Tango on Baseball Archives

Win Shares, Loss Shares, and Game Shares (November 15, 2003)

Studes, the main man trumpeting Win Shares, has now come over to my dark side and is embracing the concepts of negative Win Shares, Loss Shares, and Game Shares.

Seriously, I'm glad that someone as ambitious and intelligent as studes is putting in the super effort to try to shed light on WS, as well as offering his persepective.

He's got a few more links as well on this topic.
--posted by TangoTiger at 02:24 PM EDT

Posted 5:29 p.m., November 15, 2003 (#1) - studes (homepage)
Tango, that is too funny. Thanks for the kind words.

You know, I never meant to wind up "trumpeting" Win Shares. It's just that I've always thought Win Shares were interesting, and I thought it was a shame they weren't being presented anywhere. Then I "met" Pete on Primer and we started working together.

I'm hoping my site will have some influence -- I know Rob Neyer drops by once in a while -- and that folks will understand that Win Shares can and should be improved. I would think this could only help your WPA approach, by the way, by helping the same folks better understand the validity of your interesting system.

Posted 3:03 p.m., November 16, 2003 (#2) - David Smyth
Here is a post I made on stude's site in the Loss Shares thread.......

Tango wrote----"I don't subscribe to the Patriot/David model of absolute wins / losses. In fact, I don't even believe in absolute wins / losses. Everything is marginal from my perspective."

I'm not sure what it means that you don't "believe" in absolute runs/wins. They certainly exist. The Cubs in 2003 scored 724 absolute runs and had 88 absolute wins. That' a fact. If you are saying that it's impossible to build an analytical system based on absolute runs/wins which works, then I beg to differ. I have a framework using only absolute runs scored and allowed which I believe is every bit the equal of Win Probability Added. The "assumptions" are a bit different, and IMO, equally valid, or more so. These assumptions allow for a much simpler system which, I believe, is very logical and adds up properly. I will prepare a thread on this for FanHome...

Posted 6:42 p.m., November 16, 2003 (#3) - tangotiger
I meant that I don't believe in absolute wins/losses at the player level. Players, in a team sport, get their value based on changing the state at a marginal level. This is just my perspective.

To convert from a marginal utility to a total utility will require some weird things, like negative wins.

If you are going to say that runs scored leads to wins and runs allowed leads to losses, you are still going to have some "playing time component" to carry the context, so that you will always know what the average or expected absolute wins and losses is for that player. And even your conversion from runs to wins needs to be aware of the entire context for you to make that relationship. I think you are really hiding the marginal impact inside an asbolute total.

I look forward to seeing your post...

Posted 8:04 p.m., November 16, 2003 (#4) - David Smyth
----"To convert from a marginal utility to a total utility will require some weird things, like negative wins."

Well, why is negative wins so weird, compared to some of the stuff you come up with? :)

Thinking about it quickly in those terms, I think batters can get negative run shares and negative win shares and pitchers/fielders can get negative runs allowed shares and negative loss shares. An example would be a batter who strikes out with 2 outs and bases loaded, or a reliever who comes in and retires a batter with the bases loaded and 2 out.

I suppose I should come up with a different term than "shares" to avoid confusion.

Posted 8:38 p.m., November 16, 2003 (#5) - tangotiger
Exactly. Those things are MARGINAL. At the very least, your process starts with marginal utility.

While you and others try to convert that into total utility, I'm happy to leave it in marginal terms. Bonds had 60 win advancements and 30 loss advancements. Pretty clear. Why muddle it up by doing some conversion into total utility?

Posted 9:07 p.m., November 16, 2003 (#6) - David Smyth
Well, I don't think that's what I am doing, Tango. Maybe I am and don't know it. I'll be happy to see you debunk it if it's bad.

Posted 10:42 p.m., November 16, 2003 (#7) - tangotiger
Btw, I like a common sense approach.

You see, a win probability added approach adds up after every single pitch, PA, inning, game, season.

However, any other approach doesn't have that luxury. For example, you lose a game 5-4. In any other approach, you either have to make those 4 runs as worthless, or, you have to have a large sample of games to give those 4 runs some meaning. And, you would give a 3-4 or 5-4 result the same win impact for those 4 runs, even though in one instance they happened in a loss and another in a win.

So, I would say I can essentially debunk any win impact system by saying that it doesn't hold in at least one case.

Win Probability Added doesn't have that problem.

It has other problems, to be sure. (i.e., it requires you to have the win probability for every particular infinite context.) But, it is mathematically perfect.

Posted 8:16 a.m., November 17, 2003 (#8) - David Smyth
----"For example, you lose a game 5-4. In any other approach, you have to make those 4 runs as worthless"

Well, in terms of actual wins, they *are* worthless. That is a truth, and just because you don't like it doesn't mean you have debunked it. Have you ever applied that concept to a batter over a season's worth of games? The end result is very similar to what you would get with the usual methods. I have only checked this with made-up examples, but it seems to work.

Again, you may not think a system which attributes actual runs and wins is "fair" ("fairness" usually dictates a "hybrid" of value and ability), but that doesn't mean that it is not as "perfect" as WPA, or that it gives weird results for real players.

I prefer it to WPA (I think), at least in theory, because I'd rather deal with reality instead of "probabilities".

Posted 9:36 a.m., November 17, 2003 (#9) - tangotiger
Well, in terms of actual wins, they *are* worthless.

If you believe that, then in terms of value of a player (past tense), you should only include the performance of a player in a team win, right?

(Again, I'm not talking about establishing a player's true talent level here.)

So, Nolan Ryan's 8-16's league-leading ERA was pretty worthless to the Astros, given that they weren't able to leverage that performance.

When discussing MVP, we should only look at ARod performance in Texas wins.

Hey, I don't have a problem with this approach.... but don't try to take a player's entire season's PAs and try to estimate what he did in the wins. As long as you only include a player's performance in wins, then, you're right, this process is justifiable.

Posted 10:45 a.m., November 17, 2003 (#10) - David Smyth
Well, I'll post it so you can see if I'm doing it right. It's so simple, and yet it seems valid to me, as valid as WPA.

