Tango on Baseball Archives

What's a Ball Player Worth? (November 6, 2003)

Yet more researchers joining the "Win Probability Added" camp.
--posted by TangoTiger at 08:20 PM EDT

Posted 8:36 p.m., November 6, 2003 (#1) - studes (homepage)
See related NL Cy Young discussion from home page. Go, Gagne!

Got to admit, though, that the Halladay rating surprises me. Judging from the rankings, these guys are not splitting credit between pitching and fielding.

If a team or two buys this, Tango and MGL could be rich men!

Posted 9:06 p.m., November 6, 2003 (#2) - limbo lion
it doesnt sound like their ideas are new, since ive already seen the same kind of stuff (ie extrapolated wins, context adjused weights, leverage index) on this site. plus they seem to ignore the research that says clutch hitting doesnt exist. to be honest, their method doesnt seem better than stuff thats already freely available. i guess its all about finding the gm with his in the ground. maybe i should try to sell my secret stats like ops.

Posted 10:31 p.m., November 6, 2003 (#3) - Tangotiger
Ok, I just read the article.

1 - This is NOT a novel concept, since the Mills Brothers (PWA) did this over 30 years ago. This has since been done in some form by Albert/Bennett (PGP), Doug Drinen (WPA), Rhoids, Phil Birnbaum and yours truly (among others).

2 - I am unimpressed with their statement about fielding. They should read Primer more often. Their pitchers are probably overrated because of that.

3 - I would NOT use such a system to evaluate the "true talent" level of a player, but I would (and do) use such a system to evaluate the performance of a player. Therefore, this system is valuable for game-level type decisions more than anything.

4 - The 2 million$ / win has been repeated many many times by many many people.

5 - Their replacement level seems to be about -2 to -2.5 wins (based on the Giambi example cited). Good, cause that's what it should be.

All in all, it's great to see this kind of stuff come out.

Posted 10:50 p.m., November 6, 2003 (#4) - Andrew Edwards
Interesting work. As tango said, not novel, but good validation work.

Agree that pitchers are overrated, they almost certainly underrepresented fielding if Halalday and Delgado are their top 2 AL players.

Cool that they came up with $2 million per win too.

Posted 10:51 p.m., November 6, 2003 (#5) - Tangotiger
Just thought of something

6 - Since they don't measure fielding, they should have a positional replacement level. I would guess they don't based on their leaders list.

studes: I doubt there's riches to be made. And I don't think MGL cares, seeing that: a) he buys the STATS pbp and b) has publicly offered to GIVE his UZR to any team that wants it. This reminds me of corporate America that will only take something if they can pay for it. Linux? No! We need to hold someone accountable when something breaks down! That's the American way! Let's pay 10x more for Microsoft (the kings of the blue screen of death).

American Company to Japanese supplier: ... and finally, we want to see 2% defect rates on the product you supply.

Weeks go by, and Japanese supplier sends the product to America.

Japanse supplier: You will find the product you requested enclosed. As per your request, we have complied with the 2% defect rate. To make matters easier for you, we have sent you the defective parts in a separate box, though we don't know why you want a defective part.

Posted 10:02 a.m., November 7, 2003 (#6) - Nick S
Only five comments and pretty much everything I thought when I read this has already been said. I love the "primate studies" section.

Of course we all have the slightly indignant reaction of "Well, they're doing THAT (e.g. Apparently giving all (most) defensive credit to the pitcher) wrong, so why is this stuff in the national media while Tango's website gets 15 hits a month", but this really is a good thing. It is very hard to get any attention unless you have credentials, as most people for most subjects are not able to easily differentiate between wrong, right, good, bad, and revolutionary ideas, so they use credentials of the inventor or critic as a proxy for the idea's merit (and their certainly is a correlation). So when people read this coming from Math PhDs at Yale, they tend to believe that there is something to it. Since I believ we all agree that with a couple minor tweaks this is a perfectly good "95% there" method, it is nice to see it in the national media.

Posted 10:53 a.m., November 7, 2003 (#7) - tangotiger
It is funny that the people cited either need to be an author (Bill James, Pete Palmer) or need to have a PhD. Me? My ears would perk if Tippett and Ruane are cited, because then I know the journalist knew where to go.

