THE BOOK--Playing The Percentages In Baseball

I further commented:

The first published implementation of WPA was by the Mills Brothers in 1970, and named Player Win Average.  You can click on my name for an excerpt.  Doug carried on the tradition in fine style.  Whereas Mills’ used division, Doug used subtraction.

As for replacement level, it is, at its heart, simply the production of the player at which he would earn the minimum salary.  That level of production is roughly 2.25 wins per 700 PA, or .01 wins per IP, below the league average.  I agree with JC that you don’t need replacement level, and you can get there with just using league average.

And another comment:

Mariano has more influence to how many wins the Yanks will actually win, if he’s pitching mostly in close games than in blowouts.  Ozzie Smith will have more influence in how many runs he saves at SS than at 1B.  The former takes the same number of opps as other relievers, but makes the most of it (like buying stocks on margin).  The latter is given more opps. 

In either case, their talent level is tied in to how much impact their skills have: they are being leveraged.  As noted in the other thread, the best/easiest way to handle the reliever is to give each reliever a leverage value that is half-way between 1.0 and whatever leverage index his talent level dictates he would find himself in.

First I’ll comment on replacement versus average:  I agree that trying to figure someone’s value over replacement muddies the waters, because replacement level is a moving, fuzzy target, whereas average is self-defining.  We can easily talk about a player’s value over average and use average salary as our benchmark.  The “only” value in using the replacement level concept (I put “only” in quotes because it is important) is that it enables us to put a “real” value on the average player.  Using the prevailing salaries of average players is fine, but if we want to know the intrinsic or real value of an average player, we have to define replacement level.  Then again, when Tango or anyone else tells us the value of a marginal win (4.5mm or whatever), he is basing that on what players are actually paid and not what they are intrinsically worth (using the “replacement” paradigm).  That is as ‘artificial’ as using the average salary of the average player to determine overall value.  By artificial, I mean that it tells us what is and not what should be.

Anyway, secondly, I want to comment on JC’s notion that a player should not be valued by what leverage he is placed in, based in part on the whim of the manager/organization.  There is some merit to that thought.  His Linebrink/Cordero example is a good one.  Putz/K-Rod is another good example.  Putz is now presumably a set-up man, with an impending average leverage of around 1.5, and K-Rod is going to have a leverage of around 2.0.  Putz would be a closer on most teams and was one with Seattle of course.  So is his market value as a pitcher who throws 60-70 IP with a leverage of 2.0 or 1.5?  Good question.  Obviously for the Mets next year, it is the latter.  I don’t know the precise answer, but I don’t think that K-Rod is worth 6 mil a year either (as JC opines).  If nothing else, a very good reliever should be valued (salary-wise) based upon an average leverage index of a closer or set-up man, because that is how most very good relievers are used.  It is part of the package of being a very good reliever.  It is his “premium value” and there is nothing wrong with that.

Tango, is that what you mean by using a leverage halfway between how a pitcher is expected to be used and 1.0?  Because he is not necessarily used as we expect him to be used?  If yes, that makes sense.

Thinking about this as I am writing, I would have to completely disagree with JC, and agree with Tango.  There is simply no way to NOT give an excellent reliever extra credit for the fact that he will likely pitch in high leverage situations.  In the same vein, for an average or mediocre reliever, we assume an average leverage of around 1.0, regardless of how they are used.  If a team happens to use that kind of reliever as a closer (like a Borowski or a Danny Graves), then that team is simply employing him in an incorrect manner just like they might employ any other poor strategy which costs them money/wins.

When I use LI for forecasts, I don’t use his actual LI or expected LI, but the LI a player “deserves”.  Regardless of how Putz or KRod are going to be used, if I have a similar forecast for them, then both deserve to get paid the same amount.  If you have a 3-bathroom house, but you only use 1 of them, are you going to say the house has 1 or 3 bathrooms?

