It means the risk has to be low (like 10-20%), but that the risk can be twice as high with 0 outs as with 2 outs. So really, the adage should be, “Never make the third out at third base, but you can sometimes make the first out at third base.”

You can also just forget about the first out part of that adage. Really, the two-out break-even point is almost exactly in between the first-out and one-out one. In other words, with no outs, you need to be safe at third around 80% of the time, with one out, around 70%, and with two outs around 90%. Players should be taught that and not just the “rule of thumb.” They should also be taught that the numbers change with trailing runners, the pitcher, and who the next batter or batters are. For example, with a trailing runner, making the third out is really bad but making the first out where the trailing runner can advance is a bonus.

▪ Even in a blowout there’s something to play for; if you come close enough to make the other team use their closer, maybe he won’t be available the next night.

I’m pretty sure the evidence suggests that players play at their best (more or less) regardless of the score. That makes sense under almost any economic or cognitive theory of behavior since players get paid big money to have big numbers. Maybe they do partially because managers and coaches encourage them to do so with tidbits like that. I don’t know.

Depending on what they mean by blowout, what they’re saying is that, say you have a 5% chance of winning a game down six runs in the late innings. Now say you have a 20% chance of making it a 3-run or less game, and that means that the opponent closer comes into the game. And say that him coming into the game gives you another 2% chance of winning tomorrow because he might not be available, and an extra 1% the day after that (if it’s the first game in a series). So rather than a 5% win expectancy, you actually have a 5% plus 20% * 3% or, 5.6% WE. Is that worth extra effort? To be honest, a manager and coach is supposed to teach his players to play hard (within reason) regardless of the score for two reasons: One, because it makes for better habits when the game is close and two, at exactly what point is the game a blowout (Google the sorites paradox)?

▪ If it’s 0-2, 1-2 and 2-2, those are curveball counts and good counts to run on. That’s why pitchers often try pickoffs in those counts.

On the other hand, 0-2 is not a good count to run on because of the threat of the pitchout. As it turns out, the majority of SB attempts (around 68%) occur at neutral counts. Only around 16% of all steal attempts occur at those pitchers’ counts. So whoever said that is completely wrong.

Of course pitchers should (and do) attempt more pickoffs the greater the chance of a steal attempt. That also tends to make it harder to steal (hence the game theory aspect).

That being said, some smart people (e.g., Professor Ted Turocy of Chadwick Baseball Bureau) believe that there is a Nash equilibrium between the offense and defense with respect to base stealing (for most players – not at the extremes) such that neither side can exploit the other by changing their strategy. I don’t know if it’s true or not. I think Professor Turocy may have a paper on this. You can check it out on the web or contact him.

▪ Don’t worry about anyone’s batting average until they have 100 at-bats.

How about “Don’t worry about batting average…period.” In so many ways this is wrong. I would have to immediately fire whoever said that if it was a coach, manager or executive.

▪ It’s hard to beat a team three times in a row; teams change starting pitchers every night and catching three different pitchers having a down night is not the norm.

Whoever said this should be fired sooner than the one above. As in, before they even finished that colossally innumerate sentence.

▪ At this level, “see-it-and-hit” will only take you so far. The best pitchers are throwing so hard you have to study the scouting reports and have some idea of what’s coming next.

If that’s your approach at any level you have a lot to learn. That goes for 20 or 50 years ago the same as it does today. If pitchers were throwing maybe 60 mph not so much I guess. But even at 85 you definitely need to know what you’re likely to get at any count and in any situation from that specific pitcher. Batters who tell you that they are “see-it-and-hit-it” batters are lying to you or to themselves. There is no such thing in professional baseball. Even the most unsophisticated batter in the world knows that at 3-0, no outs, no runners on, his team is down 6 runs, he’s likely to be getting 100% fastballs.

▪ If a pitcher throws a fastball in a 1-1 count, nine out of 10 times, guess fastball. But if it’s that 10th time and he throws a slider instead, you’re going to look silly.

WTF? If you go home expecting your house to be empty but there are two giraffes and a midget, you’re going to be surprised.

▪ Good hitters lock in on a certain pitch, look for it and won’t come off it. You can make a guy look bad until he gets the pitch he was looking for and then he probably won’t miss it.

