Buy The Book
I just saw the post, so I’ll read through it, and comment as appropriate. Sean reached out to me on a couple of things, so I’m keen on seeing what the final product looks like.
UPDATE 1: I just read through all the descriptions on Sean’s site. The explanations are tremendous, and I have no major objections. I’ll give it a second read-through, and will just make some minor, sporadic comments.
More updates below…
Good job by Julian in presenting the point that reaching base on error is not the same thing as making an out.
And note that ROE *is* part of wOBA. It’s in The Book. The only reason you will not see it in some places is because in those databases, ROE is not counted at all. So, it’s hard to include ROE in a metric, if the event is not tracked!
Otherwise, in things like WPA, it’s definitely and positively included.
One of my favorite stats is RE24, which goes by other names, like “value added” or “value added by the 24 base-out states”.
The basic idea is that you are interested in the 24 base-out states, and the outcome of the performance in each of the particular states. A HR with bases empty has a different impact than a HR with men on base. A strikeout with a runner on 3B with less than two outs is hugely impactful, while with no one on base, it is no different than any other out.
To the extent that you think a player should be recognized for that outcome in that context, then RE24 gives you exactly that.
A decade ago, I wrote this little article, which focused only on the 8 base states (just for ease of explanation, and no other reason).
There is a useful chart there, and we can compare the first line (bases empty) to the second-to-last line (ROB, runners on base), so we’re only comparing those two states (was there a runner on base, or not). A HR for example is worth exactly 1 run with bases empty, but it’s worth 1.92 runs with a runner on base. While a single and walk have identical values with no one on base (0.29 runs), when you have runners on base, the single jumps up in value substantially (0.73 runs), while the walk adds a little (0.42 runs).
We see the K value has more impact than a regular out with a runner on 3B, -0.48 runs compared to -0.29 runs. (Note: since I lumped in all three out states, this gap is not as large as it should be, if I compared the K value with a runner on 3B and less than 2 outs. If you want to look at the full 24-base-out chart, there’s one right here. We see the biggest difference is when you have a runner on 3B and one out: the K value is an enormous -0.60 runs, while all other outs is -0.22 runs. In this situation, the pitcher is going to go out of his way to strikeout the batter. Of course, the batter is aware of this, and he’s going to go out of his way NOT to strikeout. There’s alot of these things game-within-a-game insight you will find with the Linear Weights by 24 base-out charts.
Anyway, to the extent you want to be aware of the impact of each event by these 24 base-out states, then the actual outcomes is captured in RE24. Given a large enough career, what we care about is RE24, and not Linear Weights (i.e., wRAA, wOBA, wRC+). That because RE24 is about outcomes based on the 24-base out states, while the other stats don’t care about the outcomes in specific states, and just assumes the performances were proportionately spread out.
***
RE24 is especially helpful with relievers, as it properly assigns the run values when a reliever enters mid-inning and/or leaves mid-inning. For a starting pitcher (or a reliever that starts and ends his own inning) RE24 is proportionate to his runs allowed in any inning where he starts the inning and ends the inning.
While RE24 is compared to the league average (and so a pitcher that allows 1 run in two innings is going to get an RE24 of 0), you can simply add the league average runs per inning (say 0.500 runs per inning) to get the total number of runs allowed by the pitcher, and be exactly matched. (Though, you have to be aware of what particular RE24 chart is being used, as Fangraphs and Baseball-Reference use park-adjusted RE matrix.)
***
I hope this helps those who are a bit flummoxed by exactly what RE24 does and how it is useful. In time, it should be part of your saber-arsenal.
David has posted the constants he uses each year (with the obvious note that 2012 is still evolving).
You can see that since 1993, things are pretty stable, with the walk being 70% of a “safe” play, the single at 90%, the double at 125%, the triple at 160%, and the HR at 200%. The SB is 25% and CS is -50%. Runs per PA is .12, and runs per win is 10. The FIP constant is 3.1 (but it depends how you handle IBB and HBP).
Average wOBA is .330, but that’s baseline to match the league OBP. The “woba scale” to convert from wOBA into runs per PA is around 1.20.
My favorite characteristic of wOBA is that it matches OBP, and so, the average safe play is fixed at exactly one (i.e., 1.000), any year, any league.
Phil gives you some results, including this one:
0.494 (.030) single
0.730 (.054) double
1.343 (.193) triple
1.465 (.054) home run
0.342 (.025) walk (including IBB)
I’ll also reference an oldie-but-a-goodie, Linear Weights calculated at the inning-level. I think it helps to explain what Phil is noticing at the game level, but makes it more forceful/apparent at the inning-level.
WAR (Wins Above Replacement) is a FRAMEWORK, one that I have developed, or otherwise helped in shaping. One of the key components is how the fielding+position is tied in. Another key component is the separation of starting and relief pitching. Those are basically the elements I look for, among other things.
