By In Stuff

My Guide to Stats: Offense

Last week, I made a mistake on Twitter. That’s a pretty common sentence, I suspect. In this instance, I was talking about how I will almost certainly (and, I suspect, stupidly) buy the iPad 2 within the first couple of days, and I said that this is because I’m a “technology geek.” I meant this as self-mockery. I meant geek in the textbook definition of the word, geek being “a person with eccentric and unhealthy devotion to a particular interest.” The trouble is, geek has taken on new definitions in 2011 America. Best Buy has a Geek Squad. It is often said that the Geeks — Bill Gates and that Facebook Guy being the most obvious examples — are taking over the world. Computer geeks are viewed as the kinds of people you want as friends, or at least friends when your computer screen turns bright purple.

Geek has come to mean “somewhat socially inept but incredibly brilliant person when it comes to one subject.” Well, I’m not that kind of geek I don’t know squat about technology. I just like buying the overpriced latest thing. It is why my wife and I owned what I have to believe was the third or fourth DIVX machine ever built (or, certainly, one of three or four LAST DIVX machines ever built), it is why I have about 50 stupid and pointless gadgets stacked around my house, it is why the other day I made a specific run to the Verizon store so I could spend a half hour looking at the new XOOM tablet even though I ALREADY HAVE an iPad and ALREADY DECIDED I’m going to get the new one as soon as possible. I have an unhealthy obsession for buying new technology though I know absolutely nothing about it. There’s no word I know for “Dumb Geek.”*


* * *

I bring this up because I have been at spring training in Florida for a while, and I thought it would be a good time to explain again some of the sabermetric baseball terms that I use quite often in these blog posts and the baseball theories that I am fascinated by. But I need to first make it clear that I am not a sabermetrician. I’m not even an amateur sabermetrician. I know quite a few of these people, and I can tell you that my own efforts to add anything of any worth to the sabermetric community have been comically inept, and my own understanding of some of these sabermetric principles is pathetically simple and probably only about 40% right.

Mozart’s genius was that he could create the brilliant music.

Salieri’s genius was the he could hear the brilliance of the music.

I’d say that I enthusiastically but barely even know what Salieri’s talking about.

But here we are, and it’s baseball season, and I do write a lot about BABIP and WAR and John Dewan’s plus-minus, and OPS+, and I do often mock wins and RBIs and batting average, and while this doesn’t get me within three European countries of Cuttingedge, it’s all I’ve got. Just remember — like it would be possible for you to forget — I’m not a baseball geek. I’m like a dumb baseball geek.

* * *

What’s the matter with batting average?

I have to admit that it stuns me when I hear prominent baseball executives and scouts publicly quote a player’s batting average like it means everything. LIke they will say: “This guy hit .305 last year, so he obviously had a really good year.”

Look there’s a very good chance that if the guy hit .305 last year he had a really good year. But as Bill James has said, ranking someone by batting average is like being a movie critic who ranks movies after only watching the first two-thirds. Hal Morris hit .309 in 1998 and, though he remains one of my favorite people, I must say that he was almost useless. Felix Fermin hit .317 for Seattle in 411 plate appearances in 1994, and was out of baseball within two years. Juan Pierre hit .327 in 2001 and led the league in stolen bases and was a thoroughly unhelpful offensive player. We can go on and on.

The problems with batting average are so obvious that it seems kind of stunning that we have overlooked them for more than 100 years. It probably says something about how once we all get going in one certain direction, it’s hard to change course. I think we would all agree that the goal of a big league baseball team is to win games. On the offensive side, this revolves around scoring runs. On the defensive side (including pitching) this revolves around preventing runs. If you score more runs, you win. If you score fewer runs, you lose. This is baseball at its simplest.

So how does batting average tell you almost ANYTHING you really want to know?

I’ve made the point before about how batting average SEEMS simple, but it is really one of the most advanced stats we have if you consider “advanced” to mean “bizarrely complicated and obtuse.” WAR and xFIP have NOTHING on batting average.

How do we figure batting average? Well, start with a players’ number of plate appearances. That would be the number of times the player comes to the plate.

Now, subtract the walks. No, seriously, just subtract those. We don’t care about those.

Now, subtract the hit-by-pitches. Get rid of them.

Now, subtract the times that the player hit a fly ball that allowed a runner to tag up and score from third base.

Now, subtract the times the batter bunted a runner from first to second base, or second to third, or third to home but still made an out. Do not subtract the plate appearance if the batter successfully made it to first base. Do not subtract it if he hit a hard smash that accomplished PRECISELY THE SAME THING as a bunt. Do not subtract it if he hit a check-swing dribbler that was KIND OF like a bunt but did not seem from the press box to be a purposeful bunt.

Remember to include the times he reached base but only because of a defensive blunder.

OK, you have that number? We call those “at-bats.” Now, what you want to do it take the number of hits and divide those by at-bats. What is a hit? Any time someone hits a ball that allows him to reach base. No, we don’t care what base he reaches. Double … triple … home runs … they’re all just “hits” when it comes to batting average.

Of course, if the batter gets on base because of a defensive error, that doesn’t count as a hit. That counts as an out. Even though he didn’t make an out. How do we determine if the defensive player made an error? Someone in the press box we call the “official scorer” will watch the game and make the determination based on whatever he happens to be thinking at that moment.