The reasoning behind using an LI that is halfway between 1 and his “deserved” LI is for “chaining”.  If that guy won’t be closing, then someone else will.  So, Mariano Rivera, deserving of an LI of 2.0 because his talent gets to put him there, doesn’t deserve the full benefits of the 2.0 because if he wasn’t there, someone else would be.

Guy made the case better, stating that we should use a “closer replacement level”, say a closer with a .570 win% (which would be a top setup guy).  And then any performance above that level gets the leverage benefit.

As it turns out, this is quickly approximated based on saying that you give the player an LI of halfway between 1 and his deserved LI.

In any case, we know we must give him SOME credit, and there’s something that would naturally stop us from giving him all the credit for the LI.  So, just by that point of view, you’d want to do something like I’m doing anyway.

Tango:

Sky and I were recently discussing Kerry Wood’s contract, which I “analyzed” using Marcels and 1.5 LI (as per your suggsted average of 1 and expected role pLI [2 for closers?]. I had just read your blog post here about K-Rod’s contract, Bradbury, etc. Could you explain the “why” of the average of 1 and expected role projection for reliver contract market value? Sorry if the explanatio is right in fron to my face here, I did look.

There are two ways to think about it.

1. Suppose you have this kind of setup:
ERA LI
3.00 2.0
3.75 1.3
4.25 0.9
4.50 0.8
4.70 0.7
4.80 0.6

Give them each 81 innings.  If you multiply their IP and ER by their LI, you come up with their leveraged numbers: 510 IP, 220 ER.

The #1 reliever goes down, everyone moves up a notch, and the 7th reliever comes into the bottom.  You now end up with 510 IP, 244 ER.
ERA LI
3.75 2.0
4.25 1.3
4.50 0.9
4.70 0.8
4.80 0.7
4.85 0.6

So, the difference between our ace and the replacement-level reliever is 24 leveraged runs.  That’s the value of our ace.

On the other hand, if we presumed nothing about leverage, then the difference would be (4.85-3.00)/9*81 = 16.7 runs.

24/16.7 = 1.44

So, that’s the “effective” leverage, when you consider chaining.

2. Guy calls it the closer-replacement level.  Take the guy with the 3.00 ERA, in a league of 4.37 average.  That’s about a win% of about .660.  Let’s presume the replacement level is a win% of .470 and the closer-replacement level is .570.

So, our guy, not considering leveage, is .660 - .470 = +.19 wins per 9 IP, and at 81 IP makes him +1.7 wins.

If we give him the leverage bonus for every win above the .570 level, then he gets an extra +.090 wins per 9 IP, or an extra +0.8 wins on top of the +1.7 for a total of +2.5 wins.

2.5/1.7= 1.47

Got it?

The chaining exercise in comment #300 is excellent.  Thanks.

Yes, the chaining comment really helped. Thanks so much, Tango. Sorry I’m so slow on the uptake of pitcher win %.

Is “averaging with 1” used for projection of reliever WAR value in general, or just market value?

Ok, there’s a problem with the chaining method in #300, or else I’m missing something:

If you find the levRAR for each pitcher in that hypothetical bullpen using chaining (using six different scenarios with one pitcher being replaced by a 4.85 ERA guy, not cumulative), they are worth 23.7, 10.2, 4.4, 2.3, and .9 runs from best to worst.  That adds up to 41.8 levRAR.  However, If you replace ALL spots in the bullpen by replacement-level relievers, the group as a whole is worth 54.8 levRAR.  Where’s the missing 13 runs?  Those 13 runs saved provide real value to the team—but it doesn’t have to pay for them?

re: chaining

Unless a pitcher’s LI tracks well from year to year, we’re valuing the closer for something that’s really the skill of a manager.  Why would we pay KRod because his manager knows how to properly deploy his relievers?