There are a few IMPLEMENTATIONS of WAR out there, with Fangraphs (that I dubbed fWAR) and Rally’s via Baseball-Reference (rWAR). I’d consider Baseball Prospectus’ WARP also as part of the WAR family (though they messed me up, as I’d like to call it pWAR!), even with my major reservation, if not downright dismissal, of using FRA as the centerpiece of the pitching version of WAR.
The latest one around is gWAR (from Baseball Guage), and it seems to have the main elements I look for. I haven’t looked at it in-depth or anything, so maybe this thread can help the discussion. On the plus side, gWAR is a great acronym, as I can imagine The Hulk saying it. gWAR.... gWAR!! Is it just me? Ok, then, forget I said that. From the looks of it, it seems to have had the fWAR philosophy to pitching (FIP-based), but then decided to go completely the other way to the rWAR philosophy (Runs Allowed-based).
Anyway, until I study it, I won’t put my approval stamp on it (for those who care for that stamp anyway).
UPDATE: I forgot to mention that gWAR’s fielding is now based on Wizardry’s system. Michael is a dedicated and passionate researcher on fielding, so, it’s a plus that gWAR is based on that.
Everything you wanted to know about OPS and OPS+, but were afraid to ask, courtesy of Patriot.
bOPS = 2.25(OBA) + SLG - .5(BA)
...
It is tempting to look at the bOPS formula, see the negative coefficient for BA, and make a statement about the merits of BA as a metric. While we could all spend the rest of our lives taking potshots at BA (and rightly so), that should not be the takeaway from this exercise. The introduction of BA here allows us to improve the intrinsic weights by changing each hit weight by an equal amount while leaving walks untouched; the alternative of changing the weight on SLG affects all hit types differently (based on how many bases they are worth, of course).In doing so, the OBA weight has been raised above its optimum level (around 1.8), but this has been offset by removing .5*BA so that walks can get an extra boost. It is therefore much more of a statement about how metrics based only on linear combinations of OBA and SLG are incapable of valuing walks properly without distorting the relationship between intrinsic weights for the other events.
Fantastic point. Since the walk appears in only one of the three terms, and the hit appears in all three terms, the best-fitting of OBP, SLG, and BA will end up causing something that looks… weird, like a higher batting average is worse. But, it’s only true in the context of the other two terms. If you were to modify SLG to include walks, even as half a base or something, then the coefficient for the batting average would change drastically. The terms are so sensitive to the construction of the other terms, that you can easily change the weighting by slight alterations.
Patriot, by the way, is awesome. He was one of the first guys that I intersected with on baseball forums, back at the old Baseball Boards (RIP). That’s the same site that I met MGL, David Smyth, Voros, GuyM, and several others (BenV, dackle, where are you guys?). It’s where I made my bones, and half of what I learned, I learned there, in no small part to all these fine guys. Debates got very heated. Very very heated. But, there was a certain level of respect I think. It was very much alot of give and take, and we all treated Baseball Boards as our home. Like arguing with your buddies at the bar, and you’d come back every day, happy to do so. I think the fact that we had ownership of that board that we basically implicitly ensured that we took care of that place. I don’t know that we could ever recreate that magic we had back then.
(That’s why I feel strongly about the blog here, that I have to treat this place as my home, because that’s the way you ensure its survival. So, the Straight Arrow readers who post here do the same. It has to be a place that is welcoming, not only for yourself, but for others. If this place becomes an unpleasant place to visit, then either I have failed, or you have failed. If that failure can’t be rectified, then there’s no sense for you the reader to continue to be here. If it’s unpleasant for you, and I can’t accomodate you, then better for you to move on.)
Patriot works his magic to show you what the equivalent OPS equation looks like. That is, OPS is OBP plus SLG. And anyone in grade school knows that you can’t add numbers of differing denominators. (Apparently, when it comes to the sports world, we ignore that inconvenience).
Anyway, Patriot takes the partial derivative and:
The formulas in this post are not estimates of OPS. They are precise, equivalent formulas to calculate OPS given that AB% is held constant.
He comes up with this:
As mentioned above, this means that a precise alternate formula for OPS given a fixed AB% of 88.59% is:
OPS = (W + 2.129S + 3.258D + 4.387T + 5.515HR)/(AB + W)
If we convert wOBA equation so that the S is fixed at 2.129, we get:
wOBA = (1.70W + 2.13S + 2.93D + 3.69T + 4.61HR)/(AB + W)
So, no surprise. OPS severely undervalues the walk, and somewhat overvalues the extra base hit. If you are going to go to ANY effort to calculate a metric that includes BB, H, and HR, it makes zero sense to put that effort into OPS.
