The limits of baseball

In calculus there is a concept called a limit. As described by Wikipedia:

the concept of a “limit” is used to describe the value that a function or sequence “approaches” as the input or index approaches some value.

Many measures of athletic performance have a limit. Every few years someone runs the mile more quickly than anyone had before. But while we are continually running the mile faster, it would be unthinkable to run the mile in negative time, or even no time. This means that there is a lower bound which our mile times are approaching, but won’t quite reach. It’s hard to say exactly what that limit is, or when we will reach it, but we know it exists.

We can also observe this phenomenon in baseball; pitchers throw much harder than they used to just a few years ago. Most estimates have the average fastball velocity as increasing more than 1 mph in the past few years. While it’s possible that teams are simply emphasizing velocity more than they used to, it also seems likely at least some of this velocity increase is real. But at some point, pitchers will stop throwing harder; without this upper bound, baseball players would eventually average infinite miles per hour.

I firmly believe that there is a higher level of competition in the major leagues now than ever before. Players are bigger and stronger, pitchers throw harder, and teams are smarter. As Ben Lindbergh wrote, many teams now employ intelligent, “sabr-savvy” GMs. This makes any discussion of “would a star in the past be a star now?” problematic. Thanks to ESPN broadcasts, I used to listen Joe Morgan occasionally engage in this discussion. He used to say that stars in the past could be stars now, but current stars may not have been as great in the past. Essentially, Morgan implicitly argued that players used to be better. His reasons, if I remember correctly, used to focus on how ballparks are smaller now, and that players are protected more.

I ardently disagree. Say we estimate that in the past 10 years, pitchers are on average capable of throwing 1 mph harder than they were before. If we extrapolate this rate, then 50 years ago pitchers threw on average around 86 mph, which seems reasonable, although I wasn’t around then. Baseball is a game in which every small change can have a large impact. Just hit the ball a fraction of an inch off the sweet spot, and you may weakly ground out or pop out. It stands to reason, then, that an increase from 86 to 91 mph is of an extreme magnitude.

We have seen evidence that the level of competition in the majors has improved a lot, both in terms of players and in terms of the evaluation methods used. And despite our tendencies to cast star athletes as immortal, we know that they are human, bounded by flesh and bones. If baseball continues to improve, then at some point, all players will be nearly equal in talent and all teams will employ optimal strategies—the limit.

What would such a world look like? And what does baseball today tell us about what it would be like?

Pitchers would certainly be different. In recent times we have seen pitchers model themselves after Roy Halladay; both Charlie Morton and Brandon McCarthy significantly revamped their mechanics and repertoire to imitate the Phillies right hander. And part of the changes they implemented have become more widespread in baseball. Both pitchers focused on developing a cutter and two-seam combination, and with good results. The cutter especially is a pitch that has increased in usage in recent years, and it’s not hard to see why. The cutter is most often used in two ways; like a fastball, or a slider. When used like a slider, its benefits are especially clear. Sliders are notorious for causing pitching injuries, while cutters are generally considered to be less strenuous. And when used as a fastball, the cutter helps to keep batters guessing with a similar velocity pitch.

The Roy Halladay model may grow in popularity. It doesn’t require a pitcher to have very good stuff, but to be able to generate ground balls by throwing a cutter and two-seamer to each side of the plate. His mechanics are also considered very clean, and should be able to be imitated by many pitchers. But of course not every pitcher would be the same. That doesn’t make sense for two reasons. Firstly, unless all pitchers are identical anatomically in the future, different pitchers have different optimal sets of mechanics and repertoires. Secondly, it would be a terrible decision from a game theory perspective, offering no variety in looks to the batter.

Change-ups may also grow in popularity. Teams may decide that they could save a tremendous amount of resources by eliminating injury-inducing sliders, which would help them get more innings out of their starters. And while much less strenuous, change-ups are not necessarily any less effective; last year two of the pitches with the highest whiff rates (swing-and-misses pitches) were Ryan Madson‘s and Cole Hamels‘ change-ups. Change-ups have another big advantage as well; most have a very limited platoon split, while most sliders have significant platoon splits. Of course change-ups are not perfect. They largely rely on deception be effective; if the batter recognizes the pitch, it’s basically just a slow fastball. Tt is a “feel” pitch, and given the obvious advantages, would probably be much more popular today than it actually is if it were easier to throw effectively.