Posted 11:20 a.m., November 17, 2003 (#11) - tangotiger
Like I said, at the very least, it should hold up at a game level. Otherwise, what you have is something that is not mathematically perfect.

Posted 11:55 a.m., November 17, 2003 (#12) - tangotiger
Oh, just to be clear. I'm not saying that a mathematically perfect process is the only way to go. I'm just saying that if you are not going to follow such a process, then you will have at least one hole in the process. How big that hole is, and what its impact is, needs to be understood.

Even a math perfect process might have other holes in it, as noted earlier.

What I'm talking about is something theoretical/fundamental, that if it doesn't add up at the actual game level, then that's an obvious hole in a "win impact" system.

Posted 1:46 p.m., November 17, 2003 (#13) - ColinM
This is some great thinking and work being done by studes. Despite that I have to say stop, don't do it! The dark side Tangotiger speaks of is just that, and once you go down the road of negative win and loss shares, you're going to lose a lot of people because the concept of negative wins and losses just doesn't make any sense.

In wins and losses, baseball already has a debit and credit system. If you have a positive contribution you can tally that in the wins column. If you're contributing negatively, you can put that into the losses column. A negative win is just a positive loss.

I think the conceptual problem with Win Shares can be summed up in one statement from Tangotiger:
"To convert from a marginal utility to a total utility will require some weird things, like negative wins."

That is exactly what needs to be fixed. You need to get away from marginal runs and use a true 0 baseline in order to calculate absolute wins and losses. Marginal runs is just a hack to deal with the fact that it is impossible to pinpoint a true 0 level for the defensive side of things. But I think I have an idea of how a framework based on 0 level might be achieved. I won't go into the details of how everything might be worked out because frankly, I'm not actually sure about all of the details myself. But I will outline the high level concepts.

This is long, so if you want just skip to the conclusion.

For simplicity's sake I will refer to Win Shares as 1 win share per real win instead of 3.

1. Just like Win Shares currently does, you need to split the offensive and defensive credit. Offense and defense both have 50-50 responsibity. So if you win 100 games and your offense is credited with 54 wins shares, then the offense will have 27 loss shares, and the defense will have a 46-35 record to work with.

2. Start with offense. Instead of using marginal runs, use a baseline of absolute 0. Calculate "Offensive Wins Shares". Except what you are calculating in this system is NOT total Offensive Win Shares. Instead, what you really have is the total number of WINS ABOVE A 0 LEVEL PLAYER. This can be defined as (WinShares-LS)/2 - (0WS-0LS)/2 where 0WS = the 0 Level Player's WinShares. Let's leave offense at that for now, we can calculate Offensive Loss Shares later.

3. Defense. By which I mean Pitching+Defense of course. So how can we calculate Pitching Win Shares using 0 level when a zero level pitcher is undefined? The answer is we can't. But the solution is to look at it backwards. We do have an absolute limit for pitchers, its just that the limit is found in the opposite direction of the offensive limit. Instead of calculating how many wins a pitcher was above a zero level pitcher, we can calculate how many LOSSES a pitcher was below a PERFECT pitcher. Using Runs Allowed (maybe combined with pythagorus) you can calculate a pitchers "Loss Shares". But just like for Offense, these are actually LOSSES BELOW A PERFECT PITCHER.

4. Here we bring it all home. Let's go back to offense. Right now we have WinsAbove0. Let's use the 100 win team to illustrate the difference between the GameShares method and the method I'm proposing. In this example the offense was credited with 54 win shares. Say its an AL team with 9 players who play every inning of every game. If every hitter were equal we would have 9 players with 6 Win Shares. Now say instead we have one player with 14 WS and 8 with 5 WS apiece. If these players all made the same amont of outs, the Game Shares method would divvy up WS and LS as

Player WS-LS
Player1 14-(5)
Players2-9 5-4

I'm saying that this is wrong. The key is to remember that the 14 is NOT total Win Shares but WINS ABOVE 0. So let's think about Loss Shares now. I would argue that a hitter contributes towards losing by making outs, so that Loss Shares for the most part, should be proportional to outs made. So in this example, everyone gets (27/9) 3 Loss Shares since everyone has the same amount of outs. Then its a simple matter to figure Win Shares. WS = (WAbove0 - LossShares)*2.
In my method, the WS-LS list would look like this:

Player WS-LS
Player1 22-3
Player2-9 4-3

Game Shares are NOT the same for each player in this case even though W above average would be. I think this is a more accurate portrayal of real life.

For pitchers a similar process is performed. Randy Johnson pitches 270 innings and we've credited him 6 Losses Below Perfect. We calculate Perfect Pitcher as having 30 wins. Therefor RJ gets 30-6 = 24 WS. LossesBelowPerfect always equals Loss Shares for pitchers since Perfect Pitcher always has 0 Losses. RJ has a 24-6 WS-LS record.

I haven't even touched the pitching/fielding split. But I think if Win Shares is to move forward what it needs is a framework similar to the one I have just described, with no negative values.

Conclusions:
1. Use absolute runs instead of marginal runs
2. Using GameShares is flawed. Win Shares as we use them now are actually Wins Above 0. Loss Shares should be proportional to outs for hitters. Win Shares are (WAbove0 - LossShares)*2. For hitters, Loss Shares are limited by outs but Win Shares are unlimited. For pitchers, Win Shares are limited by IP, but Loss Shares are unlimited.
3. Start with Loss Shares for pitchers using the Perfect Pitcher as a baseline.

Posted 2:01 p.m., November 17, 2003 (#14) - tangotiger
Good job, Colin!

I think you're on the right step with the conceptual part. This process is similar to my win advancement, in that outs lead to loss advancement and positive actions (not necessarily runs created) lead to win advancement (and the reverse for pitchers).

However, you still have to prove that "it works". The easiest way is to figure out how many wins above average your various players are in your system and BaseRuns or Linear Weights, etc. I'm not sure that it'll work out fine though. But, it's a good first step.

Posted 2:06 p.m., November 17, 2003 (#15) - Sky
Win Advancements seem pretty interesting, Tango. Please keep the info coming. Of course, if I have to wait for the book, I will.

