View Full Version : Keeping Score - New Baseball Statistic, With a Nod to an Old Standard

02-25-2007, 11:55 AM

Published: February 25, 2007

As newfangled baseball statistics go, on-base plus slugging percentage, or O.P.S., has become mainstream. Stadium scoreboards display it right alongside batting average. It has even appeared on the backs of Topps baseball cards.

What is O.P.S.’s reward for its widespread acceptance? For its simple approach of adding two official categories? Naturally, to have the statistics cognoscenti deem it inadequate.

This is not necessarily unreasonable. While O.P.S. may be the Harley to batting average’s Schwinn, merely summing on-base and slugging percentages is a vestige of the statistic’s birth in the early 1970s, when multiplication and square roots had yet to be invented (or, more accurately, were not available via Excel spreadsheets). Since they were first married, like any royal couple, on-base and slugging percentages have been known to be anything but equal, with their relationship being the subject of rampant debate.

“There’s a lot of ranging opinion over how much more valuable on-base percentage is,” said Victor Wang, a high school junior from Bloomington, Minn. “The book ‘Moneyball’ said it was three times. It goes down all the way to 1.5. But a 1-to-1 ratio? I knew that wasn’t right.”

Only 16 and dreaming of a career in baseball number-crunching, Wang was so moved to investigate this issue that he examined the statistics for every team since 1960 — via Excel, of course — to see which weights applied to on-base and slugging percentages most closely correlated with each team’s runs. He discovered that weighting on-base percentage 80 percent more than slugging percentage worked best, and he published a short article about it in “By the Numbers,” a Society of American Baseball Research journal.

Most stat-savvy baseball folks sense that on-base percentage is more valuable, perhaps drastically so, because it better recognizes the importance of not making outs. David Wright of the Mets agreed last week, saying: “You can always make things happen when you get on base. When I think of slugging percentage, I think of sitting back for the three-run homer, which might not happen.”

Wang wasn’t the first researcher to look into exactly how much more valuable on-base percentage may be. The Hardball Times, a statistics-oriented think tank out of the Baseball Prospectus mold, recently identified the same factor of 1.8 and started weighting O.P.S. accordingly. Better yet, one last simple step — dividing by four — put this new measure (called Gross Production Average) on the comfortably familiar scale of batting average, with figures generally ranging from .200 (horrible) to .265 (roughly average) to around .360 (superior). It’s a language that most fans speak.

Applied to individual players, Travis Hafner of the Indians led the major leagues last year with a .362 G.P.A., a sliver ahead of Albert Pujols of the Cardinals. Just like batting average, 10 hitters wound up .325 or higher. But they truly represented the sport’s most well-rounded batters, having weeded out walk-averse nonsluggers like the Pirates’ Freddy Sanchez, who had a .288 G.P.A. despite winning the National League batting title at .344.

Although it seems a product of the computer age, weighting statistics differently dates to baseball’s primordial days. As early as the 1860s, numbers men figured a type of weighted slugging average, only to have it hooted out of existence by singles-loving traditionalists. In 1916, the writer F. C. Lane gleefully mocked those averse to simple numerical weights — he said that when asked how much change one was carrying, nobody would reply, “eight coins” — and painstakingly derived relative values of singles, triples, walks and the like to rate players more precisely. His zeal, however, preceded that of any wider audience by several generations.

O.P.S. appeared on the scene in the 1970s, with on-base and slugging percentages being added rather than multiplied (which everyone agreed was more accurate) solely because it was simpler. O.P.S. is old enough that The New York Times published weekly top 10 leaders as early as 1985. But again, that didn’t last long. Even today, with O.P.S. the most accepted nontraditional statistic, fans still have trouble intuitively sensing if an .850 O.P.S. is good or bad.

The salvation for Gross Production Average could be how it translates a better O.P.S. into the customary .200-to-.360 scale. G.P.A.’s .300 hitters are just about as elite as traditional ones: Last year, 38 batters hit .300 in batting average, while 32 hit .300 in G.P.A. They are just not the same hitters, which is the entire point.

Having completed his investigation into the dance between on-base and slugging percentages, Wang is concerning himself with a different kind of G.P.A. these days. He had an American history test to take notes for, particularly on the Red Scare. But he said that when he was done studying, he would turn his attention back to baseball problems even older than those Bolsheviks.

“I love this stuff,” Wang said. “Even if it’s a meaningless problem. Meaningless to some people, I mean.”


Gross Production Average, a variation of OPS, but more accurate and easier to interpret. The exact formula is (OBP*1.8+SLG)/4, adjusted for ballpark factor. The scale of GPA is similar to BA: .200 is lousy, .265 is around average and .300 is a star.

