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Linear_Weights
Sunday, December 13, 2009
Well, that was fast. David has now added wRC+.
If Sean can implement the very simple change I noted here, then OPS+ would be a worthy challenger (except for the fact that RC+ includes SB and CS, and OPS doesn’t). As it stands now, OPS+ is not a worthy challenger.
If proof is required, proof will be forthcoming. Please, only ask for it if you are skeptical, and that you have an open mind. Don’t ask me because you want to challenge for the sake of challenge and will reject my findings regardless of what I show.
Friday, December 11, 2009
Well, just a fantastic job by Alex Remington.
The only (possibly questionable) issue is when he says:
and is therefore superior to non-weighted stats like OPS and OPS+.
It is superior to OPS, no question about it. But, with OPS+, it’s more tricky. See, OPS+ also starts off with a bad weighting (approx 1.2 for OBP and 1 for SLG, when it should be 1.7 or 1.8 to 1. But, OPS+ redeems itself that it also adjusts for the park. To the extent that parks matter (Coors, PETCO, etc), then OPS+ *might* be better than wOBA. I don’t blame Alex for not getting into it, and his one line statement is mostly correct. It would be totally correct with OPS, and usually correct with OPS+.
***
By the way, since Sean Forman is in charge of OPS+, any reason we can’t get him to change it to: 1.2*OBP/lgOBP + 0.8*SLG/lgSLG - 1, for OPS+? If he did that, then OPS+ would be (almost always) superior to wOBA. It gets the weights very close to wOBA, plus the added advantage of the park/league factors. Such a simple change. Listen, I have limited pull with Sean (indeed, in some cases, I have negative pull). But, if you guys speak up, he’ll listen. Write to him.
Monday, November 23, 2009
Eric Walker, one of the original sabermetricians working in MLB, takes a look at various run modelers. He finds, unsurprisingly that XR leads the way. But, you don’t test a model that’s been best-fitted to a sample, and then test it against the same in-sample.
John Jarvis for example did the exact same thing as Eric Walker did several years ago. Jarvis however tested one extra linear equation: simply a linear regression equation, with no logical underpinnings to how runs are created. Whatever it spits out, it spits out. And if you look at Table 2, you see the result: a double is worth just 0.15 runs more than a single. A SB has almost no run value. It’s ridiculous and it’s stupid (and I’m being kind). It bears no resemblance to how runs are created. We know exactly how runs are created. And the difference between a double and single is around 0.30 runs.
So, what does XR do? It has a 0.22 run gap. Why does it do that? I presume because it split the difference between the best-fit (0.15) and the true (0.30) in order to get at the “accuracy” and something reasonable.
Finally, the minimum requirement to test these things, at the very least, is for all of them to use the same parameters. You can’t have one include reaching on error, while the other doesn’t.
And which one wins? Well, Eric’s own TOP, which, probably, has been best-fitted to the data. Now, it’s possible that Eric’s method does have logical underpinnings like David’s BaseRuns. And I’m sure someone out there like Patriot or Colin will be tempted to see what comes of Eric’s method using the plus1 method, or other ways.
***
Finally, he quoted someone as saying:
Wikipedia cites Tom Tango as stating that BaseRuns models the reality of the run-scoring process significantly better than any other run estimator. (We shall see.)
Except he didn’t check that. Just because you get a better best-fit does NOT mean you have a better estimator. Correlation is not causation. (God I hate regression so much, when it’s used as the end-product.) Indeed, he does nothing to refute the claim.
Also, he says:
R = A*B/(B+C) + D
Jolly good luck deciphering that without extrinsic information. On further examination of the associated text, it turned out that what was meant was—
R = (A x [B / { B + C } ]) + D
...
(In principle, there is an implied order of precedence for arithmetic operations such that parentheses are often not needed, but not only do few people know it—I’d have to look it up—but there is never any guarantee that the writer of a given equation knows it either, or even knows that it exists.)