Probably have to fire this guy too. That’s complete bullshit. Makes no sense from a game-theory perspective or from any perspective for that matter. So just never throw him that pitch right? Then he can’t be a good hitter. But now if you never throw him the pitch he’s looking for, he’ll stop looking for it, and will instead look for the alternative pitch you are throwing him. So you’ll stop throwing him that pitch and then…. Managers and hitting coaches (and players) really (really) need a primer on game theory. I am available for the right price.

▪ According to hitting coach Dale Sveum, hitters should not give pitchers too much credit; wait for a mistake and if the pitcher makes a great pitch, take it. Don’t start chasing great pitches; stick to the plan and keep waiting for that mistake.

Now why didn’t I think of that!

▪ The Royals are not a great off-speed hitting club, so opposition pitchers want to spin it up there.

Same as above. Actually, remember this: You cannot tell how good or bad a player or team is at hitting any particular pitch by looking at the results. You can only tell by how often they get each type of pitch. Game theory tells us that the results of all the different pitches (type, location, etc.) will be about the same to any hitter. What changes depending on that hitter’s strengths and weaknesses are the frequencies. And this whole, “Team is good/bad at X” is silly. It’s about the individual players of course. I’m pretty sure there was at least one hitter on the team who is good at hitting off-speed.

Also, never evaluate or define “good hitting” based on batting average which most coaches and managers do even in 2016. I don’t have to tell you, dear sophisticated reader, that. However, you should also not define good or bad hitting on a pitch level based on OPS or wOBA (presumably on contact) either. You need to include pitches not put into play and you need to incorporate count. For example, at a 3-ball count there is a huge premium on not swinging at a ball. Your result on contact is not so important. At 2-strike counts, not taking a strike is also especially important. Whenever you see pitch level numbers without including balls not swung at, or especially only on balls put into play (which is usually the case), be very wary of those numbers. For example, a good off-speed hitting player will tend to have good strike zone recognition (and not necessarily good results on contact) skills because many more off-speed pitches are thrown in pitchers’ counts and out of the strike zone.

▪ According to catcher Kurt Suzuki, opposition pitchers should not try to strike out the Royals. Kansas City hitters make contact and a pitcher that’s going for punchouts might throw 100 pitches in five innings.

Wait. If they are a good contact team, doesn’t that mean that you can try and strike them out without running up your pitch count? Another dumb statement. Someone should tell Mr. Suzuki that pitch framing is really important.

▪ If you pitch down in the zone you can use the whole plate; any pitch at the knees is a pretty good pitch (a possible exception is down-and-in to lefties). If you pitch up in the zone you have to hit corners.

To some extent that’s true though it’s (a lot) more complicated than that. What’s probably more important is that when pitching down in the zone you want to pitch more away and when pitching up in the zone more inside. By the way, is it true lefties like (hit better) the down-and-in pitch more than righties? No, it is not. Where does that pervasive myth come from? Where do all the hundreds of myths that players, fans, coaches, managers, and pundits think are true come from?

▪ If you pitch up, you have to be above the swing path.

Not really sure what that means? Above the swing “path?” Swing path tends to follow the pitch so that doesn’t make too much sense. “Path” implies angle of attack and to say “above” or “below” an angle of attach doesn’t really make sense. Maybe he means, “If you are going to pitch high, pitch really high?” Or, “If the batter tends to be a high ball hitter, pitch really high?”

▪ Numbers without context might be meaningless; or worse — misleading

I don’t know what that means. Anything might be misleading or worthless without context. Words, numbers, apple pie, dogs, cats…

▪ All walks are not equal: a walk at the beginning of an inning is worth more than a walk with two outs, a walk to Jarrod Dyson is worth more than a walk to Billy Butler.

Correct. I might give this guy one of the other guys’ (that I fired) jobs. Players, especially pitchers (but batters and fielders too), should always know the relative value of the various offensive events depending on the batter, pitcher, score, inning, count, runners, etc., and then tailor their approach to those values. This is one of the most important things in baseball.

▪ So when you look at a pitcher’s walks, ask yourself who he walked and when he walked them.

True. Walks should be weighed towards bases open, 2 outs, sluggers, close games, etc. If not, and the sample is large, then the pitcher is likely either doing something wrong or he has terrible command/control or both. For example, Greg Maddux went something like 10 years before he walked his first pitcher.