OK, now you divide the hits by at-bats. And that is your hits percentage. We call it batting average even though it is not an average of anything. And the person with the highest average will be named the batting champion, even if we have to carry out the division to five or six or seven decimal points. The team with the highest batting averages will be listed on top of the charts even if they scored 200 runs less than another team.

It seems at least possible that there’s a better way

* * *

Why isn’t OPS+ instead called “Special Ops?”

The two most basic statistics that seem to best define hitting are on-base percentage and slugging percentage. I don’t think I need to explain them here, but I will. On base percentage is times on base divided by plate appearances. It is basically “the percentage of time the batter did not make an out.” It is not exactly that — there are a few quirks revolving around errors and sacrifice hits — but it’s pretty darned close. Of all of the basic offensive stats, OBP is probably the most important because, as has been said many times, baseball doesn’t have a clock. Outs are the clock. In football, you get 60 minutes to score as many points as you can. In the NBA, you get 48 minutes. In baseball, you get 27 outs. Every out is one more step to the end. A batter’s job is largely to not make outs, and on-base percentage measures that.

Slugging percentage is total bases divided by at-bats. It is a good measurement of how much power a player offers. If a player gets 187 hits in 623 at-bats, he’s a .300 hitter. If they are all singles, his slugging percentage is .300. If they are all home runs, his slugging percentage is 1.200. And his slugging percentage can be anywhere in between.

In 2008, Justin Morneau got 187 hits in 623 at-bats. That’s a .300 average.

In 1958, Nellie Fox got 187 hits in 623 at-bats. That was a .300 average then too. By batting average that was exactly the same offensive season.

Morneau though hit 47 doubles to Fox’s 21 doubles. Fox actually hit more triples, 6-4, but Morneau hit 23 home runs and Fox hit, um, zero. Justin Morneau had a .499 slugging percentage. Nellie Fox had a .353 slugging percentage.

Because those are the two basic stats that seem to tell us most about the players, there have been several efforts to mash them together. Bill James multiplied them and then multiplied that by plate appearances to come up with what he called “Runs Created,” which is still a great way to judge the raw offensive contributions of a player.

Last year’s Top 5 in runs created:

1. Joey Votto, 144
2. Albert Pujols, 142
3. Miguel Cabrera, 141
4. Jose Bautista, 139
5. Josh Hamilton, 134

The more famous effort to mash on-base percentage and slugging percentage is simply adding of them together, a sum which we have come to call OPS — (On-base percentage Plus Slugging percentage). The 2010 leaders in OPS are the same as the leaders in runs created, only in different order:

1. Josh Hamilton, 1.044
2. Miguel Cabrera, 1.042
3. Joey Votto, 1.024
4. Albert Pujols, 1.011
5. Jose Bautista, .995

There are several problems with OPS, one of them being that apparently you should never add together two fractions that have different denominators (on-base percentage works with plate appearances; slugging percentage works with at-bats); another is that on-base percentage is actually much more important when it comes to scoring runs than slugging percentage is but in OPS actually counts for less (because on-base percentages are usually smaller). But I think OPS, even with its flaws, is a pretty good way to measure offensive contribution, certainly better than batting average, and its become pretty popular, and if that’s our best shot to get out of the batting average dark ages then I am all for it.

Adjusted OPS+ is an offensive number I might quote more than any other — it is OPS adjusted to include context … specifically the park the player hit in and the time when he hit. OPS+ is a great stat, I think, a single number that tells you so much about what the player’s season really means.

In 1995, Andres Galarraga hit .280 with 31 homers and 106 RBIs.

In 1908, Ty Cobb hit .324 with 4 homers and 108 RBIs.

Galarraga had an OPS of .842 built largely on his .511 slugging percentage.

Cobb had an OPS of .842 built largely on his .367 on-base percentage.

Who had the better year? You will probably assume it was Cobb. You may even assume it’s not close. But OPS+ tells you — Galarraga didn’t even have a GOOD offensive year. He had a 97 OPS+ … 100 is average. He didn’t walk. His slugging percentage was largely a function of the offensive time when he played and the absurd Coors Field ballpark where he played.

Cobb meanwhile LED THE LEAGUE with a 169 OPS+. He, of course, played during deadball, when runs were at a premium. This was especially true in 1908, when Cobb led the league with a .475 slugging percentage, when only two other guys hit even .300, when only two guys scored even 100 runs and Cobb’s 108 RBIs led the league by TWENTY-EIGHT. The thing is most people do not know the history of baseball well enough to know that run scoring was ESPECIALLY bleak in 1908, and soon enough few will remember the insanity of the early days of Coors Field.

But if you put it like this …

Cobb in 1908: 169 OPS+ (led league)
Galarraga in 1995: 97 OPS+ (below average)

… you will know very quickly that there is no comparison between Cobb’s season and Galarraga’s season.

And, I don’t know why we don’t call it Special Ops. That would be awesome.

* * *

WPA? Is that a new deal?

One of the coolest stats out there is WPA, which stands for Win Probability Added, which is a name that I don’t think helps the cause much. There are certain words that scare the bejeebers out of people. Linear Weights were like that for me. I would see anything mashing those words together — “linear” and “weights” — and I would kind of freak out. For years, this prevented me from reading or thinking too much about the great work of Pete Palmer and others even though the concept of linear weights — giving values to various offensive things — is really not complicated at all.