Got it.  Bottom line is that JC’s logic fails if you think of it in this way, which is the only way you CAN think of it:

I can pay a replacement player $400,000.  That is a given.  We know or can approximate how many runs a replacement player is at any position, as compared to an average player at that position.  If I am considering any player whatsoever for that position, then his exact value is the number of wins he provides to my team more or less than that replacement player.  Period.  If you are going to use a player as a closer, then you pay him based on his innings being worth 1.5 times their number, because that is exactly how you figure his value in runs or wins above replacement (including chaining).  If you are going to use that same pitcher as a set up man, then he is worth a little less to your team.

Of course while a player’s value to a specific team is based on how that team is going to use that player (whether it is right or wrong), a player’s value outside of any specific team is based upon how the average team will use that player.  So if Linebrink and Cordero will be used in the same role by an average team, then both their expected innings should be multiplied by the same amount.  If Linebrink tends to be used not as a closer and Cordero tends to be used as a closer, and they have the same expected ERA, then Cordero is worth more, period.  It might be that Cordero can handle the closer role better than Linebrink, or it might be that teams are simply all wet in this regard - it doesn’t matter.  A player’s value is determined by his talent and his role.

To say that a player gets “credited” for how a manager or organization uses him is both true and not true.  Obviously how a manager or organization uses a player is primarily based on his talent.  It just so happens that short reliever value is not linear to their talent because of the varying degrees of leverage that each role happens to encounter.  So what.  That is the way it is.  As I said, a player’s value is by definition how many more runs or wins he provides given the role that he will be used in.  Anyway, that was the “is.” The “is not” is that in some cases, players are used in incorrect roles - at least we think they are. Like Borowski closing for several years for Cleveland and Betancourt being a set-up man.  That makes Borowski’s innings more valuable even though we think that Betancourt is the much better pitcher and should have been closing.  That is too bad for Betancourt, and great for Borowski.  But, that is their value for CLE.  If we were to try and determine both players’ value for some other team, or all teams combined, then we would have to make some guesses as to what their average roles might be.  If we think that Betancourt would be used as a closer by half the teams, then we can say that his innings multiplier would be halfway between a closer and a set-up man.

So bottom line, again, is that yes, a player’s value is, by definition, how much he is worth in runs or wins as compared to a replacement player in his place (including the chaining effect), given the role that he is placed in or is expected to be placed in, whether that role choice has anything to do with the player or his talent or not.  In most cases, of course, but not all, a player’s role is by virtue of his talent.  But it matters none (the “why” he is used as he is) in determining his value and worth in dollars.

If anyone should know that, it is an economist like JC.

Guy made the case better, stating that we should use a “closer replacement level”, say a closer with a .570 win% (which would be a top setup guy).  And then any performance above that level gets the leverage benefit.

So what does a “replacement level closer cost”? It’s certainly not $400,000, so if you’re going to do it this way, you need a whole new $/win scale. 

Personally, I don’t see any evidence that chaining actually exists in practice in MLB in terms of roster construction.  When a team loses a closer, they go out and get a new closer - they simply don’t shift everyone up a spot.  MLB teams see closer as a position the same way they see second base a position.

The replacement-closer is worth whatever a .570 pitcher is worth in his UNLEVERAGED innings.  So, for example, if he had 81 innings (i.e. 9 games), then he’s worth +.100 wins x 9 = 0.90 wins.

A closer (say a .640 closer) is worth based on his LEVERAGED innings.  So, for example, if he had 81 innings (9 games), then that counts like 18 games.  And his .640 is +.070 wins above the replacement-closer level, or an extra .07*18=1.26 wins above the unleveraged replacement-closer of .90, for a total of 2.16.

The chaining method simply accounts for the finances. The key to the chaining is not so much that teams don’t behave in terms of everyone moving up a slot, but the finances of it works that way.

If the Yanks lose Bobby Abreu, you don’t necessarily compare him to a replacement-level player, since the Yanks will pay for more to get somebody in.  A Yankees-replacement-level OF is better than some other team’s.  However, the cost of the Yankees-replacement-level OF will also be higher.  So, it doesn’t matter if you compare it in 2-steps (Abreu above Yankees-replacement-level-OF, then that guy above league-replacement-level OF) or one step (bypass the middleman).  That, in essence, is what happens with the chaining.