▪ When a pitcher falls behind 2-0 or 3-1, what pitch does he throw to get back in the count? Can he throw a 2-0 cutter, sinker or slider, or does he have to throw a fastball down the middle and hope for the best?

All batters, especially in this era of big data, should be acutely aware of a pitcher’s tendencies against their type of batter in any given situation and count. One of the most important ones is, “Does he have enough command of his secondary pitches (and how good is his fastball even when the batter knows it’s coming) to throw them in hitter’s counts, especially the 3-2 count?”

▪ Hitters who waggle the bat head have inconsistent swing paths.

I never heard that before. Doubt it is anything useful.

▪ The more violent the swing, the worse the pitch recognition. So if a guy really cuts it loose when he swings and allows his head to move, throw breaking stuff and change-ups. If he keeps his head still, be careful.

Honestly, if that’s all you know about a batter, someone is not doing their homework. And again, there’s game theory that must be accounted for and appreciated. Players, coaches and managers are just terrible at understanding this very important part of baseball especially the batter/pitcher matchup. If you think you can tell a pitcher to throw a certain type of pitch in a certain situation (like if the batter swings violently throw him off-speed), then surely the batter can and will know that too. If he does, which he surely will – eventually – then he basically knows what’s coming and the pitcher will get creamed!

There’s been much research and many articles over the years with respect to hitter (and other) aging curves. (I even came across in a Google search a fascinating component aging curve for PGA golfers!) I’ve publicly and privately been doing aging curves for 20 years. So has Tango Tiger. Jeff Zimmerman has also been prolific in this regard. Others have contributed as well. You can Google them if you want.

Most of the credible aging curves use some form of the delta method which is described in this excellent series on aging by the crafty n’er do well, MGL. If you’re too lazy to look it up, the delta method basically is this, from the article:

The “delta method” looks at all players who have played in back-to-back years. Many players have several back-to-back year “couplets,” obviously. For every player, it takes the difference between their rate of performance in Year I and Year II and puts that difference into a “bucket,” which is defined by the age of the player in those two years….

When we tally all the differences in each bucket and divide by the number of players, we get the average change from one age to the next for every player who ever played in at least one pair of back-to-back seasons in. So, for example, for all players who played in their age 29 and 30 seasons, we get the simple average of the rate of change in offensive performance between 29 and 30.

That’s really the only way to do an aging curve, as far as I know, unless you want to use an opaque statistical method like J.C Bradbury did back in 2009 (you can look that up too). One of the problems with aging curves, which I also discuss in the aforementioned article, and one that comes up a lot in baseball research, is survivorship bias. I’ll get to that in a paragraph or two.

Let’s say we want to use the delta method to compute the average change in wOBA performance from age 29 to 30. To do that, we look at all players who played in their age 29 and age 30 years, record each player’s difference, weight it by some number of PA (maybe the lesser of the two – either year 1 or year 2, maybe the harmonic mean of the two, or maybe weight them all equally – it’s hard to say), and then take the simple weighted average of all the differences. For example, say we have two players. Player A has a .300 wOBA in his age 29 season in 100 PA and a .290 wOBA in his age 30 season in 150 PA. Player B is .320 in year one in 200 PA and .300 in year two in 300 PA. Using the delta method we get a difference of -.010 (a decline) for player A weighted by, say, 100 PA (the lesser of 100 and 150), and a difference of -.020 for Player B in 200 PA (also the lesser of the two PA). So we have an average decline in our sample of (10 * 100 + 20 * 200) / (300), or 16.67 points of wOBA decline. We would do the same for all age intervals and all players and if we chain them together we get an aging curve for the average MLB player.

There are issues with that calculation, such as our choice to weight each player’s difference by the “lesser of the two PA,” what it means to compute “an average decline” for that age interval (since it includes all types of players, part-time, full-time, etc.) and especially what it means when we chain every age interval together to come up with an aging curve for the average major league player when it’s really a compendium of a whole bunch of players all with different career lengths at different age intervals.

Typically when we construct an aging curve, we’re not at all looking at the careers of any individual players. If we do that, we end up with severe selective sampling and survivorship problems. I’m going to ignore all of these issues and focus on survivorship bias only. It has the potential to be extremely problematic, even when using the delta method.