As for the "15 hits a month", this section gets about 20,000 hits a month, which is still way way behind the whole Primer site of 1 million a month. My best guess is that Primate Studies is reaching 1 unique user per 1 million internet users.

Posted 12:47 p.m., November 7, 2003 (#8) - Danil
I still have doubts about WPA....

Here's an example of a kind of question that I don't know the answer to: Consider a 9 inning game, with final score AWAY 3, HOME 2. Before the first pitch, HOME had win probability q, AWAY 1-q. So over the course of the games events, the credits and charges for the AWAY players must sum to q.

Now, rather than trying to get down and gritty with the accomplishments of individual players, suppose we simply lump everything into two categories - offense and defense (defense == pitching+fielding). How much variation is there in how the total credit is divided among these categories? That is, if the credit is distributed differently depending on when the runs are scored, what pattern maximizes credit to the offense, which to the defense, and how wide is the swing between those?

Posted 12:55 p.m., November 7, 2003 (#9) - tangotiger
Can you clarify your statement with an example. I'm having a little hard time following it.

To the extent that I understand it, on average, the swings will be exactly the same at the game level (over n games). That is, if a team plays 2 million games, and wins 1 million of them, the amount contributed by the offense and defense, given that they were equals to begin with, will be exactly the same.

Note that WPA is great in terms of answering a very very very specific question: "Given that you know the inning/score/base/out state, and given that all other things are equal, how much did the next event change the probability of the team winning? ", and it also tries to distribute that change to the players involved in that event (hitter, pitcher, runners, fielders) in some fashion. How you do that distribution is the fun/hard part, especially when you have to consider the park too.

Posted 4:17 p.m., November 7, 2003 (#10) - Michael
Also, it becomes fun/hard if you consider the context more fully. Like who the opposing team is, who is up to bat after you, etc. If the top 4 hitters on a team are really good then the 9 hitter starting an inning of with a double changes the WPA differently than the 5 hitter doings so even if they are the same base/out/score/opponent/park situation.

Posted 4:24 p.m., November 7, 2003 (#11) - tangotiger
I agree completely. Your context is actually any variable that you are aware of. It makes it very hard, for example, if you have Pedro on the mound. Right away, instead of the Sox having a .500 chance of winning, the combination of the Sox hitting, and Pedro pitching (say to an expected 27 batters) is .680, let's say.

So, before you do anything, you automatically have to give +.18 to the Sox players before the game starts! (I know, hard to believe.) Then, as the game is progressing, each marginal Pedro out is worth less than the opposing pitcher's out, simply because Pedro started from a higher win prob.

You might have some really funky stuff like Pedro being injured after 1, at which point the win prob drops down to say .55, and so you must now dock Pedro -.13 wins for being injured (but that's balanced against say the +.14 wins he gets just for being on the mound).

It's actually an extremely fascinating topic (to me anyway), and I will hope to finally implement this by opening day, 2004. But, we'll see.

Posted 6:49 p.m., November 7, 2003 (#12) - Danil
Making reasonable but consistant assumptions of the relative strengths of the two teams:

300000000
200000000

000000003
200000000

000000003
000000002

Do these lines all end up with the same division of credit among offense and defense for the winning team, or are they different. If different, by how much, and which distribution of runs maximizes the credit to the offense, and which distribution maximizes credit to the defense?

Posted 2:52 p.m., November 8, 2003 (#13) - FJM
IMO, the division of credit should be the same, regardless of when the runs were scored. Assuming a 4.5 expected run environment and using the Pythagorean formula, a team scoring 3 runs expects to win 30.8% of the time. A team scoring 2 will only win 16.5%. .308+(1-.165)=1.143. if the sum was exactly 1.00, you'd have your split already. Since it isn't, you have to normalize. .308/1.143=.269. So the offense deserves about 27% of the credit for the win and 73% goes to the pitching/defense.

Posted 3:34 p.m., November 8, 2003 (#14) - Tangotiger
FJM, with all due respect, this is not a question about opinion. Once you accept the definition of what "Win Probability Added" is, then you are forced to accept its results.