My thought is that the concept of advancements could be adapted to the entire season. "Playoff Advancements" or something like that. The goal of the season, after all, isn't just to win games, but to win enough games to make the playoffs. Now, most teams are on pretty equal footing early in the season, giving each win pretty similar value. But when you get to September, it's true that the value of ARod helping the Rangers towards the playoffs is extremely low. And wins for the Cubs/Astros during the 2003 stretch were EXTREMELY valuable.

A method like this might work: For each game, compute the probability change for a team making the playoffs. Use these probabilities as weights

I don't necessarily think this would be a great measure of player value or ability (definitely not ability), but it would definitely answer the version of the MVP question typically asked by Joe Morgan/Jayson Stark type writers.

Posted 2:15 p.m., November 17, 2003 (#16) - ColinM
Thanks Tango,

I think that WPA is exactly what a system like this wants to be and what it needs to be verified against for those seasons where PBP data exists.

And you're correct, right now it is just a series of concepts. I would imagine that straight RC above 0 would not work so well. What might be needed is a VORP(MLVR) type system for hitters where replacement would be a guy who makes all outs. And probably using pythagorus somehow for pitchers.

But the reason for the long post was simply to point out some key concepts that would make the Win Shares framework more palatable and mirror reality more accurately.

Posted 2:27 p.m., November 17, 2003 (#17) - tangotiger
Mirroring reality is always the goal.

***

I wouldn't say the goal is to necessarily make the playoffs, otherwise a player like Arod might not have value. A player's goal may simply be for his team to win THAT game, and not say 85 or 90 or whatever games. If you stretch out otherwise, the goal is really to win the World Series. I think you've got to draw a line at either one game, or the World Series, and not have anything in-between, like playoffs, etc.

Since it is far far easier to figure out (game) Win Advancement rather than (World Series) Win Advancement, I'm happy to leave it this way.

Posted 4:38 p.m., November 17, 2003 (#18) - Sky
Tango, I also believe that a player's goal is to help his team try to win each individual game, but since the MVP is decided upon based on regular season performance and many many sportswriters believe making the playoffs is basically a pre-req for winning the MVP, a Playoff Advancement metric would be the technical answer to their question. It would pretty much be a worthless stat, in my opinion, but I just thought I'd point it out.

Again, thanks for all the work on Win Advancements.

Posted 5:02 p.m., November 17, 2003 (#19) - tangotiger
Thanks for taking the time to soak it all in.

Posted 5:08 p.m., November 17, 2003 (#20) - studes (homepage)
Holy cow, Colin. That is a lot to think about. I'm still digesting it, but a couple of thoughts:

I don't understand how you can create a "baseline" offensive player whose WS=0, but somehow differs from absolute runs created. You mention a replacement level player who only creates outs, but I don't get it. Got to admit, I'm sort of hung up on the point.

The problem with going to absolutes, of course, is that you run into the curved nature of runs scored/allowed and wins. This is the main reason that James went with marginal runs (besides creating a "zero" point for the defense) -- to create a span in which that didn't matter too much. Now, maybe I've blown his intent away by going into the negative win shares, I'm not sure.

Maybe it's bad to go into negative win shares and loss shares, but I actually don't see why, unless it's the aforementioned curvilinear problem. The negative wins shares and loss shares are only there to get to WSAA, given the way I've put the system together. I think/hope that most people can understand that. Same with the way I've dealt with Game Shares. When presenting the data, we don't have to present the intermediate steps.

BTW, Games Shares (in my proposed system) do generally equal outs made for batters. So they act in the same manner that Loss Shares do in your system.

I like your ideas on the defensive side. I've started to try and think this through for the defense, and it's hard! You may be onto something by focusing first on losses.

Great stuff!

Posted 5:10 p.m., November 17, 2003 (#21) - Straggler
One problem I always run into when I try to play around with apportioning wins and losses among players is what to do about pitcher's offense. Given that pitcher offense is generally terrible, a lot of times you wind up with pitchers who wind up with offensive records of, say, 0-2. That's fine insofar as it goes, but when you try to add everything up at the end, it drags the pitchers down.

IOW, let's say you conclude that Luis Gonzalez's W-L record (or WPA record, or whatever system you want to use) is 7-3, and that Randy Johnson's record is 6-1 as a pitcher and 0-2 as a hitter for a combined record of 6-3. Intuitively, that seems wrong; the Dbacks aren't expecting much of a contribution from Johnson at the plate--nor are their opponents expecting much of a contribution from their own #9 hitters--so it seems wrong to say that Johnson's hitting drags him down to the point where he has less value than Gonzalez.

I know the easiest way to deal with it is just to ignore pitcher's offense altogether, and to measure performance against the baseline of all non-pitchers, but (bringing this back to studes's site), this isn't something that win shares does, and it doesn't sound like it's in the framework for WPA, and I think it gets you into trouble whenever you're trying to compare something like wins above average across leagues. But I'm not a stats guy, so I'm probably missing something here.

Posted 5:15 p.m., November 17, 2003 (#22) - Charles Saeger(e-mail)
studes is taking more or less the approach I take with Expected Win Shares. I could always easily partition the idea of Loss Shares between the hitting and the defense and between the pitching and the fielding; those ratios always work.

But studes is accepting that either someone needs to have an expected total, or accept a negative total. I fall into the former category; the idea of a negative Win Share means (to me) that I really, really believe this is replacement level, and I sure as hell don't have any idea where replacement really is. It becomes a philosophical divide, one not worth bridging.

Incidentally, I do take into account negative batting/pitching performances in the Expected Win Shares idea, though you need to reconcile the league totals. There's nothing too magical or original in the various concepts; basically negative claim points means you add Expected Win Shares to your original totals based on playing time. I haven't run basic tests mostly because everything is so flipping obvious. :) I spent enough time playing with the fielding formulis this spring.

Posted 5:27 p.m., November 17, 2003 (#23) - studes (homepage)
Charlie, I'd love to see your system, of course. I am struggling with the defense side of the equation, though I've really just started.

I'm glad to hear you take negative batting/pitching performances into account. As I tried to point out in the Bonds article, you run into equity problems between teams if you don't. I think this would be a problem with any system that uses a threshold.