Let’s say that a player is becoming a marginal player for whatever reason, perhaps it is because he is at the end of his career. Let’s also say that we have a bunch of players like that and their true talent is a wOBA of .280. If we give them 300 PA, half will randomly perform better than that and half will randomly perform worse than that simply because 300 PA is just a random sample of their talent. In fact, we know that the random standard deviation of wOBA in 300 trials is around 25 points in wOBA, such that 5% of our players, whom we know have a true talent of .280, will actually hit .230 or less by chance alone. That’s a fact. There’s nothing they or anyone else can do about it. No player has an “ability” to fluctuate less than random variance tells is in any specific number of PA. There might be something about them that creates more variance on the average, but it is mathematically impossible to have less (actually the floor is a bit higher than that because of varying opponents and conditions).

Let’s assume that all players who hit less than .230 will retire or be cut – they’ll never play again, at least not in the following season. That is not unlike what happens in real life when a marginal player has a bad season. He almost always gets fewer PA the following season than he would have gotten had he not had an unlucky season. In fact, not playing at all is just a subset of playing less – both are examples of survivorship bias and create problems with aging curves. Let’s see what happens to our aging interval with these marginal players when 5% of them don’t play the next season.

We know that this entire group of players are .280 hitters because we said so. If 5% of them hit, on average, .210, then the other 95% must have hit .284 since the whole group must hit .280 – that’s their true talent. This is just a typical season for a bunch of .280 hitters. Nothing special going on here. We could have split them up any way we wanted, as long as in the aggregate they hit at their true talent level.

Now let’s say that these hitters are in their age 30 season and they are supposed to decline by 10 points in their age 31 season. If we do an aging calculation on these players in a typical pair of seasons we absolutely should see .280 in the first year and .270 in the second. In fact, if we let all our players play a random or a fixed number of PA in season two, that is exactly what we would see. It has to be. It is a mathematical certainty, given everything we stated. However survivorship bias screws up our numbers and results in an incorrect aging value from age 30 to age 31. Let’s try it.

Only 95% of our players play in season two, so 5% drop out of our sample, at least from age 30 to age 31. There’s nothing we can do about that. When we compute a traditional aging curve using the delta method, we only use numbers from pairs of years. We can never use the last year of a player’s career as the first year in a year pairing. We don’t have any information about that player’s next season. We can use a player’s last year, say, at age 30 in an age 29 to 30 pairing but not in a 30 to 31 pairing. Remember that the delta method always uses age pairings for each player in the sample.

What do those 95% hit in season one? Remember they are true .280 hitters. Well, they don’t hit .280. I already said that they hit .284. That is because they got a little lucky. The ones that got really unlucky to balance out the lucky ones, are not playing in season two, and thus dropped out of our aging curve sample. What do these true .280 players (who hit .284) hit in season two? Season two is an unbiased sample of their true talent. We know that their true talent was .280 in season one and we know that from age 30 to age 31 all players will lose 10 points in true talent because we said so. So they will naturally hit .270 in year two.

What does our delta method calculation tell us about how players age from age 30 to age 31? It tells us they lose 14 points in wOBA and not 10! It’s giving us a wrong answer because of survivorship bias. Had those other 5% of players played, they would have also hit .270 in year two and when we add everyone up, including the unlucky players, we would come up with the correct answer of a 10-point loss from age 30 to age 31 (the unlucky players would have improved in year two by 60 points).

One way to avoid this problem (survivorship bias will always make it look like players lose more or gain less as they age because the players that drop out from season to season always, on the average, got unlucky in season one) is to ignore the last season of a player’s career in our calculations. That’s fine and dandy, but survivorship bias exists in every year of a player’s career. As I wrote earlier, dropping out is just a small subset of this bias. Every player that gets unlucky in one season will see fewer PA in his next season, which creates the same kind of erroneous results. For example, if the 5% of unlucky players did play in season two, but only got 50 PA whereas the other 95% of slightly lucky players got 500 PA, we would still come up with a decline of more than 10 points of wOBA – again an incorrect answer.

To correct for this survivorship bias, which really wreaks havoc with aging curves, a number of years ago, I decided to add a phantom year for players after their last season of action. For that year, I used a projection – our best estimate of what they would have done had they been allowed to play another year. That reduced the survivorship bias but it didn’t nearly eliminate it because, as I said, every player suffers from it in reduced PA for unlucky players and increased PA for lucky ones, in their subsequent seasons.