Win Probability Added is not only an offensive stat, but I’m including it for offense … the concept is that at every point in a game, each team has a certain chance of winning. Take the Pittsburgh-Milwaukee game of July 20th last year. The game started and obviously both teams had exactly a 50% chance of winning.

Milwaukee did not score in the top of the first. At that point Pittsburgh’s chance of winning moved up to 55%, and Milwaukee’s dropped to 45%.

Pittsburgh promptly scored nine runs. Yeah, nine. Each of those runs obviously increased the Pirates chances of winning the game. For fun, here is a quick chart only of the runs:

— Pedro Alvarez grand slam (Pittsburgh 4-0)
Chances before the home run: 64%
Chances after the home run: 86%

— Lastings Milledge scores on error (Pittsburgh 5-0)
Chances before run: 88%
Chances after run: 91%

— Jose Tabata hits two-run double (Pittsburgh 7-0)
Chances before runs: 92%
Chances after runs: 96%

— Delwyn Young hits run-scoring double (Pittsburgh 8-0)
Chances before run: 96%
Chances after run: 98%

— Neil Walker hits run-scoring double (Pittsburgh 9-0)
Chances before run: 98%
Chances after run: 99%

In the top of the second, Milwaukee scored three runs. This moved their winning percentage up from one percent to 5%. Alvarez homered again moving Pittsburgh’s percentage from 95% to 97%. And so on. It turned out that this was a wild game and at one point Milwaukee cut the lead to 10-9 on a Ryan Braun homer — when Braun hit that homer, the Brewers winning percentage jumped from 14% to 30%.

This is a simple concept to understand when you only talk about scoring runs. Its quite easy to understand the math when you say that the Yankees up 2-1 in the eighth have a better chance of winning than the Red Sox down 2-1 in the eighth.

What gets a little bit tougher is to realize that EVERY PLAY increases or decreases a team’s chance to win the game. If the Red Sox leadoff hitter in the eighth draws a walk, the Red Sox chances go up. If that is followed up with a single, so that there are runners on first and third, Boston’s chances chances go up yet again. If Joba Chamberlain then strikes out two, the Red Sox chances go down. If a single scores the tying run, the chances go up. And so on. Every play, from the first to the last, changes the percentages, sometimes in an almost unnoticeable way (a one out groundout in the third) sometimes in earth shattering ways (a game-winning walk-off grand slam).

What WPA does is add up all the percentages. It doesn’t only do this for hitters — it does it for pitchers and fielders too. But for now, we focus on hitters. WPA simply adds up how much a hitter changes his teams chances to win. It adds up EVERYTHING. The clutch hits. The key strikeouts. And more, much more, the mundane at-bats that our minds simply cannot keep track of.

Here were the Top 10 in WPA in 2010 by Fangraphs:

1. Miguel Cabrera, 7.42
2. Joey Votto, 6.85
3. Josh Hamilton, 6.25
4. Albert Pujols, 5.38
5. Adrian Gonzalez, 5.11
6. Jason Heyward, 4.82
7. Shin-Soo Choo, 4.59
8. Matt Holliday, 4.10
9. Delmon Young, 4.06
10. Jose Bautista, 3.93

Tom Tango is quick to point out that WPA is not a great way to evaluate the TALENT of a player, but it’s a good way to evaluate HOW MUCH THAT PLAYER CONTRIBUTED during the year. That may sound odd, but it gets another point about fairly obvious point about offense that I should make here, a point about clutch hitting.

The baseball community has long celebrated players for their ability to lift their game when the chips are down, when the moment is bleak, when the game is on the line. And the sabermetric community has for a while now scoffed at the notion that players CAN consistently lift their games in the clutch moments. The baseball community builds its case on waves of emotion and selective memory. The sabermetric community builds its case on the fact that so far nothing has been found in the numbers to suggest that players, no matter how good, no matter how celebrated for their heroics, are capable of predictably and reliably being better in the biggest moments.

So statistically, if you want to judge the talent of a hitter, you would not use WPA — would not use a statistic that rates some at-bats as being much more important than other at-bats. But if you want to judge a player based on how much he contributed to the team, there are few stats better suited for that than WPA.

* * *

Wascally BABIP.

BABIP stands for “Batting Average on Balls In Play” and it’s a different kind of stat from the rest here. It doesn’t tell you much about how good player is. It migt tell you how hit lucky he has been … and how likely he is to improve or fall off in the future.

To figure BABIP, you take all the balls in play and subtract the home runs. Then you figure the batting average. It’s really simple. Last year, batters hit .297 on balls in play. The number stays right around there. The year before it was .299. The year before it was .300. The year before that it was .303.

So it’s always around .300. Players who hit a lot of line drives will have a higher BABIP, of course. Joe Mauer has a career .344 BABIP. But in general, BABIP can swing wildly from one season to the next, and a lot of it appears to be Crash Davis luck — hitting one extra flare a week, just one, a gork, a ground ball with eyes, a dying quail.

Last year, Josh Hamilton had an abnormally high .390 BABIP. The year before that it was .319. His line drive percentage was almost exactly the same. He popped out more. But he hit many more ground balls, and those ground balls went through, and that was a big contributor to his massive season.

Is that repeatable? There’s is a lot of dispute about that. Some think Hamilton is due for a big drop-off in 2011. Others think he will have a huge season. It’s just something to think about.