Going to these examples:
300000000
200000000

The home team pitchers give up 3 runs in the first. That probably knocks say .25 wins out. The home hitters then score 2 runs, and that probably adds .15 wins. To start the top of the 2nd, the home team now has, say, a .40 chance of winning the game. From that point, to the end of the game, the off+def will lose .40 wins. Since the def is not allowing any runs to the end of the game, I'm guessing that they will gain about .05 wins per inning, while the offense, not scoring any runs, will probably lose about .10 wins per inning (I'd have to work it out exactly).

Anyway, adding it up, and we have the defense being worth +.15 wins, and the offense being -.65 wins. The total is -.50 wins. That's really just a wild guess.

000000003
200000000

In this case, the defense holds the opponent down in the first inning. Say that's worth +.03 wins. The offense gets 2 runs, and so let's say that adds +.12 wins (again, numbers just for illustration). All the way through the 8th, the def holds the opponent, and let's say that adds +.08 wins, while the off can't score any more runs, and let's say that's worth -.07 wins. So, going into the 9th, the home team now has a .72 chance of winning. The defense gives up 3 runs, and let's say knock the chance of winning all the way down to .32 (or a -.40 loss). The offense scores nothing, and so they are worth -.32 wins.

Adding it up again, and the defense is .03 + .08*7 -.40 = +.19 wins, and the offense is .12 - .07*7 - .32 = -.69 wins. I wouldn't be surprised, since both these example gave you pretty close numbers using my wild-asses guesses, that if I did it using my model that you might actually end up with exactly the same numbers.

000000003
000000002

Ok, in this one, the defense gains +.05 wins per inning, and the offense loses .05 wins per inning going into the 9th. The defense gives up 3 runs, and the home team now has a .03 chance of winning. The home team scores 2 runs, but they may as well have scored 0 or 1, as this is still worth -.03 wins.

Adding it up, and the defense is +.05 * 8 - .47 = -.07 wins, while the hitting is worth -.05 * 8 - .03 = -.43 wins.

So, if you can accept these kinds of results, the real-time change in win expectancy, then welcome to the world of "Win Probability Added". If you can't accept this kind of premise, then WPA is just not for you.

Posted 10:32 a.m., November 10, 2003 (#15) - ColinM
studes:
"Got to admit, though, that the Halladay rating surprises me. Judging from the rankings, these guys are not splitting credit between pitching and fielding."

Andrew Edwards:
"Agree that pitchers are overrated, they almost certainly underrepresented fielding if Halalday and Delgado are their top 2 AL players."

This isn't right guys, pitchers are not overrated. Say the Jays have an average defense (I doubt its even that good). If you are looking at an average starter you would expect both him and the defense to contribute 0 wins above average. Now consider when Roy Halladay pitches, how much does the defense contribute? It's still an average defense, so it still contributes 0 WAA. All of the extra wins above average should be credited to Halladay. The defense does not get any better because Halladay is on the mound, and therefor should not get any of the extra credit. I've said it before, top pitchers are typically every bit as valuable as the top hitters.

Posted 11:09 a.m., November 10, 2003 (#16) - tangotiger
Colin is dead-on. As long as the rest of the context is average, then the overall performance (whether as above-average or above-replacement), it won't change. However, as soon as the rest of the context is say a really bad fielding team (i.e., the Yanks), then things change a little.

Work it out, and assume you've got a fielding team that gives up +.02 / BIP more than league average, and assume you've got 2 equal pitchers in terms of $H and component ERA, but one gets 50% of his PA on BIP, and the other gets 90%.

Posted 2:31 p.m., November 10, 2003 (#17) - tangotiger (homepage)
Danil,

If you are so inclined, use the process that I set forth in post 14, with the theoretical or empirical data at the above homepage link, and figure out the off/def split on your examples using WPA.

Only do this if you want to get your sabermetric hands dirty a little.

Posted 3:49 p.m., November 10, 2003 (#18) - studes (homepage)
Colin, Tango:

Thanks. I think a little light bulb just started flickering in my head. Tango, I'm beginning to understand why you once said that Win Shares undervalues pitching.