Posted 6:11 p.m., November 17, 2003 (#24) - Charles Saeger(e-mail)
Charlie, I'd love to see your system, of course. I am struggling with the defense side of the equation, though I've really just started.

By contrast, that's my specialty. :) Really, what work I have put into there is trying to improve the various formulas. Most of the stuff works -- and working through the math, the stuff was more mathematically sound than I had thought at first glance -- but there were some things I know that Bill doesn't know, some things neither one of us knew until I started looking (I adjust DER for team assist rate, for example) and there's some just flat out, lame stuff -- Bill's inability to evaluate Passed Balls for anything, the idea that a position with 45 out of 100 points really meant a .450 DWP (and the subtraction of the bottom 20% of the rating that happened as a result of that). I can dig out the basics, I have them on my hard drive written up nice and neat in some folder somewhere.

Posted 7:17 p.m., November 17, 2003 (#25) - studes(e-mail) (homepage)
That would be super. I've attached my e-mail address in case you need it. Thanks.

Posted 7:18 p.m., November 17, 2003 (#26) - David Smyth
As I promised, I typed a long post in at Fanhome. But, those motherf*ckers deleted it due to some crazy crap in their program. I mean, it's fine to not let the post go thru if something is missing. But why do they have to also delete the entire post, which I spent 15 minutes typing in.

Anyway, I'll do it again when I get the urge...

Posted 7:37 p.m., November 17, 2003 (#27) - Patriot
Yep, FanHome does that fairly often. I've learned my lesson to copy the post before I hit enter.

Posted 8:53 p.m., November 17, 2003 (#28) - ColinM
studes,

When I'm talking about a 0 level player I mean a guy who contributes absolutley 0 wins. A guy who does nothing but make outs. This is what Win Shares wants to measure right? Thats why WinShares adds up to total wins, ie, wins above 0. I mentioned the VORP idea for exactly the reason you gave, how runs->wins becomes non-linear at the extremes. So What I was thinking is something like: Calculate the team pyth. record using team runs created. Then replace Player A's plate appearances with the 0 level player who makes all outs. Of course you'll end up having to adjust actual PA for all players as the 0 level player eats up so many outs. But then you can compare the original Pyth record with the new record using the 0 level player. This can be used as the "claim points" for offensive WS above 0.

You are absolutely right that Loss Shares in my system are just like game shares in yours. In fact WSAA should be the SAME in both systems. This is EXACTLY why negative win shares are unneccessary. My argument is this:
There is a limit to how much a hitter can negativley affect the outcome of a game. But there is no practical limit to how much a player can positively affect the game. If you want some backup for this check out Tango's WPA for hitters. Losses Advanced do not differ that much between the best hitters and the worst hitters. But there is a huge difference in Wins Advanced.

Now look at my example using Player1, who would be sort of a Sammy Sosa '98 I guess. In the Games Advanced method he is 14 and -5. Using my method, he has just as many loss shares as everyone else, but his WS jump up to 22. I think this is a much greater reflection of what really happened on the field, his WS+LS are more than anyone else because he had more of an impact on the game. But in both methods he would be compared to an average player of 4.5-4.5 (WS-LS) and have the exact same WSAA total. It may be that this part of my framework just differs in symantics from Game Shares, but I really think it is an important difference that makes the numbers more meaningful.

Posted 10:27 p.m., November 17, 2003 (#29) - studes (homepage)
Thanks, Colin. I understand. Is it this simple?:

Figure the W/L record of offense and defense exactly as you're suggesting, based on team runs scored and allowed vs. league average (park-adjusted, of course) and pro-rating the actual W/L of the team on top of that. Then assign offensive Wins to each player based on proportion of absolute runs created (no need for marginal or replacement level, I don't think) and pro-rate the losses based on outs made. Bingo, your win and loss shares. As you say, this is essentially what I've accomplished with WSAA.

For defense, assign wins based on outs created (splitting BIP outs 50/50 between pitchers and fielders) and losses based on runs allowed (following the same sort of split). You'd probably have to use a component ERA approach for relievers, and throw in the leveraged innings concept.

Then do lots of oddball things to assign outs and runs allowed to individual fielders.

Can it be this simple?

Posted 11:43 a.m., November 18, 2003 (#30) - ColinM
I think it can be that simple (if by simple you mean complicated :). Although you might not be able to go staight from the proportion of RC to wins, you might have to do that VORP type thing I was talking about. Or maybe you can, I don't know. It would have to be validated against WPA anyway. And remember, you'd have to adjust the hitters' Wins once you assign the Losses.

But yeah, I think thats about how you'd do it.

Posted 10:24 p.m., November 18, 2003 (#31) - jimd
Is it this simple?

Somehow, I don't think so. Remember, one of the goals of the original Win Shares was that the same (park-adjusted) stats should produce close to the same results whether the player is on a 100 win team or a 100 loss team. The player who is league average should come out near .500 no matter which team he is on, with a similar number of Win Shares/Loss Shares. That's why the Win Shares are based on marginal runs instead of absolute runs. Team wins are proportional to marginal runs, not absolute runs.

I don't think absolute outs will work for the Loss Shares for the very same reason. Teams make approximately the same number of outs whether they win or lose, so winning teams would have substantially less Loss Shares per absolute out than losing teams (if you use absolute outs). So the average player gets a lot less Loss Shares on a winning team than on a losing team. Not good.

Posted 3:44 p.m., November 19, 2003 (#32) - ColinM
I don't think the first part is right jimd. Win Shares is supposed to divide credit for absolute wins. And absolute wins are created by absolute runs, this is absolutely true. The fact that they may not proportional in a straight linear way is the reason I suggested some type of pyth. approach to claim points. An average player should still be an average player on any team.

As for the Loss Shares, it probably is the case that outs isn't the ideal thing to use. But I'm actually not convinced that Win and Loss shares shouldn't be different in different team settings anyway. Take the extreme example, a team that never loses. Would it make sense for any player on this team to have anything but 0 losses? The important thing is that the players WS above average or 0 or any given baseline remain about the same from team to team. So presumably a player who gets more loss shares on a bad team will also have more win shares in my system and therefor a greater game impact. Does this make sense? I really don't know. Does it make sense that a good player might have more overall impact on a bad team but not more overall value? Again, I'm not sure.