I can understand calculating OPS if you already have OBP and SLG in hand. But to calculate OPS by first needing to calculate OBP and SLG and then adding them together? And worse, needing to calculate OPS+? That’s a ridiculous amount of unneeded extra effort.
I’ve already provided the best equivalency for calculating OPS+, and we just need enough people to complain to B-R.com for that change to happen. So far, it seems that n=1 in that regard.
A reader wants to know why I set the coefficient for 2B and 3B as identical in my various equations, notably wBABIP.
Three reasons, none of which may be good, but, they’re the reasons I’m going with:
1. For ease
2. The quantity of 3B is so low that it won’t matter most of the time
3. I think of 3B as 2B with speed, so when it comes to batting, I like to split the 3B into two components: 2B+SB. So, I put the 2B portion in the hitting, and the SB portion into baserunning.
To me 30 2B and 10 3B and 40 SB is the same thing as 40 2B and 50 SB.
It’s not entirely true, but I see more benefit in terms of doing this than not doing this.
Michael does a good job at starting the reader from scratch. If you’ve been a bit confused by run expectancy and linear weights, perhaps this article will help you out.
Not that it makes much of a difference, I recommend this page for your run expectancy needs:
http://www.tangotiger.net/re24.html
It’s based on more data, the run environment isn’t as extreme as the oft-cited 1999-2002 page, and gives you extra charts too.
Clay starts with all the plate appearances, and removes hits, walks, and hit batters. Basically, he’s left with outs and some form of reaching base on error. He compares the actual change in run expectancy (RE24 on Fangraphs) to what it would have been if the plate appearance was a strikeout (i.e., one out, no runners advance). The leaders and trailers:
Josh Hamilton, Tex 20.1
Derek Jeter, NYY 16.2
Juan Pierre, CWS 15.7
Omar Infante, Fla 15.5
Carlos Lee, Hou 15.2
Hideki Matsui, Oak 14.9
Angel Pagan, NYM 14.8
Ichiro Suzuki, Sea 14.6
Elvis Andrus, Tex 14.5
Alcides Escobar, KC 14.4
...
Brian Bogusevic, Hou -1.3
Matt Domiguez, Fla -1.5
Brad Hawpe, SD -1.9
Brian McCann, Atl -1.9
Pedro Alvarez, Pit -1.9
Matt Wieters, Bal -2.0
Matt Holliday, StL -2.8
Ryan Adams, Bal -3.0
John Buck, Fla -3.3
David Ortiz, Bos -5.1
Because he included reaching base on error, that probably explains Jeter and Pierre and Ichiro. My preference would have been to keep them separate, but, not that big a deal.
You should also note that it’s easier to get a plus than a minus. That’s because, overall, a strikeout is more negative than a non-K out (especially if reaching base on error is included in this category). Typically, a K-out is about .01 to .02 runs worse than a non-K out (again, depending how you handle the errors). Clay shows the team totals, and the average is that a non-K out is 80 runs better for a team than a K-out. That works out to 9 runs per 162 games per player (which is about .02 runs per out), or say about 7-8 runs for a typical regular player. (And you could have figured out that yourself, since the leaders/trailers endpoints are at +14.4 and -1.3, and the halfway point of that is 6.6 runs.) It might be better if Clay readjusts his numbers above to force the zero-point.
This is how I like to visualize the various components of wOBA. Here’s what to look for:
1. The green area under the 1.000 line is equal to the green area above the 1.000 line. This implies that the average value of the events equals 1. This forces wOBA = OBP.
2. The gap in the red area gives you the value of each event above the 0.333 baseline (or whatever the league average OBP is). This gap is exactly proportional to the Linear Weights run values.
Because of these two points, you get the wOBA values, of roughly 0.7 for a walk, 0.9 for a single, 1.3 for a double/triple, 2.0 for a HR. That’s all there is to it.
There are two great implications of using wOBA:
A. Even though wOBA IS Linear Weights, I have never ever ever had to explain what a “negative run value” is. It just doesn’t exist in wOBA. It’s hidden by having the baseline lowered as I have.
B. Because it is coupled with OBP (the same mean, and the same denominator of plate appearances), and OBP is perfectly suited for the binomial distribution, wOBA takes on similar characteristics. Not exactly, but close enough for our purposes. Whereas the binomial would say p*(1-p), in this case, we’d use p*(1.1-p).
Hence, my love for wOBA.
I like debates where both sides make reasonable points.
Anyway, my opinion as to the reason that Howard is (currently) seen as elite, but should be seen as average: he has had star to superstar seasons in the past, but he hasn’t had those in the last two seasons. There’s a huge difference when you hit 45 to 58 home runs in those star seasons, and when you hit 10 to 15 fewer home runs today. We’re talking about 20 runs of value that has simply disappeared on power alone. That’s 2 wins, and that turns a star player into an average player.