We will include one more stat because it is prominent in a stat I will come back to in the end, WAR. The stat wOBA looks scary because any word where you make the first letter lower case and the rest upper case is scary. It doesn’t matter how harmless or happy the word really is. Look:




wOBA stands for Weighted On-Base Average. And as they say over at Fangraphs, this is the statistic that realizes that every time you reach base, it’s worth SOMETHING.

Here is an approximation of what each thing is worth:

Non-intentional walk: .72
Hit by pitch: .75
Single: .90
Reached base on error: .92
Double: 1.24
Triple: 1.56
Home run: 1.95

Funny, isn’t it, that reaching on error is worth just a touch more than a single, or that getting hit by a pitcher is worth a touch more than a non-intentional walk. I’ll have to look more closely at that. Anyway, you multiply all that out, divide by plate appearances and, voila, you have wOBA. An average wOBA should be about an average on-base percentage — .330 or so. Last year Josh Hamilton led the American League with a .447 wOBA. Joey Votto led the National League with a .439 wOBA.

How did they get to these numbers. If you are really interested, you can read this and then look around the Internet. But the larger point is that these weighted numbers do a pretty amazing job of estimating runs scored. And it’s worth remembering one more time that scoring runs is, in fact, the goal of the team at the plate.

OK, I have no idea if I will ever have the strength to do part two, but if I do it will be on pitching.

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48 Responses to My Guide to Stats: Offense

  1. Jon says:

    I’m surprised you used BABIP in the hitting section. People tend to talk about BABIP and pitchers a lot more because it’s less controllable for them and more stable. (Brian Bannister will not consistently give up only line drives.)

  2. NMark W says:

    All well and good that an old guy like myself is reminded again what all of these relatively new baseball equations mean. My only thought is, when the Brewers played the Pirates during 2010 season, it was never my feeling that the outcome was a 50/50 probability before the first pitch was thrown.

    Okay, switching sports to NCAA men’s basketball, can anyone explain this one to me? I was just reading scores from today’s conference tourneys and I see that New Jersey Tech (?) was playing in Orem, Utah in the Great West Conference Tournament (or Tooournamint if you ever listen to Coach John Thompson on Westwood One Radio) vs. Houston Baptist (I think). Is this just a sick joke someone who once did all of the agate typesetting in the local sports page is now playing with our minds over the www?

  3. Mark says:

    New Jersey Tech? I think my dad went to high school there.

  4. NMark W says:

    According to SI, it’s a final! 7th seeded Houston Baptist, now 5-25 for the season has upset 2nd seeded New Jersey Tech (15-15) by the score of 72-70. The HB Huskies will now play either North Dakota or ? (I forget) on Friday. The games are being played in Orem, Utah?!

    I thought our world was screwed up enough today seeing all of the crap that is occurring all over the globe…Now this. WTF?

  5. Ben says:

    On official scorers…

    Several years ago I interned at a major daily newspaper as a sports reporter. Mostly high school stuff, but one time I got to cover the local single-A team (This is likely the highlight of my reporting career, as I now work behind the desk at my paper).

    Anyway, I was in the press box with another reporter, the official scorekeeper, and a couple other people. On one borderline play, the official scorekeeper couldn’t decide if it was a hit or an error. So he just took a poll of the rest of us in the press box and decided it that way.

    I wonder how often that happens in the majors…

  6. Tim says:

    This is awesome stuff, Joe. I’ve long believed that the most convincing argument for advanced stats is how utterly convoluted the traditional stats are. BA, Wins, and the like, are far more abstruse than even wOBA or linear weights.

  7. y42k says:

    An error is worth more than a single because the defense lost control of the ball. That means other good things were more likely to happen for the offense. Is it “fair” to give a hitter credit for that? Is it “fair” to give him credit for the defensive error in the first place? You make the call.

  8. Music Guy says:

    Joe, you made one mistake in there. Batting average is technically an average, it’s not a percentage. Someone who hits .300 would have a 30% “batting percentage”; but he “averages” .3 hits per at bat. It is pretty silly to express it as an average, but that’s the way it’s expressed.

  9. Reaching by error SHOULD be part of your OBP. If you don’t make an out, that is good, and I don’t think it should make a difference that the other team touched the ball (ERROR) or just missed hit (likely scored a HIT) or they slipped (HIT) or they dropped the ball (ERROR).

    If, in fact, errors are completely out of the batter’s control, then the additional amount added to each person’s OBP will be approximately the same, and over the course of time will even out (just like BABIP).

    Of course, I believe if someone studied it, they would find the Willie Wilsons of the world more than likely reach base by error more often than the Willie Aikens of the world. And if that is true, then we have an even better reason to include errors in OBP.

  10. John Ling says:

    Can we please send a copy of this to John Heyman?

  11. It’s my goal in life to convince the baseball community of the errors of its ways. No, not in using stats, but in using them correctly. These are not percentages, these are averages. So, batting average is correct. On-base percentage and slugging percentage are not. If an average on-base percentage is .330, then the average baseball player reaches base 33 times every 10,000 plate appearances instead of 33 times in 100 PAs, which is what we’re trying to represent here.
    “apparently you should never add together two fractions that have different denominators,”
    This hurts my head. It isn’t that you shouldn’t do this, but you can’t do this, so you must find a common denominator or just divide the numerator by the denominator and then add the numbers together, which is what is done in OPS. The problem here has nothing to do with fractions but the fact that they are weighted slightly differently with slugging having the advantage because total bases are being divided by a smaller number (at-bats) than in on-base average.