Hoosier Red
02-25-2007, 12:38 PM
That's a great article, but the idea that it's easier to understand is one thing, how does it correlate to runs being scored?

And why is it divided by 4(other than to make it look like a batting average?)

Hoosier Red
02-25-2007, 12:39 PM
Oh and most importantly how does Adam Dunn rank on this list. That of course being the true measure of a statistics effectiveness.:devil:

02-25-2007, 12:47 PM
Oh and most importantly how does Adam Dunn rank on this list. That of course being the true measure of a statistics effectiveness.:devil:

OBP and SLG...he obviously will do quite well. :)

02-25-2007, 01:04 PM
Here you go.

First, last year's stats.

1 David Ross .255 .353 .579 .932 .304
2 Adam Dunn .234 .365 .490 .855 .287
3 Rich Aurilia .300 .349 .518 .867 .287
4 Scott Hatteberg .289 .389 .436 .825 .284
5 Austin Kearns .274 .351 .492 .843 .281
6 Edwin Encarnacion .276 .359 .473 .832 .280
7 Ken Griffey .252 .316 .486 .802 .264
8 Ryan Freel .271 .363 .399 .762 .263
9 Felipe Lopez .268 .355 .394 .749 .258
10 Brandon Phillips .276 .324 .427 .751 .253
11 Chris Denorfia .283 .356 .368 .724 .252
12 Javier Valentin .269 .313 .441 .754 .251
13 Jeff Conine .268 .325 .399 .724 .246
14 Alex Gonzalez .255 .299 .397 .696 .234
15 Jason LaRue .194 .317 .346 .663 .229
16 Mark Bellhorn .190 .285 .344 .629 .214
17 Royce Clayton .235 .290 .329 .619 .213

Now, PECOTA Weighted Means for 2007

1 Adam Dunn .267 .390 .574 .964 .319
2 Joey Votto .284 .366 .511 .878 .293
3 Ken Griffey .275 .344 .506 .850 .281
4 Chris Denorfia .296 .365 .459 .823 .279
5 Edwin Encarnacion .277 .350 .482 .831 .278
6 Scott Hatteberg .285 .372 .416 .788 .271
7 Mark Bellhorn .231 .344 .445 .789 .266
8 Ryan Freel .271 .361 .404 .765 .264
9 David Ross .240 .324 .459 .783 .260
10 Jay Bruce .264 .319 .460 .779 .258
11 Brandon Phillips .273 .331 .419 .750 .254
12 Jeff Conine .268 .334 .401 .735 .251
13 Jerry Gil .256 .291 .465 .757 .247
14 Alex Gonzalez .258 .309 .426 .735 .245
15 Javier Valentin .242 .314 .403 .717 .242
16 Bubba Crosby .249 .315 .376 .690 .235
17 Juan Castro .254 .292 .364 .656 .222
18 Norris Hopper .270 .312 .313 .625 .219

Votto #2. Denorifa #4. I like it. Those guys do things that lead to runs.

02-25-2007, 01:05 PM
I like that he converted it to a BA-style number.

Though, in a mathematical sense, there's two issues that need addressing in OPS. The first is every hit gets double-counted. I agree that OPS tells you value things, but it's a product of useful shorthand rather than penetrating mathematics. The second is the rate vs. distance matter. The stats community has built a belief system around rate. Actually I think it goes back to BA. We think in rate when we think about baseball. So the goal of many people manipulating stats has become how to adjust the value of OB northward at the macro level to better correlate with team runs scored and then turn that into a micro-level player stat. Why do people do it? Well, A) because they can and B) because they believe that OB should be more important. My guess is that if you believed that SLG was more important, you could hold OB static while adjusting SLG northward (because it seems that what's really being said is that by moving the OPS figure upward it will correlate better to runs scored) and you'd end up in the same basic place.

That begets two questions on my part:

1) If OPS is, to an extent, a happy accident, then will further tweaks make it better or undo the happiness of the original accident?
2) Shouldn't the grail be a stat that asks you to believe nothing?

I have to confess to being a fan of bases per plate appearance. It deals with rate and distance on a level playing field, nothing gets counted twice. There are probably sensible tweaks that could be made to it, though I don't pretend to know what they are.

Anyway, my guess is there's a better way of skinning the apple than OPS-based sleight of hand.

Hoosier Red
02-25-2007, 01:08 PM
So according to Schwartz .287 is just a little above average which sounds about right for his year last year.

Pecota's really projecting a rebound season for him aren't they.
Why does it expect him to be so much better? better luck, better lineup?
Do the authors ever explain that?