But to be honest, I have no idea what the future will bring. Maybe pitchers will throw a two-seam, cutter and change-up with greater frequency than they do now, or maybe everyone will just throw knuckeballs. But the recent proliferation of sabermetrics in the management styles of major league teams serves as a bit of reminder of this ominous limit in the future. We can see a limit where, because all teams are so similar, major league baseball is not much more than a complex coin flip; a true game of inches, if it isn’t already now. How far away is this limit and when we will get there? It’s hard, if not impossible, to know. But we are certainly approaching it.

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Comments

  1. tc said...

    Well, where to begin… I guess with the general approach which is to emphasize the physical aspects of the game,which are of course the part that sabre metrics can most easily measure. I suspect that what Joe Morgan was contending was that modern players weren’t mentally tough enough to be as successful in his era. One frequently hears from older players how the next generation is not as “tough”. Morgan probably would have mentioned pitchers like Bob Gibson and Don Drysdale, guys who snarled and threw inside. Another part of the same equation, something you frequently hear from older players is the dedication and interest in the game. In the “old days”, players sat in the clubhouse, or on the trains, and talked baseball. One frequently hears that modern players, if they are talking to each other at all, are more likely to be discussing opportunities outside baseball, that is, when they are not already out the door or plugged into their favorite device. What this supposedly leads to is a generally less mentally sharp, or “tough” ballplayer. What is baseball, 80-90% mental? So as to your question as to baseballs limits, I doubt any game, especially baseball, could ever be measured closely enough to predict real limits, and I doubt that in any real general sense we’ll ever be able to realize the games limits. And of course, this does not take into account how the games rules and equipment have changed over the years. Every slight improvement in equipment changes overall performance and strategy and thus stats.It frequently changes the pitchers and batters approach to the game. And what of the juiced ball? I have always maintained that the juiced ball had more to do with McGwire, Sosa and Bonds (and all of those lesser hitters who suddenly became sluggers) than the “juice” that they were injecting. Just like after the Black Sox scandal, MLB looked to inject interest in the game after the disastrous strike. Bye-bye baseball, it’s out of here. Finally, as to the pitches that are currently in vogue, I remember when the splitter was all the rage, right now the cutter is hot. That’ll change, just as batters approach to pitchers who throw it will or already have changed. And maybe the fastball is currently 1 mph faster, remember the early radar guns weren’t as accurate as todays, but generally speaking the harder a pitcher throws a ball the less accurate it is likely to be. If there is an emphasis on heat today, it could be a result of better physical training or it could be a general decrease, “un-juice?”, in homeruns, and perhaps the temerity to go right at the batter because of the lowering repercussions. You are right, of course, that there are limits, but I don’t believe we will ever have to worry about them, I don’t believe we will ever approach baseballs limits because humans play the game and set the rules and we are imperfect. One of the great things about Baseball are these discussions, it is the great talking game, better than any other.

  2. Todd Boss said...

    Completely agree.  Morgan is a fool (no surprise there; we’ve been listening to him call games with fellow fool Tim McCarver for years).

    Babe Ruth, were he to get into the batter’s box today, probably looks at a modern day pitcher with a low 90s slider and mutters to himself, “I can’t hit what I can’t see.”  Which is why we always need to measure players in the context of their era, using such adjusted stats.  But we already knew that right?  Why havn’t we had a .400 hitter since the 40s?  Because the game has changed radically, hitters face specialized relievers and may get 5 at bats against 3 different pitchers in a game instead of getting a 4th and 5th at bat against a hurler with his pitch count in the 120s and working on fumes.

    Furthermore, If you look at line-ups from the 40s and 50s, the last three batters in most lineups were as close to automatic outs as the pitcher was.  Now we have shortstops and 2nd baseman who hit 30 homers.  We have integration in the game, with ball players from places far and wide who have done nothing but increase the general talent level of the game every year.

