Fun with numbers (Updated)
Posted: September 1st, 2009 | Filed under: Baseball | 46 Comments »
Today was my first official day as a Senior Writer at Sports Illustrated. So naturally I spent the day …
… well, actually, there was nothing natural about it. I spent the day interviewing with Frank Deford for an upcoming Real Sports piece they’re doing on newspapers.
Yeah, that came out of nowhere, didn’t it? How about that? My first day was spent hanging out with sportswriting’s DiMaggio — the man who inspired me to become a sportswriter and triggered me to dream about working at Sports Illustrated in the first place. What a weird but happy turn of events. As everyone here knows, I don’t like doing TV or radio, in large part because I’m lousy at it. And I was no better today. But I got to take Frank Deford and producer Chapman Downes to Arthur Bryants afterward. And Frank told stories about Bob Knight and Billy Conn and others. A good day.
The absurdity of the day has put on hold a few posts I have been trying to get to for a while … I hope to work on a couple tonight. In the meantime, I’ll mention this quirky baseball statistic I’ve been thinking about lately. Everyone here who would care knows I like playing around with baseball numbers … it’s like a hobby. Well, you know, some people play golf, some people build model trains, and some people blog about Snuggies and do baseball spread sheets. And some people drink.
Anyway, i was thinking about something Bill James has told me — he doesn’t like OPS much because you add the two numbers when he thinks you should MULTIPLY the two numbers.
Well, that interested me. What happens when you multiply the numbers. I’m sure many people have played around with that concept, but I never had before, and so for fun I punched up the stats for teams the last 25 years and multiplied their on-base percentage times their slugging percentage. And then, I multiplied that by the team’s at-bats.
The formula is simply this:
(OBP * SLG) * AB.
That’s it. That’s the whole thing. Like I say, just fooling around.
Here’s what I found: By running that simple formula you can get REALLY close to the number of runs a team scores. I mean, I found it pretty eye opening. Over the last 25 years, the projected runs using that basic formula was about 99 percent accurate. And all but five teams the last 25 years landed within 10 percent of the run projection.*
*I tried and tried and tried to figure out what made those five teams outliers. I could figure it. I think stolen bases had something to do with it. And also homers. But I couldn’t quite get to the bottom of it. Copernicus, I ain’t.
It’s not perfectly accurate, but I don’t know, it’s close enough that it just seems pretty cool to me. Of course, I tried then to adjust the formula so it came out to 100 percent accuracy … and, yes, I was able to do a few things with double plays and stolen bases and sacrifices that made it even more accurate. But at that point, I think I was just moving numbers around to serve my purposes. I figure that if there’s anything to this, the Brilliant Readers will figure it out. Maybe I just rediscovered something that everyone already knows. Maybe the numbers come out this way by sheer luck. I don’t know. I’ll just throw it out there and let some of the smarter math people work on it and maybe come up with some adjustment to make the thing really, really accurate.
But 99% accuracy is pretty good. For fun, I’ll figure a few of interesting teams in history:
1976 Reds
Projection: 863 runs
Actual: 857
Actual runs divided by projection: 99%
1961 Yankees
Projection: 810 runs
Actual: 827
Actual runs divided by projection:: 102%
1962 Mets
Projection: 630 runs
Actual: 617
Actual runs divided by projection: 98%
1977 Kansas City Royals
Projection: 829 runs
Actual: 822
Actual runs divided by projection: 99%
1970 Baltimore Orioles
Projection: 764 runs
Actual: 792 runs
Actual runs divided by projection: 104%
1975 Boston Red Sox
Projection: 781 runs
Actual: 796 runs
Actual runs divided by projection: 102%
1927 Yankees
Projection: 1003 runs
Actual: 976 runs
Actual runs divided by projection: 97%
1954 Cleveland Indians
Projection: 718 runs
Actual: 746 runs
Actual runs divided by projection: 104%
1965 Kansas City A’s
Projection: 596
Actual: 585
Actual runs divided by projection: 98%
And so on. As you can see, sometimes the projections are remarkably close and sometimes they’re a few percentage points off. But they’re always in the ballpark. I guess one of the issues I have with this is I don’t really know why the projection seems to work or what keeps it from working better. That makes it tougher to play around with.*
*I think the formula would work better if I could figure out a better multiple than At-Bats. If there’s anything to this at all — and I’m not saying that there is — the key would seem to be finding what number you should multiply against the (OBP*SLG). If you use plate appearances, it goes too high. I have tried several other formulas that would incorporate stolen bases, sacrifices, doubles plays and such, but again that felt contrived — well, even more contrived than this original statistic. Like I say, maybe someone out there will want to take a swing at it.