Well, I learnt it in Grade 7 I believe. Multiplication and division precede addition and subtraction. If Eric wants to admit that he doesn’t know the precedence rules, that’s fine. But to presuppose that the general population doesn’t kmow ("few people know it") is silly and is made only to support his argument. That the BaseRuns equation HAS parenthesis automatically makes that the first equation to evaluate. And then, REGARDLESS of the multiplication/addition precedence, you either follow it left-to-right, or follow the known precedence rules, you still get the same result. Indeed, only if you believed that the addition takes precedence would you be wrong.
I believe his whole text regarding that was unnecessary, and simply was a pet peeve of his. And my pet peeve is describing your own pet peeve as something that is larger than what it actually is.
Monday, November 16, 2009
Baseball Prospectus has two key signature stats for offense: RARP developed by Clay Davenport and VORP developed by Keith Woolner.
Exactly what is the difference between the two?
Read More
Friday, October 30, 2009
Phil is back.
I’m going to disagree slightly with him that what he’s doing (which is the traditional way of doing it) is the same as his urn example. That’s because the run expectancy charts themselves are also samples. He’s relying on the fact that you have enough events that the 24 base/out matrix will look “normal”. However, even in one league-season, you will get impossible results, like being on 2b with 2 outs will lead to more runs than being on 3b with 2 outs. It has happened.
This is why you need a Markov approach, but which uses the empirical state-to-state transition rates (but you still need a sufficient sample size to get reasonable transition rates).
Wednesday, October 07, 2009
Looks like the blogosphere is all a-twitter regarding Joe Sheehan saying:
Nate McLouth is still a fourth OF masquerading as a starting CF.
First up is Colin Wyers who looks at BPro’s own metrics, as well as Fangaphs, and concludes that McLouth is at least an overall average player. Colin also links to JC, who also concludes he’s at least an overall average player. Then there’s the Primates, who either agree that McLouth is a starting MLB OF, or think that Sheehan doesn’t know what he’s talking about.
What say I? Coming into 2009, I had McLouth as a 2.5 WAR player. That put him 30th in MLB for all outfielders. Basically, if you are a 1.5 WAR player (or better), you are a starting player in MLB. To relegate McLouth as a 4th outfielder is ridiculous.
What’s the breakdown on McLouth?
Offense: he’s a .351 career wOBA hitter, and was .350 in 2009. That puts him as +1 to +1.5 wins per 162G as a hitter.
Fielding: UZR has him as -0.5 to -1.0 wins per 162G in CF. WOWY has him as -0.5 wins. The Fans have him ranked as 44th out of 50 centerfielders. Not terrible, but pretty much on the border of “get this guy to the corners, soon”. Say that’s -1 wins. So, that’s a pretty good consensus.
Position: +0.25 wins for being a CF
Overall, that makes him a +0.5 wins above average player. We are all in agreement here. And remember,if you are 0.5 wins BELOW average, you are STILL a MLB starting outfielder (on the cusp of being a 4th outfielder). Basically, Joe shot his mouth off, and he should simply retract his statement.
Thursday, September 24, 2009
Matt presents SLG on balls in play (excludes HR).
Some of you may remember when Dan Fox released his BIP spray chart app, and I suggested adding “wOBA on contacted plays”. What Matt is doing here is similar in spirit, in that you want to count the doubles and triples differently from the single.
You simply could do a wOBA and exclude BB, HB, K, HR. That means setting the single and reaching on error to around .9 and a double or triple to 1.3 (or use the .90, .92, 1.24, 1.56 numbers from The Book). If that is too much, you can try to combine baBIP and slgBIP ala OPS.
Since we know from wOBA what the target coefficients need to be, then a weighting of .55 for baBIP and .35 for slgBIP does the trick in terms of aligning it to wOBA. That gives you the proper balance, and sets it on the baBIP scale (average of roughly = .300).
Thursday, September 17, 2009
I think I linked to it when it was first posted, but just in case, I’ll do it again. It’s from SABRMatt of Baseball Fever fame. He’s also the one who provided us via Wunderground.com with all the weather data.
