Relating Batting Average and wOBA
Every baseball fan can understand batting average. Surely, if you ever played little league, you would occasionally find yourself computing your game batting average mid-game. Every team would have somebody keep everybody’s batting average. It’s fun, because it’s easy to understand and it’s easy to calculate. It tells you one thing – did the batter get a hit or not – and it does it in a very simple way – it’s pure and simple division. It doesn’t make you include bunts or walks like OBP, it doesn’t make you keep track of total bases like SLG. It certainly doesn’t make you memorize constants for some complicated multinomial expression like wOBA.
This simplicity is what makes it such an easy tool for analysts to use, whether they’re armchair analysts watching the game with you in the living room or on the air for Baseball Tonight. Of course, simple doesn’t always mean better. Guys like Bill James, Rob Neyer, Pete Palmer, and all our other sabermetric heroes have been letting us know this since the 1970s. That is not to say that batting average is a completely useless stat – it just doesn’t correlate with run scoring nearly as well as OBP, SLG, or linear weights.
For those less familiar with wOBA, let’s take a look at results from 2009. The following graphic shows batting average on the horizontal axis and wOBA on the vertical axis, so we can see how the two are related.
The correlation coefficient (r^2) for the regression line shown above is .36. Briefly, that means that although there is a positive correlation between the two statistics, it is not very strong. As we see with guys like Carlos Pena, having a low batting average doesn’t necessarily lead to a low wOBA. Conversely, with guys like Ichiro, having a high-percentile batting average doesn’t necessarily lead to a similarly high-percentile wOBA. That isn’t to say that it doesn’t help – getting a lot of hits will increase a player’s wOBA just as it increases any other offensive statistic.
What sets players apart isn’t whether or not they get hits, of course. What sets players with the same batting average apart is (a) what they do with their hits – SLG, or more aptly measured by Isolated Power (ISO, SLG-AVG), and (b) their ability to take walks – OBP, or more aptly measured by Isolated Discipline (OBP-AVG). That’s why Carlos Pena (IsoP – .310, IsoD – .129) is a better hitter than Yuniesky Betancourt (IsoP – .106, IsoD .029) and Brandon Inge (IsoP – .176, IsoD – .084), and why Albert Pujols (IsoP – .331, IsoD – .126) is the best hitter in the game.
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Love what you’re bringing to the table, Jack. Just one question – mathematically, does IsoD make any sense? You’re subtracting two numbers with different denominators, and I’m not sure what you get means anything. I get that, generally, the larger the OBP, the more patient the hitter, but it doesn’t really relate directly like that, right? If a guy, in 600 PA, has 100 hits and 100 walks, he’s got a .200 BA and a .333 OBP. If he’s got 150 hits and 100 walks, he’s got a .300 BA and a .417 OBP. Same number of walks in the same number of PA, but his IsoD changes based on the number of hits he got.
Yeah, I wanted to work with IsoD before, but realized that the fact that they have different denominators makes it so that it doesn’t “isolate” anything like ISO does (ISO being essentially Extra Bases/AB).
Jack, of course in principle I agree that walks are good, the emphasis should really be on OBP. If you have a high OBP, it doesn’t really matter how you do it. It’s just that for good OBP’s (let’s say .360), a number of hits plus walks is a lot easier to attain and sustain than an equal number of just hits, so it’s really rare to see guys like Ichiro who don’t walk and get great OBP’s.
It’s a nitpick, because again, I know walks are important, but I think the emphasis should be to “get on-base more,” however you do it, rather than simply “get more walks.”
I agree with Michael that the focus of too many is on walks than on getting on base more. Walks are important in relationship to how often the batter strikeouts but I think too many people short-hand “Walks good” and don’t understand the nuance that, looked at in an isolated basis, a hit beats a walk anyday.
I’ve been thinking about this instead of listening in class – as a commenter below pointed out I kind of like the idea of H/PA being used to calculate IsoD.
Also, maybe I didn’t stress enough that these are both tools that should be used to separate players with similar batting averages. Clearly, it’s easier for a player that hits .300 to have a better OBP than one with .200 regardless of IsoD, and same with SLG/IsoP
A nitpick – r^2 is the coefficient of determination; the correlation coefficient is r.
What if you were to divide hits/PA for a “true” batting average, or whatever you want to call it and then subtract that number from OBP?
To use the example above:
600 PA player gets 100 hits and 100 walks, “true BA” of .167 minus .333(OBP) to get a ISOd of .166
600 PA player gets 150 hits and 100 walks, “true BA” of .250 minus .417(OBP) to get a ISOd of .167
That works, the .001 difference is just from rounding.
I actually had this idea in the forums yesterday, had never seen the stat before until just now, though I highly doubted I was the first to think of it.
http://www.fangraphs.com/forums/topic.php?id=3299
We already have that… it’s BB%.
Yea…I thought of that after I got back to work, it is basically the same, unless a player has a habit of getting HBP a lot.
Hehe, yeah.
I actually thought of that H/PA thingy too for getting IsoD right, then realized we were just re-inventing the wheel.
Am I missing something? I didn’t think bunts were included in OBP, just sac flies.
