Smart Baseball

by Keith Law

  The range of slugging percentages, however, ran from .320 (Alcides Escobar, Kansas City Royals) to .649 (young Mr. Harper, again). That’s a span of 329 “points” of slugging from high to low, compared to 204 points for OBP. A similar span covering 82 percent of hitters around the middle of the slugging distribution would run from .358 to .540, about a 142-point swing compared to the 100-point swing I chose when looking at OBP. These two ratios operate on different scales, because they’re measuring different counting events on top and dividing them by different units on the bottom, with OBP’s units by definition equal to or larger than the quantity in slugging. I love pesto, and I love hot fudge, but I can’t just mix the two together and pretend I’ve only kept the best of both sauces.

  If your memory is particularly astute, or you’re about half my age, you may have thought of the way you can in fact add two fractions with differing denominators: finding the lowest common denominator of the two fractions. You do this by multiplying each figure by some fraction equivalent to one, and then adding the numerators with the new denominator staying in place. If you were to do that with on-base percentage and slugging percentage, you’d probably get a more telling number, but it would lose the ease of calculation of OPS, and the final number wouldn’t accurately weight a hitter’s ability to get on base.

  All this talk of fractions and denominators only speaks to part of the problem with OPS. The larger, more looming issue with OPS is that all bases achieved are not created equal. The hardest thing to do in baseball is to get to first base, and on-base percentage measures only that: how often the hitter, or the team’s hitters, got to first base safely—that is, did not make an out at the plate. Doing so is difficult, of course; the aggregate on-base percentage of all MLB hitters in 2015 was .317, meaning that 68.3 percent of the time all hitters came to the plate (excluding sac bunts and a few other rarities), they either made an out or did something that should have resulted in one or more outs but was mishandled by a fielder. Once that hitter is out, it’s over. He’s dead, Jim. He’s not coming back.

  Compare that to the question of the extra base once a runner has already reached first. Almost exactly one in three hits results in extra bases, but even a batter who singles can still be advanced by subsequent events, whether they’re more hits, walks, or even certain field outs. It’s much harder to get to first base than it is to advance to bases beyond that.

  If you recall the run expectancy table from chapter 5, you can see the specific boost from getting to first base dwarfs the gain from each additional base after that. Here’s the same table, reorganized to highlight what each additional base is worth:

  Expected Runs for the Remainder of an Inning from a Specific Base-Out State.

  Aside: You’ll notice that little blip in the bottom middle, where reaching third base from second with one out is the most valuable thing a hitter can do other than reaching first base to begin with. With one out (or zero), that runner can still score on many kinds of outs in play, which isn’t true with two outs. This is why the attempt to steal third base with one out is more valuable than doing so with zero outs, when any number of subsequent events might score that same runner from second, or with two outs, when you’re ending the inning for only a tiny potential gain.

  For any specific number of outs, getting to first base is the most valuable thing a batter can do. Stretching a single into a double or a double into a triple is still valuable, but the best thing the batter will do once he leaves the batter’s box is step on first base safely. Extra-base hits have additional value, which I’ll explore more when I discuss how teams think about and measure offensive performance in the chapter that explains linear weights, because they can score more runners that are already on base than a single can. The value of extra bases is not enough to make slugging percentage as important as OBP.

  Because not all bases achieved are worth the same thing, these little tangents add up to one key point about looking at on-base percentage and slugging percentage independently, and that you can’t forget when looking at OPS: one more point of OBP is worth more than one more point of slugging percentage. (A point here refers to .001, or one-thousandth, equal to reaching base one more time in 1,000 PA or accumulating one more total base in 1,000 at bats.) In Moneyball, still an essential read for anyone looking to understand more about how front offices are thinking about the game even today, author Michael Lewis quotes Paul DePodesta, at the time an executive for the Oakland A’s, as saying that a point of OBP was worth three times as much as a point of slugging, if not more. The precise value is lower than that, but he was directionally correct. If the baseball gods told you, the GM of a major-league team, that you could give one player in your system a potion that would grant that player the ability to raise his OBP by 10 points or his slugging by 10 points—or even 15 points—you’d take the OBP potion every single time.

  That should make the answer to the question at the start of the section obvious: you take the guy with the .400 OBP and .400 SLG over the guy with the .300 OBP and the .500 SLG. The first guy, Johnny Walksalot, will reach base 60 more times in a typical 600 at bat season, meaning he’ll make 60 fewer outs, than the second guy, Tommy Hackenstein. Hackenstein compensates with 60 extra bases—say, 30 more doubles and 10 more homers, or no more doubles and 20 more homers than Walksalot. But the cost of those extra bases is those 60 outs, and you would not trade 60 outs to get 60 more bases, just as you would not accept a 50 percent caught-stealing rate from a baserunner. It can seem counterintuitive if you’ve never thought about hits or bases having a cost before, but the cost in outs is real—the great Baltimore Orioles manager Earl Weaver always preached that outs were precious, since your supply of them is limited—and understanding that cost allows you to see when a player who seems to produce more stuff is actually less valuable.