You have to join the group first, and then you have access:
http://sports.groups.yahoo.com/group/baseball-databank/files/PCAManifest.pdf
Here’s his table of contents:
The PCA Manifest
Created and Published by Matthew Souders
1. Opening Statement of Purpose
1.1. What is PCA?
1.2. Underlying Philosophy
2. Pythagorean Baseball Theory
2.1. Origins
2.2. The Real Behavior of Runs and Wins (The Tango Distribution)
2.3. The Closest Approximation (Pythagenpat)
3. Top Down Strategy and Team Analysis
3.1. Baseball: The Ultimate Team Sport
3.2. DIPS Theory and Team Defense
3.3. Divisions of Labor
3.4. Margins and Degrees of Freedom
3.5. Offensive Equivalency
3.6. League Context Smoothing
3.7. Linear Weights and Correction for League
3.8. Park Factors
3.9. Evaluating a Team (Beyond Wins)
3.10. Filling in the Statistical Gaps
3.11. Dividing Wins Among the Units
4. Breaking Down the Offense
5. Breaking Down the Pitching
5.1. Defense as a Context (Modified DIPS)
5.2. Calculating DNRA
5.3. Dividing the Wins Among the Pitchers
6. Breaking Down the Fielding
6.1. Positional Claim Points
6.2. Dividing Unit Wins among the Players
7. Normalization
7.1. What is Normalization and Why Do It?
7.2. The General Normalization Method
7.3. PCA-BA
8. The Greatness Index
8.1. Defining Greatness
8.2. What is the GI Method?
8.3. Calculating the GI
9. Sources of Error
10. Future Improvements
10.1. The FSIA (A New Way to Look at Contexts)
10.2. Dynamic Linear Weights
10.3. League Quality and Total Normalization
10.4. Inclusion of Play by Play Data
11. Final Acknowledgements
Thursday, September 10, 2009
Last year, Patriot gave us the history of the bases per PA (or per out) metric, including presenting some data I gave him:
Event Average Bases
Walk 1.39
Hit Batter 1.48
Single 1.83
Double 3.23
Triple 4.46
Home Run 5.41
Stolen Base 1.10
Colin gets into the nuts-and-bolts of exactly where those numbers came from. I think these two articles are required reading for anyone contemplating creating a metric, or understanding existing metrics.
I’d put those two articles front and center in any SABR 101 course as required reading.
Wednesday, September 09, 2009
Colin Wyers, not one willing to accept a stated conclusion without seeing the evidence, decided to find the evidence himself:
But of course the question was about Elvis Andrus in 2009, and from 1980 onwards the advantage shifts to wOBA. Narrowing it down to 1993-2008, the modern offensive era:… Looking at RMSE, wOBA is better by about a run per season. I’d consider that more significant overall, and far more relevant to Elvis Andrus.
Tuesday, September 08, 2009
In Poz’s ongoing quest to finding a stat he can champion, he’s gravitating toward a “counting” number, and the name ”Production”.
I’d post at his site, but since my office firewall doesn’t like his blatant spam-triggering content (actually, it blocks blogger and wordpress software run sites), I’ll make my comments here.
As I said, the only thing someone has to do is tell me what the user requirements are, and we’ll create a stat for it. Joe has decided that he wants a counting stat, meaning that he only wants to count all the positive things. He’s ignoring outs altogether. He’s not interested in replacement or average levels (as far as I can see). Therefore, Linear Weights Ratio is NOT the stat for him. And he CANNOT use that as his basis.
Fortunately, a stat already exists that will satisfy him: it’s the weights that go into wOBA. For the uninitiated, it’s here:
http://insidethebook.com/woba.shtml
So the numbers that Poz cares about is this:
0.72xNIBB + 0.75xHBP + 0.90x1B + 0.92xRBOE + 1.24x2B + 1.56x3B + 1.95xHR
RBOE is reaching base on error. You can include 0.25 for SB and -0.50 for CS (the one exception to the positive rule). Note that these numbers change year-by-year, and those were the numbers for the 1999-2002 era. If you insist on static numbers, I can deliver those.