02-25-2007, 01:16 PM
I think people are starting to try a get a little too fancy with all of these measurements of someone's productiveness.

IMO, it is nearly impossible to measure someone's production with one equation. Most of these measurements (yes, even BA) have some value. These best way to address someone's production is to look at all of the data you have in front of you and make your own determination.

02-25-2007, 01:17 PM
So according to Schwartz .287 is just a little above average which sounds about right for his year last year.

Pecota's really projecting a rebound season for him aren't they.
Why does it expect him to be so much better? better luck, better lineup?
Do the authors ever explain that?

The basic answer to any "why does PECOTA expect _______" is inherent in how PECOTA works.

It says, let's find the players who look the most like you based on a whole bunch of things including performance, age, position, etc. Then let's find out what they did in the following year(s). Based on that, and adjusted for some things like park effects, we have a series of projections based on the likelihood of their occurrence. The weighted mean is basically the "average" projection.

So, regarding Dunn -- basically, the players throughout baseball history who are similar to Dunn (including his struggles), do awesome things at this point in their careers.

Edabbs, I agree with you to a point. There's no perfect stat which tells us everything we need to know. But even BA is a calculation based on a "raw" stat -- hits. It tells us only the frequency with which a player gets a hit. That's it. It's 1 step removed from an actual measurement of what happened on the field and thus doesn't imply very much. Sure, we can simply look at every raw number and do some magical calculus in our heads to "make our own determinations". Or, we can take all those raw measurements, and find a way to use them together to best judge performance in a way for which we can be held accountable and which we can improve.

If I just stare at PA, Hits, Walks, HR, 2B, SB, CS, FLD%, etc. and say "I think Ryan Freel is more productive than Adam Dunn", well, how can I possibly assess the correctness of that statement? How do I know if I'm right? Furthermore, how do I make decisions in the future about building a team, setting a batting order, or giving a contract offer?

Would I look at BA, OBP, OPS, or GPA and say "Without a doubt, player X is better than player Y"? Nope. Each of those things are fairly limited in what they are measuring. However, if I want to have a sense for which guy is more likely to help my team score runs, I certainly want base that decision on something other than my gut. What something like GPA says is: if you can tell me a team's OBP and SLG, I can tell you which one scores more runs with incredible accuracy. Given that, if I want to score runs, I want the things that lead to runs. Sure, it's not perfect. Speed has a role. Attitude has a role. Hustle has a role. But if I can very quickly get a very good sense of what matters the most with a single number, I'm going to give it some value.

GPA tells me that, by far, Adam Dunn does the things that strongly correlate with scoring runs better than Ryan Freel does the things that strongly correlate with scoring runs. It's not perfect at all, but it gets us a long, long way.

Hoosier Red
02-25-2007, 01:27 PM
Okay and sorry if I'm derailing the thread here, but two questions with that.

1) I've seen others quote things like line drive% and things as a predictor of success or failure. Does Pecota take that into account. (As far as other players who had similar percentages.)

2) Also when you say players who "look the most like him" What is the sample size, and how does it define how far out to spread the net.
Does it say take Pete Rose who is nothing like Dunn, and Dave Winfield who is a little like Dunn and say Mickey Tettleton(thanks Heath) who is a lot like Dunn and just give different weight to each players numbers? Or would it take something like Baseball Reference's top ten players most like Dunn?

Sorry if this is a stupid question, I'm just trying to get a better handle.

02-25-2007, 01:50 PM
Good questions Hooiser. Unfortunately I'm not Nate Silver -- I'd certainly love to have his job. :D

That said, check out the wiki entry for PECOTA -- it's a decent primer.


05-24-2007, 11:50 AM
Just wanted to roll out an update to this thread.

I didn't appreciate it well enough when WOY first posted it back in February, but of late I've been looking it over quite a lot to see if it's a really good indicator of the 'average of production.'

I tend to think it is.

A look at some of our Redlegs so far this season.

Junior - .328
Dunn - .297
Hamilton -.281
Hatteberg - .277
Phillips - .270
Conine - .265
Freel - .252
Gonzalez - .248
Encarnacion - .207
Ross - .202

I don't think anyone should be surprised by the numbers. The production we see with our eyes, without all the stats, you'd probably rank these guys this way in terms of production right now. Potential of course not applicable to this list.

I like this stat, kudos to WOY for bringing it up.

05-24-2007, 12:40 PM
I missed this the first time around. very interesting, thanks for posting.

05-24-2007, 02:41 PM
If they're going to call it GPA, they should multiply it by 10 to give us a GPA we're familiar with. Adam Dunn has a 2.97? That's a solid B!