  Yet OPS would tell you that Walksalot and Hackenstein are equally valuable, or equally productive, because each has an OPS of .800. The stat obscures useful information. So why do so many people use it?

  One obvious reason is that it’s easy. Everyone wants a single number that sums up a player. It’s much easier to say that Joey Bagodonuts is a .900 OPS guy than to start breaking him down in two or three different numbers, even though the latter approach gives you a more complete picture of the player’s abilities. And I can tell you that when discussing players on live radio or TV, you don’t often have a lot of time to make your points, so a shorthand like OPS is appealing (even though I don’t use it) because in two seconds you’ve slapped a number on that player to say he’s good or he’s bad.

  But, in spite of all the objections I raised above, the truth about OPS at the team level is that the damn thing works: it correlates better with team runs scored than OBP or SLG do alone. Where OBP’s coefficient of correlation to runs per game is .893, and slugging’s is .846, OPS’s is 0.914. It’s a modest improvement, but it is indeed better. We can fine-tune that to crank up the correlation even more, and we will do that in a later chapter to get a more precise way of valuing hitter performance, but for a quick and dirty measure of team offense, OPS does the job—in ugly fashion, yes, but it does it.

  Where OPS fails us is at the player level, yet that’s where you’re most likely to see it used—by fans, writers, even occasionally by a team executive discussing a player in the media. A player can post an .800 OPS and be a below-average hitter; he can post a .750 OPS and be an above-average one. Now, if a player has an 1.100 OPS or a .500 OPS, that’s probably all you need to know about him—the first is a star and the second one had better be a pitcher—but most of the players you’re going to want to know about fall somewhere in the great middle.

  The allure of a single number that sums up a player’s performance is tough to ignore, something I’ll return to in the discussion of WAR (Wins Above Replacement), but in this particular case you’re better off with two numbers, OBP and slugging, separately than you are with one.

  10

  wOBA/WRC:

&
nbsp; The Ultimate Measure of the Hitter (Until the Next One)

  People want a number. They don’t want lots of numbers, because that’s too many numbers. They want one number that answers the question. That’s a mixed bag, because one number destroys all nuance. It doesn’t show your work; it just gives the answer, without context. You could apply this to many spheres of life, and it’s no less true in baseball than anywhere else. Fans and writers want to point to a single number that sums the whole player up. He’s a 20-game winner. He’s a .300 hitter. Incomplete picture be damned, let’s just slap a number on that fella and call it a day!

  A single number does actually help us, because it gives us a quicker means of comparing multiple players, and eventually a team has to decide what a player’s production is worth in one dollar figure. The key is to work with numbers that capture everything a player does and weights each of those things accordingly. I’ve mentioned linear weights and Batting Runs as the way to total up the values of all a hitter’s contributions over the course of some period of time—including deducting value for the outs he makes—to give us a bulk total figure. This hitter produced 55 runs of value in 2015; this other hitter produced 46 runs of value; therefore, if you didn’t catch it already, the first hitter was a more productive hitter.

  Bulk totals, also called counting or cumulative stats, are not scaled for playing time; if Joey Bagodonuts played 162 games and Jimmy Ballplayer only played 110 games, but each produced 50 runs of value by his hits, walks, extra bases, and so on, then Jimmy was the better player on a per-game basis. Looking strictly at the bulk number doesn’t give us that information, so our desire for the One True Number leads us astray again.

  While the flaws in OPS on a player level are clear, you can at least understand the intention: to take two common numbers and combine them to get the best of both stats. There are many numbers floating around that attempt to provide a “one number” answer for hitters on a rate basis, something like batting average, maybe even that looks like batting average, but that includes everything we’d want to know about a hitter’s performance. For some time, we had runs created per 27 outs, which was wildly imprecise, followed by Equivalent (now True) Average from Clay Davenport and Baseball Prospectus, and VORP (Value Over Replacement Level) and VORPr from Keith Woolner . . . and so on. There was even Total Average, developed by Washington Post writer Thomas Boswell, a rather stunning bit of innumeracy that just added a bunch of stuff together without regard for whether these things actually should be added together, then divided it by some other stuff without regard for common decency. It had the veneer of legitimacy but, as any computer programmer will tell you, garbage in yields garbage out. None of these ever really caught on, and even the stats I like to use for this purpose have failed to make much of a dent in the public discourse.

  The best of these new rate stats is called wOBA, or weighted on-base average, and was created by sabermetrician Tom Tango to provide a rate on the same scale as OBP that considered all batter events: hits, extra bases, walks, times hit by pitch, and outs. The specific coefficients—that is, the weights assigned to each event—vary slightly by year, depending on the specific offensive environment, but the overall scale that measures wOBA is always the same.* If you look at a hitter’s wOBA and see a number that would make a good OBP, then the hitter has a good wOBA and thus is having a very productive season at the plate. A hitter with a .400 wOBA is extremely productive; a hitter with a wOBA under .300 had better be a great fielder—or a pitcher.

  To give you a sense of how wOBA works in the real world, here are the leaders in wOBA for 2015 for hitters with enough plate appearances to qualify for the batting title:

  Harper was the unanimous MVP in the National League and posted one of the best offensive seasons in major-league history; the American League MVP, Josh Donaldson, was only sixth in the majors in wOBA—behind both Mike Trout and Miguel Cabrera in wOBA—but he boosted his value with strong defense and getting help from the tired old misbelief that an MVP should come from a playoff team.