This works better than looking at the positive numbers that Joe is using from Linear Weights Ratio. The reason is because of the way the outs and PA issue is resolved. In Linear Weights Ratio, the denominator is outs, and so, the positive numbers get their Linear Weights values (proportionately). But, in wOBA, the denominator is PA, which includes outs and hits and walks. In order to get wOBA aligned properly, I need different values for the numerator. In the article I linked to, what those values are is this:
HR 1.70, 3B 1.37, 2B 1.08, 1B 0.77, NIBB 0.62.
These are the RUN values of these events, over and above making an out. So, a walk is +.62 runs better than an out. For my purposes, I found it better to increase these values proportionately so that their overall (weighted) average was exactly 1.00.
For Joe’s sake, he might prefer the HR as a +1.7 because it represents something he can say like “he created 1.7 more runs with each HR than he did with an out”. So, based on his current writings, I would say that’s the stat Joe would be favoring.
But, like I said, all we need are the user requirements. Maybe he doesn’t know what his requirements are, and how he uses his stat will implicitly tell us. We can derive it, and we can create something to satisfy it.
***
“Production” was a stat that Pete Palmer coined, which he labelled as “PRO” to describe.... OBP+SLG (i.e., OPS).
If someone wants to link to this blog from Joe’s blog, please do so.
Wednesday, September 02, 2009
Joe Posnanski wants a simple metric he can sell/use:
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 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?
First off, I have no problem with “amateurs” (whatever that means) dancing with me. In reality, I’m a below-average dancer, and my wife is an excellent dancer. As long as I am willing to learn and keep pace with her, then I deserve to be on the dance floor.
Joe wants to dance, and he wants to learn a good dance, without having to learn the Waltz or (uhhhh) Tango. (Sorry about that.) But, he also doesn’t want, I suppose, to learn the Macarena or the two-step. They’re fun, like OPS, but, you get sick of them at some point.
So, he’d like some new dance, a dance that we won’t get sick of, but also not a dance that is too complicated. He wants to be on the dance floor, and I want him there.
My proposal, so far, is wOBA because it keeps the principle of OBP and SLG alive (assigning a value for each base, and setting the denominator in terms of opportunities). Whereas SLG says a single is “1”, I say it “.9”. Where SLG says a HR is “4”, I say it’s “2”. Whereas SLG says a walk is nonexistant, I say it’s “.7”.
If you want to argue that batting average is the better scale than OBP, then I’m not onboard. Batting average is incredibly stupid, as one of Joe’s old blog posts described very well. I have no interest in that scale. Batting average is line dancing.
However, I haven’t given it much thought. I think it has to be a rate, or index of some kind. It can’t be a simple counting number, like Runs Created, because it does away with outs. RC/27 is ok, but it goes too far in terms of its implications. Perhaps another option is RC+, which would be RC/27 divided by the league runs per game. So, a guy with an RC/27 of 6 when the league scores 4 is 1.50 (or 150). OPS+ is very close to this (but it scr-ws up the individual values somewhat). Since only Sean Forman calculates OPS+ anyway, I see no problem in creating a better stat that only one person (be it Sean or Fangraphs or Hardball Times) that calculates it.
Remember though, we have history that shows how very difficult it is to get a stat into the mainstream. You have to respect that there are conditions to overcome.
What say you?
Friday, August 21, 2009
Mark Reynolds said:
“I don’t understand why the strikeout is such a bad stat,” Reynolds says. “I know when you have a man on third and less than two outs and you punch out, it’s not good. But if there’s a man on first and one out and you hit a weak ground ball to second base and it’s a double play, what good does that do? If I strike out, at least the guy on deck still has a chance.”
He’s implicitly talking about the run value by the 24 base/out states. With a runner on 3B and less than 2 outs, the K is about 0.30 runs more costly than an out. It’s a killer, like a DP. With a runner on 1B and less than 2 outs, the K is about 0.03 runs less costly than a regular out (not such a big gain, but at least it’s actually a productive-type of an out.... well, at least a non-destructive type of an out).