In any case, if there is something to this then it could be a good way to rank players. It’s so simple to figure, that it might have a chance to go mainstream. We could call it OXS runs or Runsies or my personal choice: Steve. Which stands for: Steve.
For fun, here are the Top 20 in OXS runs in baseball this year:
1. Albert Pujols, 135 projected runs
2. Prince Fielder, 116
3. Hanley Ramirez, 111
4. Joe Mauer, 110
5. Miggy Cabrera, 109
6. Ryan Braun, 107
7. Chase Utley, 107
8. Adam Dunn, 106
9. Mark Teixeira, 104
10. Michael Young, 103
11. Mark Reynolds, 102
12. Adrian Gonzalez, 101
13. Derek Jeter, 101
14. Adam Lind, 99
15. Pablo Sandoval, 99
16. Ryan Howard, 99
17. Ryan Zimmerman, 99
18. Kendry Morales, 98
19. Justin Morneau, 96
20. Andre Ethier, 96
That’s not a bad list of players. Anyway, I don’t know if there’s any point to any of this. Hey, I’m still giddy about having burnt ends with Frank Deford.
* * *
UPDATE: Several people — in particular the brilliant Tom Tango* — have pointed out what I should have known: That (OBP * OPS) * AB is simply OBP * TB which means all I did was rediscover Bill James’ simple runs created formula. He came up with this, what, 30 years ago. Well, it figures. I told you I was math challenged.
*I’m currently re-reading Tom’s “The Book” — which is really excellent. So many great, great thoughts about baseball … I was telling a friend of mine in the game that this should be REQUIRED READING for anyone who wants to run a baseball team. Hey, you don’t have to buy into all of it. You don’t have to accept that maybe the third hitter in the order is an overrated spot or that small sample sizes really mean almost nothing. But you probably at least want to KNOW about this stuff.
I continue to look for an extremely simple one-stop-shopping stat that could replace OPS. I would LOVE to get behind one. Of course I love Base Runs because it’s so mind-boggling accurate, but it’s complicated*. Even simple runs created is a really good stat, obviously, but it just seems to scare people.
*Of course, so is passer rating and for some reason people cite that all the time.
Maybe simple OPS*SLG could work as a stat.
Top 5 OXS
1. Albert Pujols, .296
2. Joe Mauer, .268
3. Prince Fielder, .245
4. Adam Dunn, .237
5. Chase Utley, .234
Trouble is, we’re SO USED to .300 being a good hitter, .265 or so to be around average, .200 to be lousy that is’t hard to look at those numbers and FEEL them.
Maybe we need OXS+. Maybe Eqa is the answer or WPA or VORP. Or maybe, as Bill James once said, an amateur like myself should just clear the floor. Tom, you got something simple for us?
Loading ...
I remember discovering that in 1986 after reading all the Abstracts. TB * OBP + 0.3 * SB – 0.6 * CS. I figured I wasn’t the first, but it was an independent discovery, so I was pleased with it. I still use it sometimes.
Mmmm, the biggest thing I miss about K.C. is a big heaping pile of burnt ends and pickles.
Isn’t that Bill’s “simple runs created?”
Either he published it as such, or someone else picked up on it several years ago … I know I’ve been using it for at least the last few years — you’re right, it’s a fantastic tool for back-of-the-envelope type figuring.
maybe to make the formula more accurate you could add walks/4 or even walks/some number slightly larger than 4. I don’t think you can make it 100% accurate and adding this might skew the percentage lower than your original.
Joe:
OBP*SLG*AB is the same thing as OBP*TB.
That’s Runs Created.
Bill made his own modifications for the SB, etc.
The next evolution was BaseRuns, which you know about.
Tom
Is the key to statistics and the way they are analysed not how complicated they are to compute (Passer rating), but how common knowledge the idea of ‘good’, ‘average’ and ‘bad’ value of a statistic is? For example, with Passer Rating or even Average, it is the ‘innate’ ability of people to look at the value given (.300/142.6) that then gives the stat it’s ‘value’?
For example, the calculations for Passer Rating and Batting Average could not be further apart in terms of complicity, yet they are both easily understood because the audience have an understanding of what is good or bad. They don’t need to know how it is calculated, but they automatically know that a PR of 60 is bad, and a PR of 120 is good.