Sorry to bring up Win Shares, but I've been working on research regarding the pitching/fielding split, so this has been on my mind. James essentially splits pitching and fielding by giving pitchers compete credit for FIP runs below the ceiling, and half credit for DER runs below the ceiling. On the surface, this makes sense to me.

I think you're both suggesting that this should be approached on a purely incremental basis, pitcher by pitcher. Am I close?

Posted 4:17 p.m., November 10, 2003 (#19) - ColinM
studes,

That might be an improvement but I don't think that the pitching/defense split itself is the problem with pitchers WS. I think the real problem is that James translates marginal runs saved directly into WS in a linear fashion. In other words, a pitcher who saves 80 marginal runs will have exactly twice as many WS as a pitcher who saves 40 (ignoring the other little pieces of the formula). But if you work out their expected winning pct. using a pythagorean type formula, you will see that the pitcher who saves 80 runs is actually MORE than twice as valuable as the other guy, because the more runs he saves, the lower actual the run environment becomes. The effect is that PWS tend to severely underrate the best pitchers when compared to the best hitters.

I think PWS can be best improved by using a pitchers pyth. W% vs. the team average, as opposed to using marginal runs in order to divvy up the shares. i can go more into detail later if you're interested, but I'm running out of the office as I type this.

Posted 4:33 p.m., November 10, 2003 (#20) - tangotiger
Studes, I don't want to comment specifically on WS, so let me just extend my above example.

Say you've got 3 pitchers, each with a $H of .280, in a league of $H, and the fielders are all league average. Let's say that one pitcher has lots of K and BB, another has low in both, and another is league average.

All these pitchers give up 4.2 RPG, and are therefore equals.

Now, let's say each of these 3 pitchers now pitch with Ozzie and a few other good fielders, so that their $H is now .260 each. The high K+BB guy won't get to benefit as much from this arrangement (not as much leverage) as the low K+BB guy. The RPG for these 3 pitchers are now 3.70, 3.75, 3.80.

Now, we can see here that the fielders with an average pitcher are worth +.45 RPG (4.2-3.75). However, the high K+BB guy essentially wasted .05 RPG simply because he didn't use them enough.

In this context, in the context that this high K+BB pitcher pitched, he's actually -.05 RPG compared to the average.

From a replacement standpoint, they'd all be compared against the same baseline, whatever it is, as long as that baseline is based against the actual fielders these guys had.

Posted 4:49 p.m., November 10, 2003 (#21) - studes (homepage)
Tango, thanks. I need to noodle on this. Sorry to bring up Win Shares.

Colin, I actually don't think that's right. Don't forget that James does use a replacement level, even though he says he doesn't. If you model it out (which I did, quickly), you'll see that a pitcher who achieves a 33% increase in Pythagoras also achieves about a 33% increase in marginal runs.

Posted 5:51 p.m., November 10, 2003 (#22) - studes (homepage)
One more comment: Halladay saved 37 earned runs against the league average earned runs (ERA vs. league ERA times innings pitched). If you attribute all those earned runs saved to Halladay, which I agree with, I don't see how you get 9 wins contributed above average. I would think it would be four to five games, max.

The Jays also scored 5.6 runs in each game he started, which certainly contributed to his fine W/L record. His BA with RISP also wasn't great, relative to his overall performance, so I don't expect Tango's WPA stats to reveal anything out of the ordinary. This ranking doesn't make sense to me. The Gagne ranking could be.

Giambi is rated ahead of A-Rod. My gut still tells me that they didn't factor fielding into runs allowed.

Posted 6:53 p.m., November 10, 2003 (#23) - Tangotiger
The "9" is wins above replacement.

Posted 12:03 p.m., November 11, 2003 (#24) - ColinM
studes,

I took the time to mock up a spreadsheet to model PWS and test my theory by playing around with different Runs allowed distributions and comparing Pyth WAA vs. WS WAA. I DID find what I was looking for but the effect was much smaller than I thought it would be. Once you I got to Pedro level, WS was about 1/2 a win under the pythagorus estimate. The results were pretty much identical for pitchers closer to the average. However, I did this assuming that since the defense didn't change, all of the extra "credit" would go towards the pitching WS total. I'm not sure if this matters.