    My problem with OPS is that it essentially is counting batting average twice, since this is a component of both on-base average and slugging. For an extreme example. Take two .500 on-base average players. One with a .000 batting average and another with a .500 BA, all on singles. The former has a .500 OPS and the latter has a 1.000 OPS. The first is a sub-replacement player while the second is an All-Star level MVP candidate, according to OPS. Is there really that much difference between them?

  12. JERRY: Did you have a good time [with The Maestro]?

    ELAINE: Yeah, he’s very interesting. Did you know that Mozart died while he was writing ‘The Requiem’.

    JERRY: (Sarcastically) Yeah, everyone knows that, it was in Amadeus.

  13. Chris says:

    I prefer an approach to ‘batting average’ where the hit type (line drive, fly ball, ground ball, popup, home run, strikeout, etc.) is incorporated and an ‘Expected Batting Average’ is calculated. Since we know how often these hit types result in a base hit (over HUGE sample sizes), this would theoretically remove the luck of the guy whose ground balls find a hole more often. The only problem I see with this approach is that someone is making a judgment call as to whether a looping liner is a line drive or a fly ball.

    Doesn’t it seem like this approach would tell us a lot more than the actual batting average? If a guy has an expected batting average of .330, but an actual batting average of .280 then it’s much easier to see how ‘lucky’ he was than just looking at his BABiP and trying to determine if that hitter’s BABiP is too high compared to his historical trend.

    The same could, of course, be applied to pitchers. It would reward pitchers that induce less solid contact (allowing less line drives, that is) and getting more strikeouts and giving up less home runs.

  14. Pat says:

    The word “rate” would probably be more accurate than “percentage” and more intuitive than “average” for these stats. So: Batting Rate, On-Base Rate, Slugging Rate.

    Not that this will ever change anyway, but still.

  15. Steve M says:

    What I wouldn’t give for Dusty Baker to be locked in a room until he finished reading this post.

  16. Justin says:

    There’s no word I know for “Dumb Geek.”*

    The word is sucker, Joe. And I hear they are born at the rate of about 1 per minute.

  17. Tim says:

    Socaltwinsfan, I’m missing the distinction you’re making between averages and percentages. Can’t percentages be correctly expressed as either decimals or whole numbers? In other words, 50 percent could also be expressed as .50 (50 per hundred or 50/100 or .50). You only get into trouble if you combine the expressions, for instance by saying .50% when you mean 50%.

    So On-Base percentage can be truly called a percentage and still be expressed as .330 in your example. As long as you’re not saying .330% (which no one would), you’re ok expressing a percentage as a decimal.

    I’m not statistician, so maybe there’s a convention against expressing percentages as decimals that I’m not aware of but it seems to me that .330 and 33% are exactly the same thing, so therefore the baseball convention of saying someone has an on-base percentage of .330 is correct.

  18. Josh says:

    One of the problems with some of the newer stats is it’s difficult for people who don’t work with them on a constant basis to get a feel for what they mean in a quick scan. BA is a flawed metric for evaluating a player, but the most casual fan can look at it and get a feel for a player or group of players at a glance.

    OPS does this fairly well too, but things like WAR & OPS+ aren’t there yet. I don’t know how much of it is just lack of familiarity, or how much of it is the stat not having enough gradiation to make players distinguishable enough from each other, but it means there’s still some work to be done.

    I have hope for some of these advanced stats, but for them to gain broad acceptance they need to be accessible to the casual fan in giving them information quickly about a player. Until the casual fan can put an OPS+ of 120 into context quickly, it’s going to struggle.

  19. “Until the casual fan can put an OPS+ of 120 into context quickly, it’s going to struggle.”

    100 is average. 120 is roughly* 20% better than average (i.e., a typical all-star).

    * The math doesn’t work out exactly, but it’s close enough.

  20. daxmontana says:

    I believe (based on sight, not numbers) that the difference in wOBA values between a hit and an error is that with an error a runner is slightly more likely to be able to take an extra base than on a hit. As far as HBPs vs. BBs, clearly the HBP is a grittier baseball play, thus warranting the enhanced value.

  21. stephen says:

    This comment has been removed by the author.

  22. stephen says:

    I have a question about general consuming, and I might sound like kind of a jerk here, but here goes: how do people justify spending so much money on “new” technology? I’m going to go with Joe’s example here, and maybe it isn’t the best example because Joe’s job requires him to do a lot of computer-based things, so having the iPad probably helps him do his job better. But: Joe already owns the original iPad. Joe is going to buy the new iPad, even though it’s obvious that he doesn’t need it and he readily admits this. The iPad, depending on version, is something like $500-$800. This seems absolutely nuts to me. Wouldn’t that money be better spent on like a college fund or, better yet and more relevant, being sent to Harvester’s?

    I’m sure it sounds like I’m being judgmental or something, but I’m not intending to. People have the right to spend their money any way they want. It makes our economy better when people do, and it’ll be great for America if Apple sells a billion iPads. Plus, we all waste a little money here and there. But I’m interested in the psychology of such a *gratuitous* waste of money. I just don’t get it. That’s SO MUCH money, for something that does essentially the exact same thing as something you already own, yet tons of people will be doing this. The nature of consuming is just fascinating.

    I’ll get off my soapbox now. Sorry if I sound judgmental or mean. I only ask these questions because I’m not part of the cutting-edge tech crowd but I want to understand. For the record, I’m 27 and have been using the same computer for 6 years (and yet it still has more than twice the memory capacity of the largest iPad).