    I’ve often wondered this fact; lore tells us that Bob Feller was the hardest thrower of his era.  But I suspect now that he may have “only” been a mid-90s thrower.  Why?  Because the average fastball of his era was (as noted) probably only around 85-86mph.  If Feller was 15% faster than the average fastball, by context someone 15% faster than the current average of 91mph is throwing 104-105… or roughly the max of what we’ve seen a modern day thrower pitch.  Makes sense to me.

    (sorry for rambling, long comment)

  3. tc said...

    Todd, I don’t know if Morgan is a fool, I never listen to him, but most “old” players tend to idealize the era they played in, especially against the next generation. I’ve been listening to that kind of thing for 60 years now, it’s always the same. As to Feller, during his peak he was throwing 300 innings per season. He was above or just slightly below that for 5 seasons. Nolan Ryan pitched 300 innings once and was at 299 one other year. And he didn’t do it consecutively. Reason tells us that if Feller were trying to throw the ball 100 mph he wouldn’t have had an arm left. Everything is relative, I think Einstein said that, and if every starter is trying to go 9 innings then their heaters have to be dialed down. So when they say Feller’s fastball was the fastest of his era, that’s all it means. That doesn’t demean his performance or enhance Ryan’s. Imagine Ryan trying to go 9 every time out, no matter what he had that day. One other thought regarding trying to determine baseballs limits. Until 1969, the mound could be as high as 15 inches, then it was lowered to 10. Think that didn’t contribute to a pitchers fastball? Or his downward breaking pitches? As you said, you can only go, era by era. Let’s just say to be the best in any era, you had to be something.

  4. tc said...

    One other thought in this notion of trying to build in expectations based on past performance. Shifting to another sport, when Michael Jordan began his NBA career many veteran players remarked at his high energy performances that if he kept that up his career would burn out very quickly. That was based on the way they had to play an 80 game regular season. So much for predictions.

  5. ChuckO said...

    I don’t know how you can conclude that pitchers threw on average at 86 mph fifty years ago. Even if one accepts your claim that they throw one mph faster than they did ten years ago, that does not necessarily mean that they threw five mph slower fifty years ago. In fact, what evidence we have would tend to suggest that the hardest throwing pitchers threw at pretty much the same velocities as modern-day hard throwers. Check this out for examples, http://www.baseball-almanac.com/articles/fastest-pitcher-in-baseball.shtml

    Note that the so-called speeding motorcycle test had clocked both Walter Johnson and Bob Feller (obviously not in the same year) in the 98-99 mph range. Such a test is not as conclusive as modern-day radar, but it’s suggestive.

    That said, pitchers now probably throw harder on average than they did fifty years ago, for the reasons that others have stated above, and because baseball currently draws from a larger talent pool than it did back then.

  6. tc said...

    I’m not a mathematician but I’m fairly certain that in any particular set of stats the standard deviation fluctuates from one period of time to the next. Since a standard deviation in any case needs interpretation and additional facts, even in one category, fielding avg. for example, what the standard deviation would tell you would not be the current talent level of fielders. Even an accumulation of stats would only tell you what the researcher “thought” were key samples. End result would be a very subjective standard deviation. Since it seems that the commentary on this theme appears to have run out it is unlikely that your question will be answered definitively, or even semi-definitively here, but I would love to hear from someone who thinks they can sum up the relative talent levels of baseball throughout history with a standard deviation. What I can say from experience is this. I have been playing and coaching baseball for over 50 years and the basic skill level of the current crop of 12 to 13 year olds is by far the worst I’ve ever seen. Kids are in little league that can’t catch, throw or know much of anything about the game. I fear that in 15 to 20 years the “American game” will no longer be so. Electronics is for sure the cause and baseball will suffer for it. 20 years from now you won’t need a standard deviation to see what has happened to the game.

  7. bob b. said...

    One thing I’ve been wondering about is that for many years the general trend in baseball stats (well, the distribution of said stats I suppose) has been for a DECREASE in the standard deviation (well, if i’m remembering correctly) but recently I believe I’ve heard that it is INCREASING. And back before it was increasing I remember reading that it was decreasing because of the INCREASE in skill (overall). So… I was wondering if the increase in standard deviation (assuming this is true) means that the overall talent level is decreasing?

    So I guess officially I’m asking two main questions:
    1) Is is true that the standard deviation is increasing after years of decreasing?
    2) If it is, does this suggest a decrease in overall talent?