I’ll make Reynolds a deal: let’s only count strikeouts with a runner on 3B and less than 2 outs, or with a runner on 2B (with 1B open) and 0 outs, and show it alongside the number of DP. His Ks will be worth about roughly half that of his DPs. Reynolds has 8 strikeout with a runner on 3B and less than 2 outs. He probably has around another 10 with a runner on 2B and 0 outs. So, that’s about 18 destructive strikeouts (I guess we can call them DK) to go with his 7 DP. His 150 other strikeouts are basically the same as all his other outs.
That’s why we say it’s no big deal. Yes, those 18 K cost his team say 3 or 4 runs (over and above a regular out). But his other 150 are regular outs, more or less. So, overall, the average K costs an extra .02 runs (that is, .02 times 168 equals 3.4 runs).
Reynolds is right. Leave him alone.
Friday, August 14, 2009
On the one side, you have my win metric of choice, WAR. There are a few implementations out there, like Rally has and Fangraphs has. They all adhere to the same basic principles that I formulated with WAR in the beginning, and they’ve added their own flavoring to “make it your own” (*). On the other side is WSAB, which is Win Shares (that I’ve highly criticized in the past) but set to some sort of reasonable baseline ("bench") by studes. It’s a step up from Win Shares, but in no way would I want to use it as anything other than initial evidence. I won’t argue for it.
(*) You will not be missed Paula.
Studes plotted the relationship of career WAR to career WSAB to get an r=.98. All to say that you can take the absolute best, and a half-decent measure, and you will end up with virtually the same thing. There’s only so much you can twist and turn performance stats to get anything truly insightful. That’s at a career level. At the individual seasonal level, things are different.
Wednesday, July 29, 2009
Looking at offensive, relief, and fielding support, Kincaid concludes:
The 18 wins above average matches up reasonably well with the statistical estimates of Vazquez’ win value. In this case, despite the surface tension between the stats and the record, the metrics are in fact in harmony with common sense perception. The stats do translate to real life wins that show up in the W-L columns. Just as common sense dictates, it takes a very good pitcher to bring otherwise substantially below-average teams up to average performance, which is exactly what we’re seeing with Vazquez.
Thursday, July 23, 2009
OPS you all know: OBP + SLG
OPS+ you might know, or think you know: OBP/lgOBP + SLG/lgSLG - 1
tOPS+ you might know, but most probably don’t: OPS+ in a particular context divided by your overall OPS+
Jim Rice, to pick someone not at all at random has an overall OPS+ of 128. His Home tOPS+ is 115 and his Road tOPS+ is 85. (Seeing that he played a virtually equal number of games at home and on the road, these two numbers must be equidistant from 100.)
But, what was Rice’s OPS+ on the road? Well, all you have to do is multiply any of his tOPS+ split numbers by 1.28 (since to get your tOPS+ number, you had to divide by 128). Rice’s OPS+ on the road is therefore 85*1.28 = 109, and his home OPS+ was 147.
Now, this may be a bit tricky, but that 147 is NOT necessarily a product of Fenway Park. Remember that OPS+ adjusts for the league and park you play in. Theoretically (as best as I can understand this), the OPS+ of Redsox hitters at home and on the road should be (overall) pretty much identical (if not in each year, likely for any five-year time period).
So, what Rice’s 147 OPS+ at home suggests is that he took exceptional advantage of his home park.
***
This fellow here however knows enough about OPS+ to be too dangerous. I don’t blame him necessarily. But, he came out guns blazing too fast for something that is not readily apparent what it means. I do know that on other pages Sean shows sOPS+ that would have shown the 109 for Rice’s road OPS+. I don’t know why it doesn’t appear on this particular page.
***
In any case, OPS+ is not a great measure. Well, it’s decent, but it does not deserve the prominence that b-r.com is giving it.
Monday, July 13, 2009
Here are the per PA (excluding IBB, SH) numbers for 1999-2002, but I generated it with an old source of data. I should rerun it at some point. Treat it as 99% accurate.
The sum of the frequency of all events (Single through OtherOuts columns) will total to 1.000 at each base out state.
The state “10” means runner on 1b, 0 outs. The second digit is the out. The first digit is:4=1b,2b; 5=1b,3b; 6=2b,3b; 7=BL; 8=empty.