  23. David says:

    Josh said: “One of the problems with some of the newer stats is it’s difficult for people who don’t work with them on a constant basis to get a feel for what they mean in a quick scan. BA is a flawed metric for evaluating a player, but the most casual fan can look at it and get a feel for a player or group of players at a glance.”

    This isn’t a problem with the newer stats. It’s simply a matter of exposure and familiarity. The reason fans have a seemingly intuitive sense of what a good (and a bad) batting average is is that they’ve been exposed to batting averages their whole lives. There’s nothing inherent in OBP or WAR or WPA or anything else that makes it more difficult to tell a good one from a bad one, other than the fact that not everybody is used to seeing those stats all the time and thinking in terms of them. Exposure will bring familiarity.

  24. Tim, percent literally means “per 100.” So, .330% literally means reaching base .33 times per 100 PAs or 3.3 times per 1,000 PAs or 33 times per 10,000 PAs. If you want to use percentage, that’s fine, just express it as a percentage. A .330 average would be 33 percent or 33 hits per 100 at-bats. Percentage is used correctly in basketball. “He makes 75 percent of his free throws.” Why it can’t be used correctly in baseball is frustrating to my anal retentive mind.

  25. Pat, rate would be an excellent word to use.

  26. Chris W says:

    Juan Pierre, 2001: 2.0 bWAR

  27. Chris W says:

    I’m sorry–offensive bWAR…he was 2.4 overall

  28. Tim says:

    Socaltwinsfan, that’s exactly what I said. Since we say the the obp is .330 rather than the obp is .330%, then we’re using it correctly. .330 = 33%. And an average, in this case, can be the same thing as a percentage.

    It’s all different ways of saying the same thing. You could say, that Player X averages three tenths of a hit for every at bat he registers, or you could say he gets a hit in 30% of his at bats, or he gets 30 hits on average for every 100 at bats. They’re all ways of expressing the same thing. No one says his batting average is .300%, just as no one says his OBP is .400%. So baseball is not incorrect.

    I guess you’re quibbling with the fact that people say his on base “percentage” is “four-hundred” when a player does not in fact reach base 400% of the time. But it’s just a short-hand way of saying that his OBP can be expressed by the figure .400, which is just another way of saying 40.0%. It’s not that people are using “average” or “percentage” the wrong way, it’s just that the convention in baseball has always been to express these percentages/averages in their decimal value when written and as a three-digit whole number (e.g. Three-hundred or three-twenty-eight) when spoken. If you want to say a player’s on-base percentage is “forty-point-two,” I suppose you could. The rest of us will just stick to “four-oh-two.”

  29. Tim says:

    And yes, rate might be a more apt term, but I don’t think using “averages” or “percentage” in these contexts necessarily gets it wrong.

  30. Mark Daniel says:

    David, exposure will bring familiarity but I’m not sure it will bring acceptance very quickly. Those stats are just too complex to accept at face value. The most complex traditional stat is SLG, and that can be explained by saying that it’s basically batting average except a double counts as 2 hits, a triple 3 hits and so on.
    How do you simply explain WAR? The simplest explanation I’ve seen is from Fangraphs, which states that WAR is “simply” wRAA and UZR added together, followed by the addition of a positional adjustment, followed by converting the numbers so that they are relative to a replacement level player at that position.

    I think some of the defensive metrics will gain widespread acceptance before WAR because they are simple in concept, i.e. measuring the number of balls a player gets to relative to his peers. If they didn’t convert those numbers to a run or win value, they would be even simpler.

    WAR contains too much manipulation with the positional adjustments, the conversion to wins, the relation to replacement level players and so on.

    I’m not saying WAR is useless, mind you. I pay attention to it. I just think it’s unlikely it will make it into the mainstream any time soon.

  31. Tim says:

    The interesting thing about batting average is the way it crystallizes those early writers’/fans’ understanding of the game and preserves it through time. They felt that the batter’s job was specifically to hit. If they walked, it was because the pitcher didn’t give them fair pitches, not a reflection of their own skill. If they moved the runner over despite recording an out, that is something that definitely contributes to the game and should be credited to them. If this is what you believed, then it makes sense that you’d come up with a formula like H/(PA-BB-HBP-Sacrifices).

    Nowadays we (at least many of us), have a more accurate understanding of what goes into winning games, as described by Joe above, so we look at things like OBP, OPS, wOBA, etc. But we can’t shake those century-old notions of what baseball was supposed to be, so we still have BA.

    I studied linguistics in college, and an ongoing debate in the field is about the extent to which our spoken language determines the way we think and see the world. You’ve all heard about how the Eskimos have 400 words for snow, so they understand snow differently from us since we only call it snow (the Eskimo thing is actually a myth, see, but you get the idea of the debate). I think BA is the baseball equivalent of this type of effect. Our forebears came up with a “word” for how good a hitter is called batting average (and another one called RBI). And since we still speak that language, many of us have come to understand a player’s offensive worth in those terms. That’s why so many people (and professional baseball writers) still don’t care about walks and thinks 100 RBI makes you a great player.

  32. Tim says:

    Mark, I disagree, slightly, about WAR. While the math going into it might be way too much for most fans to bother with, the number that it spits out is much easier to grasp. Your team wins this many more games by playing Player X instead of the platonic ideal of a AAAA player. As long as you trust whoever came up with the math, I think that WAR is a very elegant and easy-to-grasp concept.