I still think that WS causes people to undervalue good pitchers. The main reason is probably that most people look at the raw WS total as opposed to above average or above replacement. But the expected WS total for a pitcher is generally going to be a fair bit lower than that of a position player. If you look at WSAA, the best pitchers start to look a lot better. This is especially important for relievers.

It may also be that there are a number of small factors that add up to have larger effect such as:

- Save adjusted innings. WS adjusts relievers totals upwards to reflect higher leverage situations. But the extra WS credited to the relief ace are pulled from the general pool, when if I remember correctly, Tango showed that starters LI should still be around 1.

- Pitching/Defense split

- The Slight undervaluing of extemely good pitchers

- The "Other stuff" which may tend to pull claim points towards the average.

In general, now that I've taken the time to look at PWS, they seem to work better than I expected. But most research I've seen and done suggests that a top pitcher is just as likely to be the "best" player in the league as a position player. Until win shares reflects that, it doesn't seem like a good idea to use them to compare pitchers and hitters with each other.

Posted 1:48 p.m., November 11, 2003 (#25) - studes (homepage)
Colin, thanks a ton. I appreciate the time you took to model PWS. You're right about leveraged innings taking Win Shares away from starters, though I'm not sure that's a bad thing.

My gut tells me that this may indeed be an issue and, if it is, it's an issue in the way WS handles marginal runs allowed and splits them between pitching and fielding. I plan to take some time analyzing it over the next month or so. I'll let you know if I make any progress. Thanks again.

Posted 7:02 p.m., November 11, 2003 (#26) - Sky
If you were to find what the average value of a homerun is in regards to Win Probability Added (ignoring score, base state, and number of outs), would it hold the same value as it does in linear weights? I guess that's really two questions in one. Should it, by definition have the same value. And if not, does it end up being close, anyways? Are there specific stats that have comparable value in WPA and linear weights, and stats that don't? This thought was triggered by the fact that an IBB has some value in linear weights, but basically zero value in WPA.

Posted 12:30 p.m., November 12, 2003 (#27) - tangotiger
You will find that most events will have a WPA figure that is in the same proportion to the run probability added figure (i.e., LWTS). IBB and defensive indifference would be 2 that would standout against this rule.

***

I'm working, on and off, on my own WPA. The preliminary results shows that Randy Johnson and Pedro, from 1999 to 2002, were around 21 wins above average, if we assume that half their BIP values would be split half/half with their fielders. (In any case, Pedro/RJ did not have performance on their BIP that was much different than average.) So, a top level pitcher, is worth +5 wins above average per year.

At the tier below that, Schilling, Maddux, Mussina, Brown, they were 10 wins above average, or about +2.5 wins per year above average.

Assuming around 2 wins below average being replacement, and 2 million$ / win, I get RJ specifically as being +8 wins and worth about 16.8 million$, on average, from 1999-2002. Pedro was +6 wins, and worth 12.8 million$, Schilling +5 and 10.3 million$. After that, you've got a good number of pitchers at the 8 million$ level.

Interestingly, Armando Benitez came out as the best reliever in that time period! The relievers were Benitez, Nen, Foulke, Hoffman, Remlinger, Rivera. A top reliever is worth around 7 million$ / year.

I've got Pettite as worth 5 mill / year, and the Yanks would be crazy to pay him at the 10 mill level.

I have not accounted for the park yet and a few other things. This is still a work-in-progress.

Posted 2:59 p.m., November 12, 2003 (#28) - ColinM
Tangotiger,

I understand if you don't want to give too much away before your WPA is finished, but do you in fact find that the top couple of pitchers each year are about as valuable as the top position players? I don't think it is fair to compare 4 year averages since pitchers tend to be injured more frequently. But I would expect to see Pedro, Randy and Schilling ranking right up there with the top (non Barry) players in the majors when they are healthy. In my own ranking system I usually expect to see about 2 pitchers among the top 5-6 players and 8 or 9 pitchers among the top 30 players in a typical year.

Underrating of star pitchers has been my primary criticism of pitcher win shares and I would be curious to see this validated (or not). For example I rank the following pitchers as the best player in the major leagues over the last 20 years:
00 - Pedro
99 - Pedro
97 - Clemens
95 - Maddux
94 - Maddux
89 - Saberhagen
86 - Scott
85 - Gooden

Win Shares certainly sees things differently.