Joe-
Regarding OPS*SLG, isn’t the On Base %portion of OPS considered more valuable? It would seem that doubling the OBP in the formula would be more effective.
But I have no idea what kind of numbers that would give you…
You should do what the real mathematicians do…just add an epsilon on to the end of the formula.
Given your love of statistics, spreadsheets, numbers, etc., I was shocked when you said that you’ve never owned a stock. Stock analysis would seem to be right up your alley (business knowledge is overrated).
I have to admit to being a little stunned that Adam Dunn keeps showing up on STEVE and the other measurements. For all the badmouthing he gets from some (yes, J.P., looking at you) it looks like he’s actually a pretty good ballplayer. Think how good he’d be if he enjoyed the game.
Billy Butler just hit a triple. This is surely deserving of a post in its own right, Joe.
Math is hard.
And if we did the calculation for pitchers (simple runs created against?) who would be on top this year?
Or is that just more or less ERA?
Big D is just one of those players who, when you watch him for a while, doesn’t seem that great…but the numbers always say that he’s pretty “great” (or still very good, even when he’s hitting .240 or so). And he’s probably been “really great” this year.
(Talking hitting only here…Adam Dunn is a walking–actually, lumbering–definition of the term “designated hitter.” In a genius piece of sarcasm, Manny Acta described him as “not Torii Hunter.” It’s almost cruel that he’s been stuck in the NL.)
Adam Dunn is one heck of a frustrating guy to try to figure out (I suppose drawing walks with RISP is a good thing…I suppose.) Meanwhile, he’s moving quickly towards 500 HR, and could go well beyond. Seriously, is he really great, or not? Any Reds/Nats fans out there? Granted, he’s having his best year…but is this guy a Hall-of-Fame caliber player, or a one-dimensional above-average player?
The most amazing thing when looking at Adam Dunn’s career numbers is that he took 19 (*nineteen!*) bags in 2002 and got caught 9 times. That means that on at least 28 occasions, Dunn had the green light to go.
I’m sure the 22 year old version of Dunn was more fleet of foot, but that’s just funny to think about. Of course, in 2002, Big Puma played center field and was 3.1 runs above average per UZR, which is also funny to think about.
I guess I’m going to have to turn HBO back on if Deford and Posnanski are going to be on. That should be great watching my two favorite sportswriters talk.
Say, that reminds me of a joke I know:
A grasshopper walks into a bar and orders a beer.
The bartender says: “Hey, you know that we serve a drink named after you.”
The grasshopper say: “You have a drink named Steve?”
You see, the grasshopper’s name was Steve.
I’ll shut up now
“Seriously, is he really great, or not?”
Yes, Adam Dunn is a really great hitter. However, he’s also a really bad fielder*. His positives outweigh his negatives (positive WAR every season), but not enough to classify him as Hall-of-Fame caliber.
* – based on current , but perhaps not accurate, fielding metrics; however observation of Dunn also indicates he’s a bad fielder relative to others at his position.
Joe, I think the problem with at stat like OPS is that it treats OBP and slugging as if they’re equal, and they’re clearly not. 1.000 points of OBP would mean infinite runs, while 1.000 points of slugging could be a home run and three outs, which is not infinite.
What needs to be done is someone needs to find out just how much more valuable OBP is than slugging. I don’t know the answer to this. You could simply double OBP and then add slugging and come up with a number, but doubling it is simply arbitrary. Is it really twice as valuable as slugging? I don’t know what the exact value is, but if you could figure that out then you could multiply OBP by that number and then add slugging to come up with a stat that’s more telling than OPS.
All that said, I think OPS is just fine. It’s crude but it’s something. If you could find a specific number of OBP in relation to slugging, I think you’d have a very accurate statistic. But I don’t even know where to begin to figure that out.
“Trouble is, we’re SO USED to .300 being a good hitter, .265 or so to be around average, .200 to be lousy that is’t hard to look at those numbers and FEEL them.”
Aaron Gleeman had an answer for that some years ago.
Don’t know if anybody cares anymore – those as knew about it were already comfortable with measurements that didn’t match the AVG scale, those who weren’t were unlikely to fetch statistics from Mom’s basements when RBI tells you everything you need to know.
You tested that formula on great offensive teams and got in the ballpark numbers…
what about testing some of the WORST teams and see if the percentages still tell a similar story?
[...] post: Joe Posnanski » Blog Archive » Fun with numbers (Updated) This entry is filed under fun. You can follow any responses to this entry through the RSS 2.0 [...]