    I do think it has a big barrier to catching on though, and that’s the fact that there are two competing formulae (baseball reference and fangraphs) that make it possible to be right whether you say that Joey Votto had 6.2 or 7.4 WAR last year.

  33. Stephen- with you all the way. Our consumer culture is more unconscious than conscious. I WANT an iPad. I think 100 hungry people getting a meal is a lot more important than me having an iPad, but I don’t feel the same tug (though of course it does feel good to buy food for those who need it). Also, other than personally distributing it, I’m not sure how to get food to the hungry. I could probably track down a charity, but I would ideally want to evaluate them first. None of this is all that difficult, but if you don’t feel that tug to do it, what are the odds you’ll see that through to the end? This isn’t a “that’s just the way it is” rant, it’s a “how can we adjust our mentalities?” rant. Also feel the need to echo Stephen’s statement that this isn’t meant to be judgmental on Joe or anyone else, but I think it’s worth our attention enough to second your chime in, even if the forum is a little random.

  34. Jonathan says:


    Is that Brtet Farve? 🙂

  35. On the linear weights stuff, my guess is that an HPB is worth a little more than a non-intentional walk because HBPs occur pretty much at random across plate appearances (or nearly so), and NIBBs do not. A pitcher is probably more likely to nibble and issue a walk with a base open and two outs than with the bases loaded and no outs, for instance, but the base/out situation has almost no effect on the likelihood of an HBP. So on average, the walk hurts the defense less than the HBP.

    A reached-base-on-error is probably worth more than a single because the hitter almost always winds up at first base on a single, but he has a greater chance of winding up somewhere else after an error.

  36. Broken Yogi says:

    Great article.

    It brings to mind one of my problems with “slugging percentage”.

    If slugging percentages is based on “total bases”, which of course includes walks (but not errors), why doesn’t it include “advancing the runner”, or in some parlance “sacrifices”? If a hitter acts in such a manner as to advance a runner, even if he doesn’t get on base himself, why doesn’t that count as part of his “total bases”?

    In other words, say there’s a runner on second, and the batter hits the ball to the right side, and the runner is able to get to third, even though the batter makes an out. Why doesn’t that get counted as a “total base”? It seems that the effect of the batter’s time at the plate was to add one base to the team’s effort to win the game. It ought to count as a “total base”.

    Now, sure, there’s times when this happens almost by accident. But a lot of hits happen by accident too. It would seem valuable to credit all batters with advancing runners in this manner, just as getting a hit advances runners. Good hitters will, over time, advance more runners than bad hitters, so it seems an important part of the metric of winning baseball games and measuring a hitter’s contribution to that end.

    Is there any metric in baseball that includes this in their stats? Someone ought to, I think.

  37. pft2 says:

    OBP is basically (BA + BB/AB+ BB) (left out HBP for simplification). SLG is basically BA + (TB-H)/AB.

    OPS is thus basically


    or something like that.

    Basically, OPS and OBP have balls while SLG and BA do not, and OPS is a union between these balls and the ball-less stats, while OPS+ is it’s offspring. BA and AB is part of it’s DNA.

    OPS+ suffers from a defect known as park adjustments. For example, does anyone think Ichiro is affected much if at all by SAFECO. Doubt it. Yet compare him and Damons OPS and OPS+

    Damon had a 756 OPS and Ichiro a 754 OPS in 2010. Yet Ichiro has a 113 OPS+ to Damons 106 OPS+. Damon was certainly more adversely affected by his park than Ichiro, but Ichira gets treated like he is Adrian Beltre, when he is not.

    Now for wOBA. You said.

    “.. statistic that realizes that every time you reach base, it’s worth SOMETHING.

    Here is an approximation of what each thing is worth: etc……

    But the larger point is that these weighted numbers do a pretty amazing job of estimating runs scored. And it’s worth remembering one more time that scoring runs is, in fact, the goal of the team at the plate.”

    The only time the scoreboard changes is when a run scores, and most runs score with an RBI which we have been told has no value. Never saw the scorebard change 0.7 runs for a walk. Also, while the weighted numbers do a good jump of estimating runs scored at the team level, one can argue that there is little evidence that they say anything about how many runs an individual hitter actually produced.

    The use of the weighted numbers assume a league average team made up of league average hitters at every spot in the lineup, and a league average run environment. The numbers are actually quite different when you consider context, team and where you hit in the order, who hits behind you, etc. For example, was a walk or base hit by Ichiro in Seattle really worth that much given the motley crew hitting behind him. Is a 1st inning grand slam off another teams 5th starter that puts your team up 7-0 really worth more than as a 3 run walk off HR of another teams closer?

    Estimates are wonderful of course, but they are riddled with assumptions, some of which are not obvious, that are often not true, and have uncertain uncertainty.

    A HR is always a HR, as is an RBI, and yes, even BA is a real number. You may argue with their value, or if they were lucky or not, but there is 0 uncertainty to them. I will take a real number over an estimate that does not bother to estimate it’s uncertainty any day.

    This is not to say wOBA and OPS+ do not have value, but the numbers are riddled with uncertainty, and this is ignored by those who use them as if they were exact numbers.