Posted 3:05 p.m., November 12, 2003 (#29) - tangotiger
Actually, since you've got top pitchers over those 4 years that were not hurt, then I really don't see an issue in this particular case.

And even if they were, it would be a simple matter for you or someone else to extrapolate that to a full-4 years.

Posted 3:19 p.m., November 12, 2003 (#30) - tangotiger
As for Win Shares, can someone post RJ and Pedro's WS totals over 1999-2002 (as a total), as well as the number of WS that a league average pitcher would have been expected to get given the # of PA (or IP) of RJ and Pedro.

Posted 6:42 p.m., November 12, 2003 (#31) - jon tenney
Win Shares

pedro 89
RJ 107

don't have what a league average pitcher would get

Posted 8:06 p.m., November 12, 2003 (#32) - Tangotiger
Using IP (though PA is probably a better approach), RJ had 1030 IP from 99-02, and Pedro had 746.

Assuming ARI,BOS had 162 GP each:

Avg Pitching WS = 162 GP x .5 W / GP x 3 WS / W x .35 WS = 85

IP = 162 x 9 = 1458

WS / IP = .0583

So, an avg pitcher over 1030 IP would have 60 WS. Over 746, it would be 44.

RJ therefore was 107 - 60 = +47 Win Shares above average = +16 wins above average. I have him at +24 I think.

Pedro was 89 - 44 = +45 Win Shares above average = +15 wins above average. I think I have him at +20.

Win Shares is way below what it should be for pitching.

And remember, I'm looking at it from a PA-by-PA basis. I can also perform the same calculation simply using component ERA or any other measure.

James is saying that Pedro/RJ were +4 wins above average from 99-02, and I'm saying there were a bit over +5 wins above average.

James, to the best of my analysis, is wrong.

Posted 8:37 p.m., November 12, 2003 (#33) - ColinM
Thanks tangotiger for running through that. I think before WinShares can be taken seriously for pitchers it would have to produce numbers in line with WPA for the seasons where WPA is available. I'm sure there's a bunch of us really looking forward to seeing what you've come up with when you do roll out WPA.

Posted 11:56 p.m., November 12, 2003 (#34) - studes (homepage)
I'm even more convinced than ever that the issue lies with the pitching/fielding breakout AND the absence of Loss Shares. It's going to take a bit of time, but I think I can pull those out of Win Shares.

See the link to the latest article on the home page. If any of you have any comments, I'd appreciate them.

Posted 1:14 a.m., November 13, 2003 (#35) - Michael Humphreys
Tango and Studes,

For what it's worth, DRA shows Pedro as the best player in all of baseball in 1999, though not quite as valuable as SLWTs values A-Rod and Barry in 2000. During the 1997-2001 period, he was worth comfortably more than 50 runs a season on average.

Posted 8:04 a.m., November 13, 2003 (#36) - Tangotiger
Thanks to studes, if we include pitching+fielding+hitting, pitchers (AL and/or NL) get 36% of win shares.

So, pitcher win shares = .36 x 243 = 87.5
non-pitcher WS = .64 x 243 = 155.5

Give an average pitcher 7 IP x 36 starts = 252 IP

This pitcher's WS = 87.5 x 252 / (162 x 9) = 15

For a non-pitcher playing average at an average position (3b? cf?), if this player played 140 full games, he'd also have 15 win shares. (140 x 155.5 / [162 x 9] = 15).

So, who here believes that these 2 players are equals? That is, an average pitcher, pitching 7 IP / game for 36 games, has produced the same win/loss impact as an average hitter/fielder at an average position over 140 games?

Posted 12:29 p.m., November 13, 2003 (#37) - studes (homepage)
Tango, one math comment. For the everyday player, you multiplied the denominator games by nine. I assume this is for nine players on the field, but you've already separated one of those nine players (the pitcher). So I think you mean to multiply 162 by 8, which gives an average player 17 Win Shares, vs. 15 for an average pitcher. I'd buy that.

Of course, this is assuming the National League.