Post 302 was marked for moderation and is now open.

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“Is “averaging with 1” used for projection of reliever WAR value in general, or just market value? “

It’s the same thing.

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“However, If you replace ALL spots in the bullpen by replacement-level relievers”

I’m presuming that that’s not really a model to worry about.

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“Unless a pitcher’s LI tracks well from year to year...”

Well, it does track well year-to-year. 

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Felipe Lopez was the worst fielding SS according to WOWY through 2006.  Guys like that, who are below-average hitters, I don’t even want to see on my team.

"Well, it does track well year-to-year.  “

Fair enough.  Is this a skillset of the player though?  This seems to be 1) an artificial creation of LI since it values the 9th more than the 8th, etc. and 2) dependent, in large part, on the manager.  The player has little if any control over this yet your assessment has us paying them for a cascade effect throughout the relief corp.

I don’t know what “artificial” means in this context.

Let’s talk about Mariano Rivera, and I’ll ask you very specific questions, and I’d like very specific answers, with no tangential issues.  That is, don’t take this opportunity to do anything other than treating this as a court of law.

1. If Mariano Rivera posts a 2.30 ERA in a league environment of 4.60 ERA, and he pitches 81 innings, does this mean he is worth 20.7 runs more than average?

2. If he is worth 20.7 runs more than average, and if takes an average of 10.35 average runs to convert to a win, does this mean that he is worth 2 wins more than average?

3. In the entire history of baseball, has any pitcher been as good as Mariano and pitched as little as he has (outside of injury)?

4. Are we going to presume that a run is a run is a run, and that Mariano will just as well pitch in a 9-1 blowout and have as much value to his team as pitching in one-run games?  Or, are we going to presume that the reason that one of the best pitchers of our generation pitches so little is because he has more value that way?

5. Presuming he does have more value in close games, does this have anything at all to do with Mariano himself and his talent level?

6. Presuming that Mariano does have some influence, via his talent, as to how he’s used (similar to say Ozzie Smith playing SS and not 1B), how much of the “opportunity context” do we assign to him?

After you answer my questions, I will answer any of your questions under the same conditions.

“However, If you replace ALL spots in the bullpen by replacement-level relievers”

I’m presuming that that’s not really a model to worry about.

Tango, you’re really not concerned that the individual pieces don’t add up to the whole?

Let me ask it this way.  In the example, do you believe that bullpen is worth 41.8 lvRAR or 54.8 lvRAR?

Things don’t always need to add up.

If you got 41.8 by replacing only one reliever each time with a repl-level player, then that’s the one I go with.

When we talk about repl level players, I am ONLY using it in context to determine financial value.  It is to determine what performance value a player has in order to get paid 400K.  It is not to construct a team of all-repl players.  If you do that, then a walk is not worth +.32 runs.  It’s worth alot less (while the HR remains at +1.40 runs).

Having technical difficulties posting my answer.  Does the site not like certain text or is there a size limit?  I click the preview button and get taken back to the top of the screen. . .

Sometimes the software doesn’t like links, or certain HTML tags, or if you use alot of caps.

I have a predisposition to contrariness when I know I’m being led down a path I wouldn’t otherwise take but I’ll do my best to answer these objectively.

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1. Yes.

2. Yes.  I’m on board with unleveraged WAR valuations.

3. None worth quibbling about.

4. A run is a run is a run—yes. And here’s where I start to take issue.  The implication is that Rivera is going to pitch to the score and I’m disinclined to believe that pitchers a) do this and b) really affect their performance even if they claim they do.  That is to say that even if Rivera thinks or tries to pitch to the score, I don’t know that it really affects how much his cutter cuts or whether he strikes out fewer batters or whatever.

Jumping ahead a little to Q#6 and tying these together—if Rivera posted a 2.30 in low leverage situations (less than 1.0) for # years in a row would we assume that he’s less talented?  Would his raw numbers be better in a low leverage situation?