Not only that, but we get the same effect within years. If two players have .300 wOBA true talents, but player A hits worse than .250 by luck alone in his first month (which will happen more than 16% of the time) and player B hits .350 or more, who do you think will get more playing time for the remainder of the season even though we know that they have the same talent, and that both, on the average, will hit exactly .300 for the remainder of the season?

I finally came up with a comprehensive solution based on the following thought process: If we were conducting an experiment, how would we approach the question of computing aging intervals? We would record every player’s season one (which would be an unbiased sample of his talent, so no problem so far) and then we would guarantee that every player would get X number of PA the next season, preferably something like 500 or 600 to create large samples of seasonal data. We would also give everyone a large number of PA in all season ones too, but it’s not really necessary.

How do we do that? We merely extend season two data using projections, just as I did in adding phantom seasons after a player’s career was over (or he missed a season in the middle of his career). Basically I’m doing the same thing, whether I’m adding 600 PA to a player who didn’t play (the phantom season) or I’m adding 300 PA to a player who only had 300 PA in season two. By doing this I am completely eliminating survivorship bias. Of course this correction method lives or dies with how accurate the projections are but even a simple projection system like Marcel will suffice when dealing with a large number of players of different talent levels. Now let’s get to the results.

I looked at all players from 1977 to 2016 and I park and league adjusted their wOBA for each season. Essentially I am using wOBA+. I also only looked at seasonal pairs (with a minimum of 10 PA in each season) where the player played on the same team. I didn’t have to do that, but my sample was large enough that I felt that the reduction in sample size was worth getting rid of any park biases even though I was dealing with park- adjusted numbers.

Using the delta method with no survivorship bias other than ignoring the last year of every player’s career, this is the aging curve I arrived at after chaining all of the deltas. This is the typical curve you will see in most of the prior research.

1977-2016 Aging Curve using Delta Method Without Correcting for Survivorship Bias

curve1

 

Here is the same curve after completing all season two’s with projections. For example, let’s say that a player is projected to hit .300 in his age 30 season and he hits .250 in only 150 PA (his manager benches him because he’s hit so poorly). His in-season projection would change because of the .250. It might now be .290. So I complete a 600 PA season by adding 450 PA of .290 hitting to the 150 PA of .250 hitting for a complete season of .280 in 600 PA.

If that same player hits .320 in season two in 620 PA then I add nothing to his season two data. Only players with less than 600 PA have their seasons completed with projections. How do I weight the season pairs? Without any completion correction, as in the first curve above, I weighted each season pair by the harmonic mean of the two PA. With correction, as in the second curve above, I weighted each pair by the number of PA in season one. This corrects for intra-season survivorship bias in season one as well.

1977-2016 Aging Curve using Delta Method and Correcting for Survivorship Bias

curve2

 

You can see that in the first curve, uncorrected for survivorship bias, players gain around 40 points in wOBA from age 21 to age 27, seven points per year, plateau from age 27 to 28, then decline by also around seven points a year after that. In the second curve, after we correct for survivorship bias, we have a slightly quicker ascension from age 21 to 26, more than eight points per year, a plateau from age 26 to age 27, then a much slower decline at around 3 points per year.

Keep in mind that these curves represent all players from 1977 to 2016. It is likely that aging has changed significantly from era to era due to medical advances, PED use and the like. In fact, if we limit our data to 2003 and later, after the so called steroid era, we get an uncorrected curve that plateaus between ages 24-28 and then declines by an average of 9 points a year from age 28 to 41.

In my next installment I’ll do some survivorship corrections for components like strikeout and walk percentage.

Now that Adam Eaton has been traded from the White Sox to the Nationals much has been written about his somewhat unusual “splits” in his outfield defense as measured by UZR and DRS, two of the more popular batted-ball defensive metrics. In RF, his career UZR per 150 games is around +20 runs and in CF, -8 runs. He has around 100 career games in RF and 300 in CF. These numbers do not include “arm runs” as I’m going to focus only on range and errors in this essay. If you are not familiar with UZR or DRS you can do some research on the net or just assume that they are useful metrics for quantifying defensive performance and for projecting defense.