And remember outs is just a guess at a proxy to use for real negative impact. In a loss every result of an at-bat that isnt't a home run is actually conributing in some way, however small, towards the loss. So perhaps in light of this, it would make the most sense to include RC in any Loss Shares calculation.

I think the most important thing to remember is that we are trying to model reality. When we attempt to assign absolute wins and losses to a player what we are really trying to do is answer the question: In games that this players' team won, what percentage of those wins is this player responsible for? And the reverse question for losses. And the fact is, negative wins and losses don't make any sense as an answer to these questions.

Posted 4:42 p.m., November 19, 2003 (#33) - tangotiger
When we attempt to assign absolute wins and losses to a player what we are really trying to do is answer the question: In games that this players' team won, what percentage of those wins is this player responsible for?

If this is your question, then you should at the least split up a player's record as to whether the team won or lost.

Then, in all the team's wins, you don't care if a player went 0-20 or 0-150, as he didn't contribute to his team winning (though he made it harder for his team to win). So, there are no losses to hand out here.

And the reverse question for losses. And the fact is, negative wins and losses don't make any sense as an answer to these questions.

At the same time, you don't care if someone went 150-300 in his team's losses, since against, it wasn't enough. So, there's no wins to hand out. As for losses, I suppose you could just make the outs proportional to the losses.

Of course, we don't have players records by team won/losses for most of history.

So, if you were really serious, you would try to estimate that. For example, let's say that when a team wins, they score 6.5 runs and allow 2.5 runs. You would create a complete batting line as well. Then, you take your player's overall performance, and translate into a team win and team loss setting, so that overall it still adds up. (Complicated, but doable).

Then, you can apply your absolute win/loss concept.

(Btw, I still think marginal win/loss advancement is the way to go, but this is just for those who want to go to the logical conclusion on absolute win/losses.)

Posted 5:08 p.m., November 19, 2003 (#34) - jimd
As I understand it, the goal of Win Shares was to model real teams, not hypothetical nearly undefeated teams. It has obvious problems at either end of the Pythagorean scale, just like classical physics has problems with relativistic speeds. (An example of Pythagorean effects on a good team: adding Barry Bonds to a .500 team will add more wins than adding him to the 1998 Yankees; on the latter team too much of Bonds added value contributes to bigger and better blowouts instead of converting losses to wins, so he can't receive as many Win Shares. The Win Shares of everybody on that team actually goes down when Bonds is added because that team is beyond the point of diminishing returns.)

Any system that can deal with the Pythagorean problems caused by hypothetical teams while coming up with similar (or better) answers with "real" teams is a theoretically sound improvement. So taken in that light, what you say makes sense. When a player (or team) is so good (or bad) that the Pythagorean effects become noticeable then something has to give, which includes the ideal of similar results from similar stats. How extreme do these players or teams have to be for the Pythagorean effects to become visible? (The offensive/defensive split is a separate issue; it has problems in the published WS system.)

I'm with you on the negative numbers. I understand them in the abstract (like complex numbers) but they don't convey any meaning to me.

Posted 12:06 p.m., November 20, 2003 (#35) - tangotiger (homepage)
Studes has another installment at the above link.

Posted 12:24 p.m., November 20, 2003 (#36) - studes (homepage)
BTW, I've played a little bit with the abolute approach, but haven't made it work yet. I think it's doable, but, frankly, the relational approach doesn't bother me one iota. Either approach is just as valid, and either approach will yield results that will be expressed as plus/minus vs. average, or replacement level.

So I probably won't spend more time on it (my family is ready to kill me, anyway) and I plan to move onto pitching and fielding.

Posted 8:52 p.m., November 20, 2003 (#37) - ColinM
jimd,
That's a great explanation of the problems with the pythagorean scale. Its certainly a hurdle for any absolute wins type system.

tangotiger,
This is the first time I've been been able to check out this site since yesterday afternoon and you pretty much pulled the thoughts right out of my head. I think thats exactly what you have to do in an absolute system, go only positive in wins and negative in losses. It seems your discussion with David Smth may have touched on this concept a bit. The more I think about it, the more I think that using outs as a proxy for loss shares was a bad idea. If you go the absolute route, even a triple in a loss will be worth some negative "points". I wouldn't argue that an absolute system is better than a marginal approach, just different and another source of data for comparison.

studes,
If you're done with it, I'd like to play around with the absolute concept a bit more myself. I've got a few more ideas and see some errors in my orginal thoughts. If nothing else, I may have some small ideas that might merge with the relational approach as it is. Keep us updated with the pitching and fielding, you've done a great job with this so far.

Posted 9:11 p.m., November 20, 2003 (#38) - studes (homepage)
Colin, that is great. Makes me feel better about not having the time to devote to it.

If you flesh it out some more, I'll be happy to try your ideas with the Win Shares database that Pete has put together.

Posted 4:34 p.m., November 21, 2003 (#39) - tangotiger
I posted the following at fanhome, in response to David Smyth's comment on absolute wins.

====================

A guy hits a leadoff triple in the game, and the next batter hits a SF. Then, 53 consecutive outs get recorded.

Now, in the system that I construct that models the real world, I give each team a .50 chance of winning the game, because this is the environment in which each team finds itself (let's assume equality for my purposes). The leadoff triple will bring the win expectancy to say .59, making that triple worth +.09 wins. This win expectancy, .59, assumes a typical run scoring distribution to the end of that inning, and the game.

The next batter gets the SF, and brings the WE to .60, making that SF worth +.01 wins.

To the end of the game, the leading team's pitching will add about +.60 wins, and its batters will add about -.20 wins.

So, winning team has added +.09 + .01 + .60 -.20 = +.50 wins

To the end of the game, the losing team's pitching will add about +.20 wins, and the hitters will add -.60 wins.

So, the losing team has added -.09 -.01 +.20 -.60 = -.50 wins

I submit that this model captures how the fan sees the game unfolding, and how that fan attributes the performance of the various players involved.