5. As game strategy, I’d always want to use my best reliever in the most important situation but I’m not sure that means he’s “more valuable” in those situations.  He’s more valuable in the sense that he’s a better reliever than others but that should be captured in an un-leveraged WAR valuation.

6. This makes me think of positional adjustments for players—i.e. there’s value in the scarcity of their role beyond what they do offensively and defensively.  My answer is I don’t know.  Flip this around though. If a manager was really dumb and used Rivera in low leverage situations for years on end, would we then think that Rivera was less valuable because a) he’s not as talented as his numbers say or b) his manager is dumb? In both cases, I feel like the answer is that his true talent level encapsulates this whether he’s pitching the 9th or the 6th inning of a blowout.

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Hopefully those answers didn’t stray from the question.  I may come back with some more questions—I want to let this stew a little bit.  My brain needs more processing time but I appreciate the discussion.

In all my questions, I presumed that Mariano would pitch as well in any game situation, and therefore, his talent level doesn’t increase as the leverage increases.  He’s a “2.30 ERA” pitcher all the time.

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Your answers therefore suggest that Mariano should be paid as a 2.30 reliever with 81 innings pitched, and count his innings as 81, and not as 50% or 100% higher because you get to utilize him in a more optimal fashion. 

That is, that while you acknowledge his talent, and you acknowledge that he can be used when the game matters, you will not value him any more than him pitching 81 innings.

Because, to you, a run is a run is a run.

Have I summarized your position well, based on your responses to my questions?

If you replace a replacement pitcher with another pitcher in whatever role you are going to use him in, the value of that pitcher is exactly equal to the difference in the team’s expected win percentage between the replacement pitcher and the pitcher in question.  Why?  Because that is the way we define value.

So forget about leverage.  How many wins does Rivera allow versus that replacement pitcher given that Rivera will pitch mostly in the 9th with a 1,2, or 3 run lead.  That is all you have to answer.  Once you do that, that is your answer to the question, “What is Rivera worth in marginal wins, as compared to a replacement pitcher?”

As it turns out, the way to calculate that is to take the difference between Rivera’s expected RA per 9 innings and the replacement pitcher’s and multiply that by the number of IP Rivera pitches times 2.0.  If you take the difference in RA per 9 and multiply it by the number of innings that Rivera or any other closer pitches, as you would with a starter, you will come up with the wrong answer, so you can’t do that!  You will come up with an answer that is about half of what the true number is (if you ran everything through a sim, or tracked a lot of real live games).

As Tango said, it is the same thing as if you want to figure the value of a certain SS.  Your role or context is that the player plays SS.  If he played another position, which he might with some teams, then his value is going to be different.  Same thing with a very good reliever.  His value includes his role.  If he is likely to be used as a closer then the way you figure how many wins he adds as compared to a replacement closer is to multiply his IP by 2 and then you multiply that by the difference between his a replacement pitcher’s RA per 9.  If you think he will likely be used as a set-up man, then you use 1.5 rather than 2.0.  Etc.

Forget about leverage and forget about whether a pitcher “deserves” to be rewarded in his value for the fact that most teams will or will not use him as a closer.  It does not matter.  His value simply depends on what role he is playing and how good he is on a pitch by pitch basis.  How much that has to do with him or his manager is irrelevant.  Obviously it has SOMETHING to do with him or with his class of pitcher, because most very good relievers are used as closers or set up men and the best of the best are usually used as closers.  It is exactly like defensive positions.  A player’s defensive position is determined by his overall defensive skill (the best defenders play SS and CF, and the worst play 1B and the corner OF, etc.) and by the manager and team.  And as I said, a player’s value will vary according to the defensive position he plays because as a SS, he gets 3 chances per game and as a 3B he gets less than 2 chances a game.  That is just like the closer versus the middle reliever.  As a closer he gets to pitch in more important innings (like “more chances") than as a middle reliever of even a set-up man.