In 2016 Eaton was around -13 in CF and +20 in RF. DRS was similar but with a narrower (but still unusual) spread. We expect that a player who plays at both CF and the corners in a season or within a career will have a spread of around 5 or 6 runs between CF and the corners (more between CF and RF than between CF and LF). For example, a CF’er who has a UZR of zero and thus is exactly average among all CF’ers, will have a UZR at around +5.5 at the corners, again a bit more in RF than LF (LF’ers are better fielders than RF’ers).

This has nothing to do with how “difficult” each position is (that is hard to define anyway – you could even make the argument that the corner positions are “harder” than CF), as UZR and DRS are calculated as runs above or below the average fielder at that position. It merely means that the average CF’er is a better fielder than the average corner OF’er by around 5 or 6 runs. Mostly they are faster. The reason teams put their better fielder in CF is not because it is an inherently more “difficult” position but because it gets around twice the number of opportunities per game than the corner positions such that you can leverage talent in the OF.

Back to Eaton. He appears to have performed much better in RF than we would expect given his performance in CF (or vice versa) or even overall. Does this mean that he is better suited to RF (and perhaps LF, where he hasn’t played much in his career) or that the big, unusual gap we see is just a random fluctuation, or somewhere in the middle as is often (usually) the case? Should the Nationals make every effort to play him in RF and not CF? After all, their current RF’er, Harper, has unusual splits too, but in the opposite direction – his career CF UZR is better than his career RF UZR! Or perhaps the value they’re getting from Eaton is diminished if they’re going to play him in CF rather than RF.

How could it be that a fielder could have such unusual defensive splits and it be solely or mostly due to chance only? The same reason a hitter can have unusual but random platoon splits or a pitcher can have unusual but random home/road or day/night splits. A metric like UZR or DRS, like almost all metrics, contains a large element of chance, or noise if you will. That noise comes from two sources – one is because the data and methodology are far from perfect and two is that actual defensive performance can fluctuate randomly (or for reasons we are just not aware of) from one time period to another – from play to play, game to game, or position to position, for various reasons or for no reason at all.

To the first point, just because our metric “says” that a player was +10 in UZR that does not necessarily mean that he performed exactly that well. In reality, he might have performed at a +15 level or he might have performed at a 0 or even a -10 level. It’s more likely of course that he performed at +5 than +20 or 0, but because of the limits of our data and methodology, the +15 is an estimate of his performance. To the second point, actual fielding performance, even if we could measure it precisely, like hitting and pitching, is subject to random fluctuations for reasons known (or at least speculated) and unknown to us. On one play a player can get a great jump and make a spectacular play and on another that same player can take a bad route, get a bad jump, the ball can pop out of his glove, etc. Some days fielders probably feel better than others. Etc.

So whenever we compare one time period to another or one position to another, even ones which require similar, perhaps even identical, skills, like in the OF, it is possible, even likely, that we are going to get different results by chance alone, or at least because of the two dynamics I explained above (don’t get hung up on the words “luck”, “chance” or “random”). Statistics tell us that those random differences will be more and more unlikely the further away we get from what is expected (e.g., we expect that play in CF will be 5 or 6 runs “worse” than play in RF or LF), however, statistics also tells us that any difference, even large ones like we see with Eaton (or more), can and do occur by chance alone.

At the same time, it is possible, maybe even likely, that a player could somehow be more suited to RF (or LF) than CF, or vice versa. So how do we determine how much of an unusual “split” in OF defense, for example, is likely chance and how much is likely “skill?” In other words, what would we expect future defense to be in RF and in CF for a player with unusual RF/CF splits? Remember that future performance always equates to an estimate of talent, more or less. For example, if we find strong evidence that almost all of these unusual splits are due to chance alone (virtually no skill), then we must assume that in the future the player with the unusual splits will revert to normal splits in any future time frame. In the case of Eaton that would mean that we would construct an OF projection based on all of his OF play, adjusted for position, and then do the normal adjustment for our CF or RF projection, such that his RF projection will be around 7 runs greater than his CF projection rather than the 20 run or more gap that we see in his past performance.