In the "absolute model", we start with the end of the game, 1-0. We then give 1.00 wins to the only players involved in the scoring, and in this case, it's the first 2 batters, and presumably, we give each batter 0.5 wins. The pitcher who threw to those two guys gets 1.0 losses.

Does anyone really think this captures reality?

I further submit that reality is that players contribute towards trying to win. That is, reality is that players have marginal contribution in a given real-time context. This is how we perceive and react to things (be it baseball or life).

I think that absolute wins have no meaning whatsoever to individuals that are involved in a group. NASA's space shuttle may blow up (wins = 0, losses = 1), but there are thousands of people that made substantial marginal contributions, but there was one person or a small group of people who failed miserably.

Furthermore, not only does absolute wins at a player level not even model reality, its application is so limited as to be useless. It won't even come close to capturing a player's true talent level, it won't have any predicatability, it won't have any other potential secondary byproducts.

Marginal wins on the other hand has these properties. While that doesn't validate marginal wins, it's a happy by-product that makes marginal wins very attractive.

Posted 1:13 p.m., November 24, 2003 (#40) - ColinM
"In the "absolute model", we start with the end of the game, 1-0. We then give 1.00 wins to the only players involved in the scoring, and in this case, it's the first 2 batters, and presumably, we give each batter 0.5 wins. The pitcher who threw to those two guys gets 1.0 losses.

Does anyone really think this captures reality?"

Maybe, but not as you've described it. I would think that the pitcher(s) for the winning team would get the biggest share of the "credit". I also think any reasonable system would not simply split the credit 50-50 between the two batters. You may end up with .8 going to the pitcher, .15 to the first batter and .05 to the second batter, or something along those lines. I would also guess that the hitters on the losing team would receive most of the "blame" for the loss, with a very small amount going toward the pitcher.

I doubt there's any single "right" model that can be used to assign credit in an absolute system. Who knows, some models may even be based off of some type of win probability in order try and capture the impact of each event.

And as much as I do like the idea of a marginal wins system, I also think that you can run into reality problems just as you can within an absolute system. Take your example with the leadoff triple, where the winning pitcher ends up with about .6 wins. Now say that instead of the triple-SF combo coming in the first inning, it happens in the bottom of the ninth. I assume that more wins added are now credited to the two hitters than in the first example, and the pitcher has less wins added. But is the pitcher's shutout really any less valuable than in the first example? Does this capture reality?

An absolute system may treat both shutouts the same. Again, I'm not saying absolute is better, just different, and may capture some things that marginal wins doesn't, just as marginal wins can capture things that an absolute system may miss.

Posted 2:33 p.m., November 24, 2003 (#41) - David Smyth
Yes, Colin M has it right--I did not give .50 to both the 3b and SF.

I could launch another response rehashing what I have already said on the "absolute" method, but it's pretty much all there on the Fanhome thread.

Posted 2:52 p.m., November 24, 2003 (#42) - ColinM
David, how can I view the fanhome thread?

Posted 3:05 p.m., November 24, 2003 (#43) - tangotiger
I assume that more wins added are now credited to the two hitters than in the first example, and the pitcher has less wins added. But is the pitcher's shutout really any less valuable than in the first example? Does this capture reality?

In the case where the batters would score say the 1 run in the bottom of the 9th, I think the pitcher on the winning team would get about +.45 wins, the two batters would get +.35 wins, and the rest of the batters would get -.30 wins. (On the losing team, the pitcher would get +.10 wins, and the batters would get -.60 wins.) Again, I'd say, yes, this captures reality, since the impact, in real-time, is felt much much more in the bottom of the 9th than in the top of the 1st.

After-the-fact, of course they are the same. That's the difference between an absolute model, and a marginal model. One thinks in real-time, and the other in after-the-fact.

Win Shares tries to do both at the same time, by looking at things after the fact (and over a span of games), but still trying to give some credit to anyone who did something good, even if it did not result in a run or a win.

Posted 3:06 p.m., November 24, 2003 (#44) - David Smyth
---"David, how can I view the fanhome thread?"

I'm not sure what you mean, Colin. Go to fanhome.com, go the the baseball forum "Strategy and Sabermetrics", and click on the Absolute Wins Produced thread. If you want to post a reply, you have to register.

Posted 3:11 p.m., November 24, 2003 (#45) - Fanhome thread (homepage)
.

Posted 3:25 p.m., November 24, 2003 (#46) - ColinM
Thanks David, that is what I was looking for, I'm just not familiar with fanhome.

Tango, I think we are actually in agreement. Although I find value in a system which sees the two pitchers as the same after the fact, using the additional information of who won. I also see a marginal wins system as valuable.

As for WinShares, it wants to be after the fact, but since it covers all of baseball history it can't split up performance in wins and losses, so it has to approximate. I don't think there's anything else it can do.

Posted 3:39 p.m., November 24, 2003 (#47) - tangotiger
Colin, I think we reached an agreement here, which is rather boring!

Posted 6:09 p.m., November 24, 2003 (#48) - David Smyth
Colin wrote---"Tango, I think we are actually in agreement.", after seeing the fanhome thread.

What does that mean? Does that mean that you think that Tango successfully debunked my viewpoint? If so, please be specific. My interpretation of Tango's "conclusion" is that my method (or some refinement of it) is essentially sound, but not his particular "cup of tea".

For me, this "exercise" (as Tango called it) has sort of opened my eyes to something. And that is that baseball is actually simpler than we (statistical analysts) have been making it. Baseball consists of a few fundamental elements (bases gained and lost, runs scored and allowed, outs made and gained, and wins and losses). Most of the fancy statistical "gyrations" (probabilities, exponential formulas, multiple regressions, etc.) are necessitated due simply to lack of complete data. The more data you have, the simpler the analysis should become. Instead, the more data that becomes available seems to be leading to more mathematically complicated analyses. I submit that this is because people are not seeing the fundamental relationships which emerge from a concrete analysis of complete data (although even PBP data is not complete enough to avoid the use of some probabilities or partial-bases). I am usually regretful that I do not have the technical statistical training or computer ability that some others possess. But sometimes, as in this case, I wonder if that might be a blessing, since it forces me to try to "see the forest for the trees".