  And now, the worst hitters in 2015, also by wOBA:

  Owings, Segura, and Escobar are all shortstops, with Owings and Escobar considered above-average defenders. Ramos is a catcher, and Taylor, who lost his job after the season, is a center fielder. It’s not a coincidence that hitters this bad all play in the middle of the diamond, where it’s harder to find players capable of playing those positions; a corner player with a sub-.300 wOBA shouldn’t last very long, because it’s easier to find players who can handle those positions and can hit a little more capably. In 2015, nineteen players qualified for the batting title and posted wOBAs below .300; only three played corner positions, and two of the three lost their jobs before the following season.

  The main deficiency in wOBA is that it is not park-adjusted—that is, it does not make any adjustment for the ballparks in which the hitter played. A wOBA of .350 in Coors Field in Denver, a tremendous hitter’s park at an elevation of 5,200 feet, is not the same as a wOBA of .350 in Petco Park in San Diego, the majors’ best pitcher’s park, located a mile below sea level (latter figure may be approximate). This matters because in a park where offense is harder to come by, a positive offensive event is worth more, since it takes fewer runs to win a game.

  Fangraphs offers a park-adjusted analogue to wOBA called wRC+, weighted Runs Created, which takes a hitter’s offensive contributions, adjusts them for park, compares them to the league average, and produces a number around 100: if a hitter’s offensive value is greater than league average, his wRC+ will be higher than 100, and if it’s lower than the league average, it’ll be lower than 100. (The league averages in this case exclude those of pitchers hitting.) The two rate stats are similar, both using the same linear weights model underneath, but wRC+ adds park adjustments while creating a less intuitive, nonlinear scale.

  Although comparing any player’s production to the league average is useful in an industry where “average” is extremely valuable and the language of evaluation has always included references to above- or below-average tools or players, I think wRC+’s scale can be misleading. Some is simple arithmetic—a player who is twice as productive as the league average will have a wRC+ of 200, 100 points above the average, while a player who is half of league average will have a wRC+ of 50, 50 points below the league average. But the bigger problem is that value in baseball is nonlinear—that is, a player who produces twice as much as another player is not simply “worth” twice as much, because roster spots are limited.

  Mike Trout’s production at the plate alone has been worth about 53 runs a year above average in his career through 2016. If you could trade Trout for two players who have been worth 26.5 runs per year apiece—assuming for the moment that other stuff, like salary and age, are equal—would you do it? Looking just at the baseball rationale, you shouldn’t. Getting those 53 runs of production out of one spot on your twenty-five-man roster is better than getting 53 runs out of two spots, because Trout’s production frees up another roster spot for you to go find another productive player. If roster spots were unlimited, then player value might be linear—that is, the player who produces twice as much would probably be worth twice as much, in baseball terms or in financial terms. But with roster spots a scarce resource, getting more production out of a single roster spot is particularly valuable because it gives you more ways to improve in other roster spots. This, incidentally, is why fan- and writer-proposed trades for superstars are nearly always terrible: they assume that throwing five or six names at the Angels (for Trout) or Nationals (for Bryce Harper) would simply overwhelm the team with the superstar into acquiescing. It’s almost impossible to get fair value back in a trade for the best player in baseball, and if you could, the other team probably shouldn’t do it.

  To return to my issue with wRC+, it’s the best publicly available, park-adjusted rate stat for hitters . . . which makes it sound terrifying, but in fact, that’s the number we want if we’re trying to get a sense of how go
od a hitter was over a season or the year to date. Add up the values of what he did, compared to the outs he generated, and adjust it for the environment(s) in which he played.

  Either of these stats would suffice as the One True Number for hitters, assuming you’re just looking for a rate statistic that would fill the role since vacated by batting average. “He’s a .300 wOBA hitter” doesn’t have the same ring to it—I’m still not really comfortable with saying “wobba” instead of just spelling it out, because it’s a good way to sound like an idiot—but it answers the question of how good a hitter the player is. I happen to prefer wOBA, even without the park adjustments, because the scale is more intuitive to me and to my regular readers, although I rarely present it without also providing the triple-slash line of average/OBP/slugging. You could also use wRC+ if the scaling doesn’t bother you and you prefer a park-adjusted number. If you want that one number to sum up a hitter’s offensive rate of productivity, either of these would fit the bill.

  11

  ERA and the Riddle of Pitching Versus Defense

  Let’s get back to the pitcher, evaluating whom has been at the heart of many statistical advances and sabermetric debates, inside and outside of front offices, over the last twenty years.

  We’ve dispensed with the anachronism of pitcher wins and the two-steps-back “progress” of the save rule, but we have to judge pitchers by something. Why not earned run average (ERA), that old standby of baseball cards and on-screen graphics that complements won-lost record to try to give us a more complete picture of the pitcher’s performance? His job is to avoid giving up runs, so a stat that reflects how many runs he gave up per game should be good, right?