Even relying on the old school stats, Ryan Howard had 136 to 149 RBIs from 2006-2009, and in these last two seasons, he’s down at least 20 RBIs. His runs scored was 94 to 105 in his peak, and he’s down now at least 10 runs scored.
If you look at his wOPS (weighted OPS): from 2010-2011, among the 30 1B+DH with at least 810 PA, he’s #11. So, just on the hitting side among his peers, he’s barely above average. Add in his below average fielding and running, and you have yourself an average player.
He has been very clutch though. And I think that is what keeps his elite status in play (among his supporters, anyway).
The work I’m most proud of is the Markov calculator. Baseball is a really simple game: you get on base, you move over, until you make too many outs. It’s one of the easiest thing to program. You can’t run backwards, you can’t jump bases, you can’t have 4 outs or 2 outs in an inning. It’s very structured, very easy to program. Every single person who reads this site needs to try out the Markov calculator. Seriously.
(The only limitation to the calculator, and what makes baseball a bit tougher to code, is that you can have runners out on base. This would turn a very simple program into a fairly complex program. I’ve offered the simple one, for free, with the source code available to all.)
Anyway, using the default values, you hit calculate, and we see that that team will score 4.905 runs. Now, what happens if this team does not hit any HR? Well, click the back button, change the “1” to a “0”, and change the hits from 10 to 11.2. (This is because trading a HR, which has a wOBA value of 2.0, for 2.2 singles, which has a wOBA value of 0.90, is a fair trade. So, we lose a HR, but gain 1.2 hits.) You end up scoring 4.944 runs. That’s 0.039 more runs scored by NOT having a slugger.
Basically, alot of the value of singles and walks is not realized, because you get HR hit. By not having any HR hit at all, each of those events takes on greater importance, as they feed off each other.
As an aside: Ty Cobb and players of his era should not be judged by standard linear weights. The run value of a single shoots way up when there are no HR hit, by something like +.07 runs per single. But the value of an out also has more impact by an extra -.04 runs per out. Cobb gets more hits and makes fewer outs, so his value goes up more than what we’d use with standard linear weights.
Fangraphs has had it for a while. In the section “Background on WAR”, there’s a link to a 15 part article as to how to calculate WAR. I also had a basic thread on the matter three years ago.
This post is in response to a Primer reader who said:
I again ask where I can find a detailed breakdown of how WAR components are calculated. I don’t see it on Sean’s site or on b-r. If the answer is that this information is not public, then that’s the answer. Is that the answer? Is this stuff black box?
You can also see all the leaders here, with the breakdowns (and David allows you to export it to Excel too). One thing I’d like to see from Fangraphs is to combine fielding+position (as an option). This way, you can better display the “best fielders”, when you do a sort. I understand you may want the two separate. I’m just saying to have both (separate, and as a group of two).
a) WAR is wins above replacement.
b) WAR is a framework.
c) WAR presents the performance of a player into a single number.
d) WAR is limited to the data points it considers.
e) WAR is limited by the bias in the data.
f) WAR is not all-encompassing.
So, what does all that bullsh!t mean?
Someone at BPro was asking about the value of a called pitch. This is how I explain it quickly:
A crude way to think about the run value of a strike or ball is this way:
The run value of a walk is around +.30 runs, and the run value of a strikeout is around -.27 runs.
So, going from an 0-0 count to a 4-0 count means that each called ball is +.075 runs.
Going from 0-0 to 0-3 means that each called strike is -.09 runs.
That means that switching a called ball to a called strike is going from being at a +.075 run state to a -.09 run state, or around a .16 run swing.
So, getting that one call every game for 150 games means .16 runs x 150 calls = 24 runs.
This is just a quick crude way to try to frame the expectation.
May 26 13:33
Do pitcher’s reach back for velocity when needed?
May 26 13:18
What makes for a successful GM?
May 26 07:27
“Why Kickstarter works”
May 26 03:03
Pete Palmer’s new book: Basic Ball
May 26 01:11
Largest demonstration in Canadian history?
May 25 19:41
What sabermetrics is NOT
May 25 16:59
Howard Stern
May 25 12:51
Chad Curtis
May 25 11:26
Lack of hustle during a game
May 25 10:58
Rooting for laundry
THREADS
May 26, 2012
What makes for a successful GM?
May 25, 2012
Pete Palmer’s new book: Basic Ball
May 25, 2012
“Why Kickstarter works”
May 25, 2012
Chad Curtis
May 25, 2012
Which pitchers are the forecasters betting on a good rest-of-season?
May 25, 2012
What sabermetrics is NOT
May 25, 2012
Sports pic of the year?
May 25, 2012
Do pitcher’s reach back for velocity when needed?
May 24, 2012
Largest demonstration in Canadian history?
May 24, 2012
Rooting for laundry
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