Posted 6:33 p.m., November 24, 2003 (#49) - David Smyth
---"Again, I'd say, yes, this captures reality, since the impact, in real-time, is felt much much more in the bottom of the 9th than in the top of the 1st."

Why should we care, in the context of analysis, where the imact was "felt"? I don't care whether fans were more on the edge of their seat in the 9th than in the 1st. And ditto for the players or managers.

If you can show evidence that what is "felt" materially affects the performance of a typical player (IOW, clutch), then I will have more affinity for it. But absent that, what is the big deal about holding players to the base/out/score/inning impact? Do those things have more of an effect on performance than some of the things in my system, such as a pitcher's offensive and bullpen support? As far as we know, most "non-ability" factors are pretty much random in terms of impact. And if that is true, then why "stop", in terms of a value system, where WPA stops? Why not simply forget about intent, and focus only on the final result? The final result is wins and losses, runs scored and runs allowed, outs made and outs gained, and bases gained and bases lost.

Posted 7:38 p.m., November 24, 2003 (#50) - Tangotiger
There are many viewpoints, neither of which is necessarily better, but rather different.

Here, we have the marginal approach in real-time, and there's the absolute approach after the fact.

In the absolute approach described by David, it has very limited application. We cannot directly use it to establish a player's ability, since he is, by definition, removing all performances in hitter's losses, and pitcher's wins.

In the marginal approach described by me, its applications are also limited in some sense. It can describe somewhat a player's abilities.

You can have other marginal approaches that only considers the base/out, or even no context. And the less context, the more you can describe a player's abilities, and less you can describe how much impact he had in a given game or inning.

It's a long scale, with value on one end, and ability on the other end.

What metric you choose should be based on what you want to describe.

In the two metrics we are discussing, I'm saying the better model is the real-time marginal approach, because fans follow in real-time, and decisions are made in real-time. And ALL performances count, whether in a win or loss.

I have no qualms with David's approach, either. I just don't like it too much.

Posted 10:48 a.m., November 25, 2003 (#51) - ColinM
David,

I hadn't actually read the fanhome thread yet (just didn't have enough time at work) when I posted the response to Tango. When I said we were in agreement, I was referring to what had been said so far on this thread. I meant that I think we both understand the difference between an absolute or marginal system even though we may value them differently. (This crossover thread between fanhome and here kind of reminds me of when Buffy and Angel were both running on the WB. Can I be Spike?)

Now that I have read the fanhome thread:
Tango might be OK with it, but I have some serious issues with your system for crediting absolute wins. You really have to deal with hitters performance in losses, and pitchers in wins. Consider two hitters, one who goes 0-4 and the other who goes 4-4, in a loss. Now I agree that in an absolute system neither hitter can get any positive credit because the team did not win. But that doesn't mean that they shouldn't be assigned any responsibility for the loss! In reality, every player on the losing team should be assigned some share in the loss. It's just that the first player will get a lot more "loss shares" than the second.

I don't yet know HOW such credit would be assigned, but just because it is more difficult to do doesn't mean it isn't the right way to go about it.

Posted 11:12 a.m., November 25, 2003 (#52) - tangotiger
Well, David's assumption is that hitters create runs and runs create wins. Pitchers allow runs and runs allowed created losses.

If you can't buy into that, then you won't buy into David's system.

So, right away, David completely removes essentially half a player's performances. And, he's right to do so, under the above assumption.

And, as David has pointed out elsewhere, when you compare to an average player, things do balance out somewhat ok. For example, a pitcher with 34 starts may get 0 wins created (by definition) and 6 losses created (say Pedro), but that an average pitcher would have been 0 and 12. So, from that standpoint, Pedro was 6 better than average.

But, you have to be able to accept his initial assumption. If you can't get past it, then you will not care at all for his approach.

What I like about this is that it doesn't try to take some marginal / win probability crack at it. He doesn't say, "well Pedro only gave up 1 run, and even though it was a 1-0 game, I know he did something good, so I've got to give him some positive win contribution, and I'll balance that out against the hitters", even though you may think like this. You see, this thought is a marginal approach thought, that people are trying to fit into some absolute construction (with the eventual result of things like negative wins, etc).

David's approach is completely different.

Posted 3:33 p.m., November 25, 2003 (#53) - ColinM
Tango, good news, we disagree again! Well not completely but close enough. First, I don't understand why you need to have this hard seperation between marginal and absolute. Everything is marginal, whether you start from average or 0. Absolute wins are built with marginal contributions. It's the value of these marginal contributions that differs depending on whether you look at them real-time or after the fact.

I actually think I'm OK with the concept that hitters create wins and pitchers create losses. So let's go with that. Where I may differ is in the initial conditions.

Here's another way to think about it (which I've only partially thought out). The hitters start with 0 runs and therefor 0 wins. So what happens if the initial conditions do not change, if no runs score? The team loses. So is it valid to to say that the hitters START a game with an implicit loss? This is balanced by the defense, where the initial condition is 0 runs allowed, or an implicit win, so the overall state is 0.

If a game ends in a 2-1 loss, the final state is -1. The responsibility of the defense for the loss is proportional to the amount of "marginal losing" it has contributed below its inital state of 1 win. The contribution of the offense to this loss is proportional to the amount left in its implicit loss after subtracting its "marginal winning", which in this case, results in more "loss shares" credited to the offense then the defense.

Posted 8:01 a.m., November 26, 2003 (#54) - David Smyth
Tango wrote,---"Well, David's assumption is that hitters create runs and runs create wins. Pitchers allow runs and runs allowed created losses.....If you can't buy into that, then you won't buy into David's system."

Yes, it is an "assumption", and one that I did not set out to make. But as far as I can tell, it is the only assumption that will hold water, in the context of an *absolute* system. If someone can figure out how to handle it with a more *conventional* assumption, and not be unknowingly reverting to a marginal concept, I'll be glad to see it. But I doubt it can be done. And if not, that means that my "assumption" is correct. And if it is correct, then it doesn't matter whether most people choose not to "buy into" the system. I can choose not to "buy in" to the theory that matter is made of atoms, but if that theory is correct, then I'm only hurting myself by not accepting it.

I'd love it if so PBP analyst would buy into it enough to try it out and get some actual results.