VoiceofUnreason beat me to GPA, which is also defined here at The Hardball Times:
http://www.hardballtimes.com/main/statpages/glossary/#gpa
Note that it was TangoTom that derived the 1.8*OBP + SLG, while Gleeman’s sabermetric contribution was to divide it by four.
Although now I see it could be 1.7*OBP+SLG:
http://www.insidethebook.com/ee/index.php/site/comments/why_does_17obpslg_make_sense/
or 1.5*OBP+SLG:
http://www.tangotiger.net/ops.html
It depends on the data.
What if you created a team that had exactly a 1.000 slugging percentage. This team also had a .250 on base percentage. In other words, they hit a home run every fourth at bat. That’s it. I think we could figure out how many runs that team would score per game. (I think it’s 9, correct?)
Okay, now create a team that does nothing but hit singles. How often do they have to hit a single where they will have a OBP high enough to score 9 runs per game? Somehow, someway, if you figured that out maybe you could then determine the relative values of OB% and SLG%.
“Somehow, someway, if you figured that out maybe you could then determine the relative values of OB% and SLG%.”
Sounds like one of my old experiments: can we develop a decent run estimator using only walks, home runs, and outs. My eventual conclusion was “no”. But it was an entertaining problem to work on.
Joe,
When you (or someone else here) has time to play with numbers, I would be curious to know some of the following numbers in regard to Greinke:
1. Total runs scored by the Royals in his starts
2. Total runs scored by the Royals while Greinke is pitching
3. Number of innings Greinke has pitched in which the Royals had yet to score during that game.
4. I would also be interested in seeing a comparison of Greinke’s ERA vs. his average run support in comparison to some of the other top pitchers.
“We wanted to learn about the future of the newspaper business….so we came to Kansas City to talk to a really talented guy who just quit the newspaper business.”
Honestly, looking forward to seeing this segment. How about giving us a preview of what you had to say to Deford??
Chris @ 20.
From my own mothers-basementing using OLS, I’ve usually seen the OBP multiplier is about 1.7x that of the SLG multiplier, so for starters, you can estimate that a 1 point gain in OBP is about 1.7x as valuable as a 1 point gain in slugging to run production. Of course, there’s the problem of OBP and SLG being interdependent. I would probably have to find a way to differentiate the two to really reflect the difference. For now, though, it’s a decent baseline.
I would give up trying to find a run predictor that is 100% accurate. Nothing will ever be that accurate; it would actually be suspect to me if it was. Real-life events have variance; if we knew for sure that according to the predictors the Yankees or Sox would always beat the Royals in a pennant series and the Nationals in the World Series, there’d be no point in our watching, or even their playing.
In real life, the 116-win Mariners go up in smoke and the 83-win Cardinals win the championship. In real life Appalachian State wins in the Big House, and Chaminade beats Virginia, and NC State and Villanova are champs. In real life, Eruzione scores and we believe in miracles.
I like OBP*SLG/(1-AVG) because it incorporates all three “slash” stats and represents simple runs created per out. If you multiply it by about 25.5, you get simple runs created per game (roughly 1.5 outs per game occur on the bases), which you can then compare directly with the league average. My informal studies suggest that the ratio of an individual’s RCG to the league RPG correlates fairly well with OPS+.
In my dream Frank Deford would beat Burt Sugar to death with his own fedora.
Nightfly @ 30.
Obviously the point of number crunching isn’t to determine outcomes. It’s to better equip people to predict the outcomes of events, and way more importantly for a fan, to quantify the value of players to more accurately compare player A to player B. Just because luck factors in to a point of perversion sometimes, especially in baseball, doesn’t de-value the numbers.
“I continue to look for an extremely simple one-stop-shopping stat that could replace OPS. I would LOVE to get behind one. ”
Um, not only are you re-reading the book, but Tango posts here, and wOBA doesn’t even come up?
It’s easy enought to make your own spreadsheet for it, or it’s publicly available at Stat Corner or FanGraphs… no need to pay for the stuff.
Joe – I agree with devil_fingers – wOBA (or anything based on linear weights, but wOBA is both freely available and available in rate form) is the answer.
The basic formula is:
(0.72xNIBB + 0.75xHBP + 0.90×1B + 0.92xRBOE + 1.24×2B + 1.56×3B + 1.95xHR) / PA
Which anyone is capable of doing with a simple calculator or spreadsheet in a matter of moments. It is more accurate than the formulas behind VORP or EqA, which are also much more complicated and more difficult to find the formulas – yep, formulas – for (it took me over a week to write the code to figure those two, while I can generally code wOBA in about 20-30 seconds flat, depending on what I need).