To examine this question, I looked at all players who played at least 20 games in CF and RF or LF from 2003 through 2015. I isolated those with various unusual splits. I also looked at all players to establish a baseline. At the same time, I crafted a basic one-season Marcel-like projection from that CF and corner performance combined. The way I did that was to adjust the corners to represent CF by subtracting 4 runs from LF UZR and 7 runs from RF UZR. Then I regressed that number based on the number of total games in that one season, added in an aging factor (-.5 runs for players under 27 and -1.5 runs for players 27 and older), and the resulting number was a projection for CF.

We can then take that number and add 4 runs for a LF projection and 7 runs for a RF projection. Remember these are range and errors only (no arm). So, for example, if a player was -10 in CF per 150 in 50 games and +3 in RF in 50 games, his projection would be:

Subtract 7 runs from his RF UZR to convert into “CF UZR”, so it’s now -4. Average that with his -10 UZR in CF, which gives him a total of -7 runs in 100 games. I am using 150 games as the 50% regression point so we regress this player 150/(150+100) or 60% toward a mean of -3 (because these are players who play both CF and corner, they are below average CF’ers). That comes out to -1.6. Add in an aging factor, say -.5 for a 25-year old and we get a projection of -2.1 for CF. That would mean a projection of +1.9 in LF, a +4 run adjustment and +4.9 in RF, a +7 run adjustment, assuming normal “splits.”

So let’s look at some numbers. To establish a baseline and test (and calibrate) our projections, let’s look at all players who played CF and LF or RF in season one (min 20 games in each) and then their next season in either CF or the corners:

UZR season one UZR season two Projected UZR
LF or RF +6.0 (N games=11629) 2.1 (N=42866) 2.1
CF -3.0 (N=9955) -.8 (23083) -.9

 

The spread we see in column 2, “UZR season one” is based on the “delta method”. It is expected to be a little wider than the normal talent spread we expect between CF and LF/RF which is around 6 runs. That is because of selective sampling. Players who do well at the corners will tend to also play CF and players who play poorly in CF will tend to get some play at the corners. The spread we see in column 3, “UZR season two” does not mean anything per se. In season two these are not necessarily players who played both positions again (they played either one or the other or both). All it means is that of players who played both positions in season one, they are 2.1 runs above average at the corners and .8 runs below average in CF, in season two.

Now let’s look at the same table for players like Eaton, who had larger than normal splits between a corner position and CF. I used a threshold of at least a 10-run difference (5.5 is typical). There were 254 players who played at least 20 games in CF and in RF or LF in one season and then played in LF in the next season, and 138 players who played in CF and LF or RF in one season and in RF in the next.

UZR season one UZR season two Projected UZR
LF or RF +12.7 (N games=4924) 1.4
CF -12.3 (N=4626) .3

 

For now, I’m leaving the third column, their UZR in season two, empty. These are players who appeared to be better suited at a corner position than in CF. If we assume that these unusual splits are merely noise, a random fluctuation, and that we expect them to have a normal split in season two, we can use the method I describe above to craft a projection for them. Notice the small split in the projections. The projection model I am using creates a CF projection and then it merely adds +4 runs for LF and +7 for RF. Given a 25-run split in season one rather than a normal 6-run split, we might assume that these players will play better, maybe much better, in RF or LF than in CF, in season two. In other words, there is a significant “true talent defensive split” in the OF. So rather than 1.4 in LF or RF (our projection assumes a normal split), we might see a performance of +5, and instead of .3 in CF, we might see -5, or something like that.

Remember that our projection doesn’t care how the CF and corner OF UZR’s are distributed in season one. It assumes static talent and just converts corner UZR to CF UZR by subtracting 4 or 7 runs. Then when it finalizes the CF projection, it assumes we can just add 4 runs for a LF projection and 7 runs for a RF one. It treats all OF positions the same, with a static conversion, regardless of the actual splits. The projection assumes that there is no such thing as “true talent OF splits.”

Now let’s see how well the projection does with that assumption (no such thing as “true talent OF defensive splits”). Remember that if we assume that there is “something” to those unusual splits, we expect our CF projection to be too high and our LF/RF projection to be too low.

UZR season one UZR season two Projected UZR
LF or RF +12.7 (N games=4924) .9 (N=16857) 1.4
CF -12.3 (N=4626) .8 (N=10250) .3

 

We don’t see any evidence of a “true talent OF split” when we compare projected to actual. In fact, we see the opposite effect, which is likely just noise (our projection model is pretty basic and not very precise). Instead of seeing better than expected defense at the corners as we might expect from players like Eaton who had unusually good defense at the corners compared to CF in season one, we see slightly worse than projected defense. And in CF, we see slightly better defense than projected even though we might have expected these players to be especially unsuited to CF.