Posted 9:35 a.m., November 26, 2003 (#55) - tangotiger
Colin, from that standpoint then, there should be no problems with a negative total utility (i.e., negative win shares).

David, I can buy into it, it's just that I don't think it's terribly useful or revealing. Essentially you are only including those PAs of a player that leads to a run and in games with a win. So, imagine a player with 150 runs produced in 162 games, with 81 wins. You are basically only going to count 100 his 650 PAs (100 of his 150 RP would be in a win).

What I think absolute wins are going to reveal is very little, in my view.

What is good about this is that it draws a line as to what is an absolute looking-backward system, and what is not. If we compare it to Win Shares, Win Shares essentially assumes that a certain amount of hits and walks lead to runs, and assumes that a certain amount of those runs were in wins. It really hides what it really wants to do (after the fact look at contribution in wins), by making these assumptions.

Your system lays it all out, and is proud to only consider 15% of a hitter's PAs.

Posted 10:07 a.m., November 26, 2003 (#56) - David Smyth
"What I think absolute wins are going to reveal is very little, in my view."

Well, that is your expectation, but I am not quite so sure. It will reveal a "performance layer" which we now don't have. It will add to our knowledge of what really happened in a ball game. It should be useful in answering certain relevant questions.

For example, it might have been helpful in answering the Bonds/Pujols MVP question (as might WPA). If their Slwts were the same (I'm not saying that they were), but one guy had a significant edge in AWP (or relative AWP), that would be enough to sway my vote.

Posted 11:20 a.m., November 26, 2003 (#57) - tangotiger
I agree that WPA and AWP would be THE best measures to evaluate MVP (probably the least-important, yet the most discussed topic ever!).

But again, no offense to you or your system, how many people will buy into the AWP assumption? That is, look at the game after-the-fact, consider only performances that lead to a run in games that led to a win (for hitters). If you tell them that you only looked at the 15% of the PAs that the player had, what do you think they will say?

With WPA, the assumption is that you are measuring the performance in real-time, and all of the player's PAs. (I'm not tooting my own horn here, since this was first described as Player Win Average by the Mills brothers).

I dunno, but I guess that 90% of people would buy into WPA more than they would into AWP, from a "modeling reality" standpoint.

Furthermore, WPA has more application since it considers all of a player's performances. So, while that technically doesn't make it better, its side benefits easily trumps AWP.

Again, limiting the discussion to "modeling reality", I don't think that AWP does (or at least it's doesn't model reality as most people perceive it, would be my guess). However, it IS better than Win Shares.

Posted 2:41 p.m., November 26, 2003 (#58) - ColinM
"Colin, from that standpoint then, there should be no problems with a negative total utility (i.e., negative win shares)."

Maybe, although I'm not necessarily taking that standpoint, just trying to point out that there are some other ways to look at the reality of the situation. And I think that it is a lack of reality that is the problem with Davids absolute system. I'm know I'm going to contradict some things I've said at the beginning of this thread, and I admit that is true, but I've learned a lot over the course of this discussion, it's really made me think. And if you can't learn and change your views then it is probably not worth reading forums like these anyway.

It seems to me that the problem with an absolute system is that there really is no absolute when measuring the value of a player. All value, all contributions are relative. This has to be true, since there will always be 9 players on the field and in the lineup. You can't start a game without any hitters, someone will always come to the plate. If a player can't play someone will replace him. So when you attempt to answer how valuable a particular player was in the context of a game, you are ALWAYS making a relative comparison against some hypothetical replacement. The concept of trying to determine a players contribution within a particular game is the same as asking one simple question: "Given the end state of the game (W or L) what is the probability that the opposite state would have resulted had this player not played in that game?". I really can't see any other way to look at it. While the question may be simple, the answer is not because the answer depends on how the player would have been replaced had he not played.

Even Davids absolute system is actually a relative estimate of value. In his system the player in question is replaced with a player of absolute 0 value. So in this context, yes, Davids method is the right way to go about it. Because if the team loses anyway, taking Player A out of the game and replacing him with the 0 value player will lead to a 0% increase in the chance that the team would have won the game (assuming all other results remain the same). He can then disregard a hitter's performance in all losses.

The problem with this is that a 0 value player does not exist in reality. And if this is true then wins above 0 do not reflect any type of reality. Even Bill Bergen was able to contribute something offensively above 0. And as soon as you move that "replacement level" to anything above 0 you have to start to consider hitters performance in losses. By taking any of the losing hitters out of the lineup there is a chance that the team could have won the game with the replacement in his place.

So, after all of this, I'm finally forced to conclude that there is no absolute value, only relative value. And there is really no "right" answer for where to set the line for relative comparison, only best guesses. And value above 0 is not a realistic one.

Posted 8:23 p.m., November 26, 2003 (#59) - David Smyth
---"If you tell them that you only looked at the 15% of the PAs that the player had, what do you think they will say?

Well, if that's *all* you tell them, then of course. But if you also tell them that the reason is that those 15% of PAs contain all of the *tangible* value, and the other 85% are just noise, maybe some of the brighter ones would get it. I don't want to sound like some sort of snob, but I am not going to limit myself by what the "average person" will understand or accept.

And Tango, you keep comparing the virtues of AWP with those of WPA. But I have not urged that AWP should "replace" WPA--just that it be part of the arsenal.

---"It seems to me that the problem with an absolute system is that there really is no absolute when measuring the value of a player."

Agreed. I have always said (I think) that value is relative, and that to use AWP to measure value you have to relate a player's result to some standard, such as how many AWP an avg or repl batter would have generated. I have not thus far posted my idea on how to do this in the best way, but now that there is some interest in the method, I will do so.

Posted 10:28 p.m., November 26, 2003 (#60) - Tangotiger
David, that's a fair enough point. If you have 2 win-based systems that work in completely different ways, and they both tell you the same thing about Pujols, let's say, then that leaves little room for discussion.

Since both WPA and AWP are grounded in their very specific assumptions, unlike Linear-Weights-converted-into-wins or Win Shares or anything else (where these try to assume a standard conversion process from runs to wins using seasonal data, and since they both have very different perspectives, they can both live in harmony.