I’m sure he means sacrifice bunts, and yes, they are included as a plate appearance.
I’m hoping this person has been banned already… removing their comments would be nice as well.
We all know it’s not really joser.
Jack – I’m liking your stuff. Keep it up!
To explain why batting average and hits are pointless “metrics” by which to measure a hitter’s abilities and run scoring, we must consider first what is a hit. To put it most simplistically, a “hit” is a ball put into play which is not converted into an out. The question is not what is a hit, but why is it a hit, which illustrates the futility of the metric. Does the hitter truly earn his “hit?” In theory, yes. A ball smoked to the gap is clearly an “earned hit.” But why was the hit earned? Where is this “gap?” Is it a fix position? No.
A hit is simply this: a ball put into play that slips through the defensive positioning and ability of the fielders. Are either of these factors within the control of the hitter? No, not really. The difference between a double to the gap or a caught liner is simply “was the shift on?” A hit up the middle versus a double play can be a question of whether or not the shortstop was holding the runner at second on. The difference between a liner down the line and a caught ball is whether or not Ryan Howard was playing 1B or DH in an interleague game.
Clearly the hitter controls or exercises some control over the direction of the ball and the strength of contact by “timing” and “squaring” the pitcher’s offering, but once the ball is in play, whether or not that balls is a “hit” is almost entirely depending on the positioning and ability of the defense. The glaring exception to this rule, of course, is the home run. That is a “hit” truly and 100% earned, although fielders can even steal those sometimes.
In short, hits are not something a player particularly controls. There is a lot of luck involved and over long enough sample sizes, luck tends to average out. It is not shocking, therefore, that over 162 games against 20 or so teams, a player’s collective “balls in play” (BIP, non-HR balls put into play) which are converted into hits tend to fluctuate between a normative band of numbers (usually between .290 and .310, though a player’s BABIP varies based on his speed, types of contact (each of GB, FB, LD are differently correlated with BABIP), and strength of contact). Last season, the lowest BABIP a team had was .285 (the Reds) and the highest a collective team had was .326 (the Angels). Only four teams did not have a collective BABIP between .288 and .312 last season. The MLB average BABIP last season was .302.
Thus, knowing that BABIPs tend to normalize and that hits are mostly defendant on BIP averages, it is not so difficult to conclude that hits are a poor measure of a hitter’s ability — if for no other reason than a hit is more in the fielder’s control than that of the hitter.
Is batting average also a poor metric by which to measure a player and team’s ability to score runs? I will pretend that you answer my rhetorical question by stating “of course it isn’t, that’s why we have RBIs” because 1) runners being on is situational and independent of a hitter’s ability, 2) the normalizing effects of BIP do not cease effect in high leverage (clutch) situations, and 3) clutchiness really does not exist (read the link for more info on why).
To answer my question, I posed another question: how does one score runs? Scoring runs is accomplished by a two-step process: putting runners on and moving them over. Putting a runner on base is measured by On Base Percentage (OBP), which accounts for both hits and walks. Hits are largely a function of luck, while walking is more of a skill (a player’s ability to read the strike zone and determine a pitch’s trajectory is not dependant on outside factors other than an umpire’s [in]ability to call balls and strikes). Moving the runner over is measured by the hitter’s power, or ISO (Slugging Percentage (SLG) minus Batting Average (BA)). A double will move a player over more bases than a single and a triple more than a double, while a home run will clear the bases and score the batter. The higher a player’s power, the higher his SLG. Because SLG is measured as ((1B)+(2*2B)+(3*3B)+(4*HR))/(AB), a player with absolutely no power (hits only singles) would have a SLG of 1B/AB, where H (hits) would be equal to 1B. Thus, a player with no power’s SLG would be equal to his BA (BA=H/AB). As a player has more power, his SLG becomes larger than his BA. This is why a player’s power is measured by ISO.
Where, I dare ask you, is “hits” a component of this runs-scoring model? It exists, hidden away in getting on base and to some extent moving the runner over, but the “ability to get more hits than the average guy” component of the game that most people attend to when they say “he’s a good hitter” is better encapsulated in a hitter’s strikeout rates. A player who puts more balls in play will have a better batting average (as determined by BABIP). Of course, this comes at the trade off of putting runners who are already on base at risk of the double play. “Batting Average” is too luck oriented (for the reasons mentioned above) to be “the” reliable input of OBP. If you want a higher BA-based OBP, you should look less to BA and more to a player’s K-rates (and BB%, although you probably don’t want to get rid of guaranteed-on base points (walks) in exchange for maybe-hits).
Thus, BA, though not entirely useless, is a misleading and inefficient metric by which to measure runs scoring ability. It’s a part of the equation, but it is a misnomer to point to batting average as a point of leverage in the equation. The best metrics which account for runs scoring are OBP (which encapsulates BA (which does account for 50-65% of OBP)), ISO, and K%.
this was all taken in part from:
http://gameofinches.blogspot.com/2010/01/quintessential-sabermetrics-argument.html
But of course, BA generally makes up 60% of OBP, which contact is necessary to produce SLG…