I also included the IBB and SH, so those numbers represent the “ratio” of IBB to PAs that exclude IBB and SH.
***
The HR rate drops by 20-30% in these base/out states:
2b, 0 outs
3b, less than 2 outs
2b/3b, 1,2 outs
The BABIP is lowest for these states for each of these outs:
at 0 outs: 2b, and it’s not even close
at 1 out: 2b, and it’s not even close
at 2 outs: 1b/2b, followed closely by 2b and bases loaded
It’s clear that with 2b and 0 outs something is happening. However, we can go through all 24 states and something is happening in each of them. That’s called situational hitting and situational pitching.
For example, with runner on 1b and 2b open, and less than 2 outs, BABIP shoots up. In the less than 2 outs category, the highest BABIP is with runner on 1B only, followed closely by runners on 1B/3B. Clearly, having the runner at 1B means there’s a hole on the right side. In The Book, we showed how LHH take the most advantage of this situation, as you would expect for pull hitters to take advantage of the hole.
***
Here’s the data:
Read More
Tuesday, July 07, 2009
Rally gives us his updates.
4. Pitchers have a new set of columns, showing how far above/below average they were in several independent categories. This is meant not as a value measure, but more a descriptor. Not “How great a pitcher was he?”, but “What kind of pitcher was he?” This shows that practically all of Randy Johnson’s value came from his strikeouts, he was essentially an average pitcher if he didn’t whiff you. Roger Clemen’s value lies more in a mix of strikeouts and homerun prevention. Tom Glavine, on the other hand, was below average in strikeouts but excelled in keeping the ball in the park and stranding runners.
I like this, and I do it (or something like it anyway) myself. I like how it creates “profiles”, rather than the catchall single number that is all too easy to dismiss. By breaking things down into components, you have to discuss at the component level. This is why I like the Fans Scouting Report: it’s easy to say that someone’s UZR of +20 might be influenced by whatever. But, if the Fans are saying that Endy Chavez is a 70, 80, or 90 across the board at the component level (on a scale of 0-100, with 50 as average), then it becomes hard to argue if you see him with a high UZR.
To that end, I like how The Baseball Cube breaks down a player’s stats into something easily understood:
Scouting Report
Power: 21
Speed: 85
Contact: 90
Patience: 33
Based on a rating of 100, scouting scores are statistically derived and do not use any subjective analysis by The Baseball Cube, scouts or any third party publications. Though statistical, the methodology is, for the most part, basic. The ratings represent a player’s ranking compared his peers and has nothing to do with a pre-determined bench mark. In other words, there are an equal amount of 100s, 50s and 1s for each stat category.
Wednesday, June 24, 2009
Inside The Book blog reader asks his blog readers this question:
I was catching up on the issues of By the Numbers and read the following quote in the the November 2008 issue:
“An OPS of .800 will always generate more runs than an OPS of .700, given the same amount of playing time.”
I know the above statement is not always true, but do you? I want to give out a prize and decided that I the first person to prove that it is false, using math, will get to choose the first team I will study in depth with my new disabled list database. I know it is not much, but that is all I can really offer. Hopefully there will be more of these to come in the future.
One of his readers already gave out the answer, and not the theoretical mumbo-jumbo I am about to give below. He actually found real-life examples (though I suspect that maybe SB was in there, or park factors, or something). It’s for this reason that I want OPS to die a quick death among serious analysts (as well as its offshoot, the less obscene OPS+). It can survive for quick things. Anway here’s my answer:
Read More
Tuesday, June 23, 2009
Hat tip: Patriot as he highlights a site dedicated to Barry Codell, inventor of what has been popularized as Total Average. This is what baseball analysis would look like if Linear Weights didn’t take hold. And here is their glossary of what can essentially be described as “let’s add and divide numbers”.
Codell paved the way. This site has gone to great lengths to make a religion out of it. Pluto is also a dwarf planet, unless you also accept Eris as the tenth planet. You can’t stick with just nine planets.
from Amazon
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