  38. Barry says:

    Joe – please understand how blessed we are to have you. What made Mozart brilliant is that he created complex music but it had a simple quality – almost as if the music simply existed already and he documented it. The ability to simplify the complex – as you did in this article – is truly the mark of brilliance – thanks!

  39. ethegolfman says:

    There is no better example of the follies of batting average than the race for “Batting Champ of the 2000’s”. It came down to Ichiro and Pujols with Pujols edging Ichiro (& actually if you include 2010, they essentially tied). However, they couldn’t be more different hitters if you tried – Pujols is among the greatest to ever play the game and Ichiro is a solidly above average hitter but nothing special.

  40. Christopher says:

    re: reaching on error vs. a single. I could be way off base here, but I would imagine the reason reaching on an error is worth slightly more than a single is due to the non-zero chance that a batter who reaches base on an error actually ends up on second base. Obviously, being on second is more valuable than being on first – a batter who reaches on a single ends up on first, a batter who reaches on an error where the ball was thrown away will often make it to second.

  41. I could be wrong on this (so someone please correct me if I am), but I believe a hitter who tries to stretch a single into a double and is thrown out at 2nd is credited with a single and an out. In other words, if a no-hitter or perfecto is on the line, this kind of “hit” would break it up even though the batter is out Is this correct?

    If so, that could explain some of the difference between a hit and an error. Some hits are actually outs, whereas errors are never outs. Again, if this is true, its just another example of how screwed up you get when you try to calculate batting skills.

  42. Broken Yogi says:


    Ah, the same thing can happen with an error. A runner can reach base on an error, try to stretch an extra base on top of that, and get thrown out. So an error can also become an out. In both cases, however, the odds of that happening are probably about equal. Meaning, pretty low.

  43. John says:


    You make a good point about linear weights not accounting for context. How much that matters depends on how much hitters can actually control their results based on context. The point of individual stats is to whittle away everything outside of the individual player’s control so we can analyze his performance as clearly as possible.

    In general, while hitters affect their results a little by changing their approach (like taking vs. swinging away depending on how valuable a walk would be right now), they’re mostly the same regardless of context. I don’t have the link handy, but most advanced studies have found that there’s little to no difference between a hitter’s “clutch” performance and their ordinary performance beyond what you’d expect from chance. So weighing all singles equal to each other, all doubles equal to each other is a simplification, but not as big a simplification as you might think.

    As for RBIs, you have the certainty that a run definitely scored, but you introduce uncertainty by including a team-dependent factor (runners on base) in an individual stat. A player’s RBI total is as much a measure of the hitters in front of him as it is of the player himself, which is why the stat has fallen out of favor.

  44. JakartaDean says:


    The term you were looking for in paragraph 1 is “Gadget Whore” or “Gear Whore.” While this sounds a little disparaging, please don’t take it that way. It just fits, and many, many wonderful and successful people can be tagged this way. Geek implies an ability to explain the science behind the device being discussed, which I think you have suggested is not your interest.

    I’m a little out of touch with modern baseball stats, living far away. I was, however very, very impressed with the WPA. That seems like a bit of absolute brilliance in the way it isolates the impact of a players performance, not just his performance. I hope you continue to track it and let us know of its predictive ability. BABIP and wOBA almost seem like solutions looking for a problem: why replace understood and familiar metrics with something having no documented (and for wOBA, discernable) advantage?

    Loved the article.

  45. denopac says:

    Slugging pct (or avg if you will) is an imperfect indicator of actual power. It treats four singles exactly the same as a home run, so you have cases like these teammates on the 2009 Mariners:

    I. Suzuki .352/.386/.465
    J. Lopez .272/.303/.463

    Practically identical SLG, but Lopez outhomered Suzuki 25-11, with 21 more extra base hits overall.

    A better proxy for power is Isolated Power, which is simply SLG with the singles removed, or simply SLG-BA. Here the difference is obvious: Suzuki .113, Lopez .191. ISO is easy to calculate from the slash stats, and is easy enough to understand that it shouldn’t scare off the old school.

  46. Jim says:

    Percentage is used correctly in basketball. “He makes 75 percent of his free throws.” Why it can’t be used correctly in baseball is frustrating to my anal retentive mind.

    Let’s fix all of the mathemetical problems with traditional stats in one fell swoop … knock off the thousands place as a significant digit. Now a .280/.360/.450 hitter becomes .28/.36/.45 — a “twenty-eight” hitter with an OBP of “thiry-six” and a slugging percentage of “forty-five.” We’re speaking in terms of the percentage, and we’ve knocked out the annoying nonsignificant digit. There’s no darn difference between a .275 and .284 hitter anyway, at least not one that anyone could notice over the course of a season. (While we’re at it, we’re also knocking the hundredths place off of ERA.)

  47. Alex says:

    “I think we would all agree that the goal of a big league baseball team is to win games.”

    You know what I completely agree with this, but, and I never really thought about this until now, I’m not sure that, historically, many fans’ (and perhaps even a lot of scouts’ and evaluators’) primary goal in consuming baseball was to see their team win. This really might be a key to the problems we have with some entrenched baseball thinking.

    Instead, fans want to see line drives (even if it results in outs 70% of the time) instead of “boring” walks. They want to see cannon-like throws from a RFer (who otherwise isn’t that good) even if that means the chubby, nonathletic, but run-producing player has to sit on the bench. They want to see daring on the base paths (which is almost never worth it in the long run) instead of a station-to-station, “base-clogging” offense.

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