Let’s look at players, unlike Eaton, who have “reverse” splits. These are players who in at least 20 games in both CF and LF or RF, had a better UZR in CF than at the corners.

UZR season one UZR season two Projected UZR
LF or RF -4.8 (N games=3299) 1.4 (N=15007) 2.4
CF 7.8 (N=3178) -4.4 (N=6832) -2.6

 

Remember, the numbers in column two, season one UZR “splits” are based on the delta method. Therefore, every player in our sample had a better UZR in CF than in LF or RF and the average difference was 12.6 runs (in favor of CF) whereas we expected an average difference of minus 6 runs or so (in favor of LF/RF). The “delta method” just means that I averaged all of the players’ individual differences weighted by the lesser of their games, either in CF or LF/RF.

Again, according to the “these unusual splits must mean something” (in terms of talent and what we expect in the next season) theory, we expect these players to significantly exceed their projection in CF and undershoot it at the corners. Again, we don’t see that. We see that our projections are high for both positions; in fact we overshoot more in CF than in RF/LF exaclty the opposite of what we would expect if there were any significance to these unusual splits. Again we see no evidence of a “true talent split in OF defense.”

For players with unusual splits in OF defense, we see that a normal projection at CF or at the corners suffices. We treat LF/RF/CF UZR exactly the same making static adjustments regardless of the direction and magnitude of the empirical splits. What about the idea that, “We don’t know what to expect with a player like Eaton?” I don’t really know what that means, but we hear it all the time when we see numbers that look unusual or “trendy” or appear to follow a “pattern.” Does that mean we expect there to be more fluctuation in season two UZR? Perhaps even though on the average they revert to normal spreads, we see a wider spread of results in these players who exhibit unusual splits in season one. Let’s look at that in our final analysis.

When we look at all players who played CF and LF/RF in season one, remember the average spread was 9 runs, +6 at the corners and -3 in CF. In season two, 28% of the players who played RF or LF had a UZR greater than +10 and 26% in CF had a UZR of -10 or worse. The standard deviation of the distribution in season two UZR was 13.9 runs for LF/RF and 15.9 in CF

What about our players like Eaton? Can we expect more players to have a poor UZR in CF and a great one at a corner? No. 26% of these players had a UZR greater than +10 and 25% had a UZR less than -10 on CF, around the same as all “dual” players in season one. In fact we get a smaller spread with these players with unusual splits as we would expect given that their means in CF and at the corners are actually closer together (look at the tables above). The standard deviation of the distribution in season two UZR for these players was 13.2 runs for LF/RF and 15.3 in CF, slightly smaller than for all “dual” players combined.

In conclusion, there is simply nothing to write about when it comes to Eaton’s or anyone else’s unusual outfield UZR or DRS splits. If you want to estimate their UZR going forward simply adjust and combine all of their OF numbers and do a normal projection. It doesn’t matter if they have -16 in LF and +20 in CF, 0 runs in CF only, or +4 runs in LF only. It’s all the same thing with exactly the same projection and exactly the same distribution of results the next season.

As far as we can tell there is simply no such thing (to any significant or identifiable degree) as an outfielder who is more suited to one OF position than another. There is outfield defense – period. It doesn’t matter where you are standing in the OF. The ability to catch line drives and fly balls in the OF is more or less the same whether you are standing in the middle or on the sides of the OF (yes it could take some time to get used to a position if you are unfamiliar with it). If you are good in one location you will be good at another, and if you are bad at one location you will be bad at another. Your UZR or DRS might change in a somewhat predictable fashion depending upon what position, CF, LF, or RF is being measured, but that’s only because the players you are measured against (those metrics are relative) differ in their average ability to catch fly balls and line drives. More importantly, when you see a player who has an unusual “split” in their outfield numbers, like Eaton, you will be tempted to think that they are intrinsically better at one position than another and that the unusual split will tend to continue in the future. When you see really large splits you will be tempted even more. Remember the words in this paragraph and remember this analysis to avoid being fooled by randomness into drawing faulty conclusions, as all human beings, even smart ones, are wont to do.