OK, now that I’m done drooling over the BBQ (Colorado BBQ sucks, which, you know, sucks), I’ll just ask one question. How many stats do we really need to tell us that Pujols is awesome? We KNOW he’s awesome.
1.000 slugging percentage could also indicate infinite runs if the person hits a single every time up.
Joe (33) – don’t get me wrong, I enjoy good stats analysis as one tool to help evaluate players. If I wanted to get all Moneyball about it, I could even say that current professional analysts completely undervalue things like wOBA and WAR, and analysts who specialize in those metrics can compete very effectively against their big-market couterparts at ESPN.
My point is just that the endless tinkering with the formulae comes at ever-decreasing gains for ever-increasing complexity and hassle. There comes a point where, realistically, a metric is as good as one can expect it to be. Any further time spent on it is then time not spent enjoying the games or discussing the relative merits of teams and players. It would be like a handyman spending all one’s time building the perfect garage, endlessly polishing and obsessing over the finest tools and gadgets… and then never actually using them to build anything.
nightfly, the problem is that inaccuracies in run estimators aren’t always randomly distributed.
Let’s take OBP*SLG*AB, or Basic RC, for an example. (This is – did you know? – the run estimator that’s at the heart of VORP. True story!)
Is it typically close to accurate at the team level? Sure is! At the team level, you tend to see diminishing returns on accuracy very quickly as you move to other run estimators.
So should we use Basic RC to evaluate individual hitters?
No. Emphatically no.
Because Basic RC (and OPS and OPS+ and a lot of other things – I mean a LOT of other things) overvalue hitting for power and undervalue the walk. So they “work” pretty well for players who are roughly average, or who hit for power and take a lot of walks, and who don’t take walks or hit for power.
But they work very poorly for players who hit for a lot of power but don’t take walks, or players who hit for little power but take plenty of walks.
And when you see what looks like a very incremental increase in accuracy at the team level, it’s not a correspondingly small increase at the individual player level – for most players it makes very little difference but for those players it affects it makes a huge difference. They’re fine if you’re looking at large groups of players and you don’t care how accurate your estimator is for any particular one of them.
But if you actually care about how valuable, say, Billy Butler is, those other metrics will be wrong. (Okay, so more wrong, but wrong in a consistent, predictable and fixable way).
Colin – I see your point. I wasn’t distinguishing between individual and team metrics, just talking more on an abstract level. I’d never want to see the metric become more important than the events it measures.
btw, in the above wOBA formula, what does “RBOE” stand for? I’ve seen a couple of different tweaks of the formula but I can’t puzzle out that bit in this version.
nightfly:
The only thing that would fit is “Reached Base on Error,” right?
Math is religion:
http://www.pastemagazine.com/blogs/lists/2009/01/06/calvinstrip.jpg
[...] Joe Posnanski: I continue to look for an extremely simple one-stop-shopping stat that could replace OPS. I would [...]
I opened a thread on my site asking the readers to propose something:
http://www.insidethebook.com/ee/index.php/site/comments/the_poz_challenge_to_simplicity/
The basic question to ask, in order for Joe to get his answer, is: what value should the average player get?
Is it:
a) around .260 to coincide with BA
b) around .330 to coincide with OBP
c) exactly 1.00 (or 100) because that’s how indexes work
The consensus seems to be c). I’m all for that, and that’s what OPS+ is. OPS+ has construction issues that is correctable. As I noted on my blog, you can get a linear-weights based metric that does what Joe needs done.
Post 26 on that thread has the details.
All you need to do is petition Fangraphs, Hardball Times or BR.com to do it.
The question is not how close you get how often.
Rather, the question is how much of the variation of one is explained by variation of the other. That, if one goes up by 10%, what happens to the other? Is that relationship consistent?
That correlation. How much does changes in one predict changes in the other.
Then, if you have the strong correlation, all your need is a constant multiplier to get REALLY close to the actual outcomes.
So, Joe, look at correlations when you are trying to see if some new stat works or not.
(Disclaimer: I didn’t read the above comments, so this could be a duplicate.)
Allen Barra in his book, Clearing the Bases, lobbies for using SLG*OBP instead of OPS because it properly gives singles more weight than walks.
He calls this stat: SLOB.
I personally use SLOB when evaluating strat-o-matic hitting over OPS, and I find that it’s often more accurate than OPS.