Posted 1:46 p.m., November 13, 2003 (#38) - tangotiger
Good point. Ok, so that's 125 NL games and 140 AL games. That by itself is a little troubling no?

So, we are saying that the following will all have 15 win shares:
- an average everyday NL player, playing in 125 complete NL games
- an average everyday AL player, playing in 140 complete AL games
- an average pitcher, either league, throwing 252 IP

Thanks studes, you just convinced me even more about how poor the scale is between non-pitchers and pitchers.

Posted 1:49 p.m., November 13, 2003 (#39) - ColinM
I dunno, I don't buy it. A pitcher who can throw 252 average innings is less valuable than an injury prone average CFer?

Look at it this way, say we use a replacement baseline of .75. For pitchers it would be about 1.22 assuming an average defense.
(2*(1/.75) + 1)/3.
So assume 5RPG average, pitcher gives up 140 runs. Player creates 78 runs. Pitcher saves (140*1.22-140) = 31 runs. Player adds (78-78*.75) = 19.5 runs. The player gets no more credit for defense because studies show replacement defense is close to average anyway.

Whoa..whoa..whoa. Hold on a sec. Let's think about that last sentence. Could it be that Win Shares is suffering from the same double counting effect that Tango found at BaseballProspectus?!

Think about it. As some of the guys have pointed out around here, a replacement player who gives you .75 offense should still give you about a 1 defense. But what is WinShares doing? It sets its 0 level replacement level at 1.52 for both pitching AND defense. Does this make sense?

Is it possible that what we need is somehting like differing 0 levels for pitching and defense? In this type of system FWS over average remain the same, but total FWS go down and PWS go up bringing pitchers and hitters more in line with each other. I don't know, I need to think about this more...

Posted 2:02 p.m., November 13, 2003 (#40) - ColinM
Michael,

When you say that Pedro finishes a little behind Bonds and ARod in 2000 are you comparing them in terms of runs? If so, it may be that Pedro still jumps ahead when you convert the runs to wins. You know, the old a run saved is worth more than a run added. Just think of how low the run environment is in games that Pedro pitches.

BTW, nice job so far on the DRA articles.

Posted 2:42 p.m., November 13, 2003 (#41) - Michael Humphreys
ColinM,

Good call. I *was* just looking at gross runs better than league average. Normally the differences between runs saved and added are not great, but when you're talking about Pedro and a dramatic reduction in runs, the difference is probably greater--non-linearity increases as you approach zero runs allowed. In addition, I didn't adjust for park effects, and Fenway is probably still pro-hitter, though not nearly as much as before.

Thanks re: DRA. I haven't focused on the pitching as much, because fielding seemed to be the bigger problem. I just wanted to add my support to the idea, ably expressed here, that pitchers , even today, can be the most valuable players in baseball.

Posted 3:20 p.m., November 13, 2003 (#42) - studes (homepage)
Tango, I don't think that's quite right, because you're adding back in pitching and fielding shares of a designated hitter, although he doesn't play defense. I'd have to think a bit about how your scenario plays out in the AL.

One small note: not piching in the AL actually helps most pitchers, because their negative batting marginal runs aren't impacting their totals.

I also agree with Colin. A pitcher who throws 250 innings with an ERA of 4.00 is a good pitcher, IMO.

Colin, you may be onto something with the replacement level for fielding and pitching. I have to work this out over the next couple of weeks, but I think the Win Shares issue is this: once you compute Loss Shares for fielders and pitchers, you're going to find that most, if not all, fielders hover around the .500 mark. That is, the variability won't be high.

Pitchers, however, will vary widely. In fact, the superstar pitchers will incur negative Loss Shares (at least, in the way I'm thinking about it) and I am interested to see what will happen to their pitching Win/Loss Share totals, compared to everyday players, when that happens.

At least, that is what I think will happen. Sheesh, I've got a lot of work to do.

Posted 3:42 p.m., November 13, 2003 (#43) - studes (homepage)
One other thought: using averages in this example may be misleading, because the variance among pitchers may be wider than the variance among batters, particularly once Loss Shares (or something) are added. Different distributions will skew your analysis. The median might be a better point of analysis.