  8. David P Stokes said...

    While I don’t doubt that the overall level of play has generally increased over time, I’m don’t necessarily buy that pitchers on average are throwing harder than 50 years ago.  Pitchers nowdays don’t use full windups and really high leg kicks as much as pitchers in the past, and while I’ll admit that I’m not an expert on the matter, it would seem that those things increase velocity somewhat.  Also, throwing harder is better, all else being equal, but everything eles isn’t necessarily equal, which is why Steve Dalkowski never even made the majors, much less the Hall of Fame.

  9. Paul E said...

    Men of merit exist in every generation, but mankind in general prefer the meritorious of their own generation…..

    1)  The DH sucks…let’s get the 38 -43 year old hangers-on and relics off the field

    2) The Selig era – expansion, expanded playoffs, and steroids – sucks. I witnessed in back-to-back visits to Camden Yards in the mid-to-late 1990’s the two longest 9 – inning contests in history thanks to intentional walks andching around 30 HR middle infielders on roids

    3) It all went downhill when Reggie Jack-off-son stood in the batter’s box and watched his Detroit All Star game HR nearly clear the roof and no one stuck it in his ear in the next AB

  10. Marvin Leibowitz said...

    A very interesting article by Josh Weinstock .  Congratulations on very interesting topic.  The limits of baseball.  The idea of a limit, or wall has been around for quite a while.  There is no doubt a wall, but Josh reaches, I think, a very wrong conclusion.  For Josh, and for all interested in this concept I refer you to an
    article firstbpublished in 1986, written by the great Stephen Jay Gould, paleontologist, evolutionary biologist, and historian of science.  His great passion was baseball.  His only genetic disorder was a that he was 2nd generation Yankee fan.  He wrote a great number of baseball articles one of which was entitled “Why No One Hits .400 Anymore” in which he gave his rationale for predicting that there would be no more .400 hitters. Included in this article was his detailed reasoning behind his theory of the “wall” or “limit”.  The article was more recently in his 2003 book entitled “Triumph and Tragedy in Mudville” A lifeling passion for baseball.  Every true baseball fan would love this book.

  11. Marvin Leibowitz said...

    Congratulations to Josh Weinstock on a very interesting topic.  The limits of baseball.  The idea of a limit, or wall has been around for quite a while.  There is no doubt a wall, but Josh reaches, I think, a very wrong conclusion.  For Josh, and for all interested in this concept I refer you to an article published in 1986, written by the great Stephen Jay Gould, paleontologist, evolutionary biologist, and historian of science.  His great passion was baseball.  His only genetic disorder was that he was 2nd generation Yankee fan.  He wrote a
    great number of baseball articles one of which was entitled “Why No One Hits .400 Anymore” in which he gave his rationale for predicting that there would be no more .400 hitters. Included in this article was his detailed reasoning behind his theory of the “wall” or “limit”.  You can read this article which is one among many in his book the “Triumph and Tragedy in Mudville – A lifeling passion for baseball”.  Every true baseball fan would love this book.  Two other great articles in the book include one about William Ellsworth “Dummy” Hoy, a deaf ball player, and a superb analysis in which he lays out the case for what he declares is the greatest feat in baseball history, Joe DiMaggio’s fifty-six game hitting streak.

  12. Norman said...

    “I have always maintained that the juiced ball had more to do with McGwire, Sosa and Bonds (and all of those lesser hitters who suddenly became sluggers) than the “juice” that they were injecting. Just like after the Black Sox scandal, MLB looked to inject interest in the game after the disastrous strike. Bye-bye baseball, it’s out of here.”

    I think there is a lot to this. In cricket (a sport I only casually follow) the governing bodies have been much more conscientious about not monkeying the ball and more resistant to rule changes. What you see there is that there has been no great leap forward in athletic ability and much more consistency of results. In fact, the greatest batsmen of the game, Donald Bradman, holds the batting record with a career test average of 99.74, nearly 40 runs higher than his closest competitor, and he played from 28-48. http://stats.espncricinfo.com/ci/content/records/282910.html

    Clearly, he was a freak of nature, every generation will have its share of these, and they are for the most part comparable. Our athletes could play with the greats of the past, an the greats of the past could have played today.

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