You wouldn’t value all position players as if they all got the same number of chances per game regardless of where they are likely to play, would you?  So why do you want to do the same for relievers?

(I am ignoring chaining in the above discussion.)

"Have I summarized your position well, based on your responses to my questions? “

As of now, yes.  I’m still open to persuasion but the underlying issue that has always led me away from leveraging is that a run is a run is a run, imo.

@MGL/23

“So forget about leverage.  How many wins does Rivera allow versus that replacement pitcher given that Rivera will pitch mostly in the 9th with a 1,2, or 3 run lead.  That is all you have to answer.  Once you do that, that is your answer to the question, “What is Rivera worth in marginal wins, as compared to a replacement pitcher?”

As it turns out, the way to calculate that is to take the difference between Rivera’s expected RA per 9 innings and the replacement pitcher’s and multiply that by the number of IP Rivera pitches times 2.0.”

I agree that the goal is to calculate the number of wins Rivera represents versus replacement level but there’s a huge leap in logic between that statement and how you claim we should go about calculating it.  Can you elaborate as to why we should be multiplying the number of IP by 2.0?

MGL’s illustration just shows that if Mariano is out, and instead you go with a .500 pitcher, the Yanks will not win 2 fewer games, but 4 fewer games. 

If you instead replace him with a crappy pitcher, the Yanks will win even fewer games.

But, by treating a run is a run is a run, then who gets those 2 or 3 extra wins that the Yanks actually got, if not to Mariano?

If you want to say that you want to create a “timing” bucket, and therefore, there are 2 extra wins in the bucket because the manager was “smart” enough (or “lucky” enough) to be able to leverage his best pitcher to be used in the most opportune time, then fine.  That’s your position.

But, part of that optimization is the obvious selection of having the best pitcher on your staff available.  Mariano deserves some of that leveraging.  He doesn’t deserve all of it, because he didn’t create that scenario.  But, he makes himself available for that scenario because of his talent.  If he didn’t put out that fire, someone else (not as good, but not as bad as the crappy guy) would do it.

Not every fire is a fire is a fire.  And if you call in the big guns to put out the big fire and save more lives, then that fireman gets more praise.

Can you elaborate as to why we should be multiplying the number of IP by 2.0?

Because that is the average leverage index for Rivera or any other closer used somewhat optimally.

The way you calculate the win value of one player versus another is always the difference in unleveraged win value - for pitchers, that is simply the difference in RA per 9 divided by around 10 - times the average leverage index of the innings in which that player plays.

Maybe Tango can explain it more thoroughly.  I basically am saying, “Because that is the way it is,” which is not a very good explanation, I am afraid.

Look at it this way:  Let’s say that you want to know the difference in wins between a 5.00 RA (per 9) and a 3.00 RA pitcher, and you are assuming that they pitch in games only when they are down by 10 runs in the 9th.  Obviously the team will lose just about all their games with both pitcher, so there is no win difference, even in say 90 innings.  Since there is a 2 run gap per 9, and presumably that 2 run gap should be multiplied by 10 (90 innings divided by 9) to yield a 2 win difference, something must be going on such that the score differential affects the win value.  Intuitively, you would know that if they both pitched only with a 1-run lead (or a tie game) in the 9th, that the win difference would be pretty large.  In fact, it is larger than the 2.0 win “unleveraged” difference.

So, as it turns out, in order to figure the win difference between 2 different players, you do, in fact, multiply the unleveraged (average of all possible situations) win value by the leverage to come up with the correct win value, given the game situation.

Why is that?  What is the mathematical justification? It is only be definition (of leverage index) really.  The way Tango comes up with the leverage index in the first place is to figure out the win difference between a good and bad player and then divide that by the average win difference in all situations.  LI is sort of reverse engineered.

My explanation for why LI is included in a player’s value is a little different from Tango’s.  I say that it doesn’t matter whose “responsibility” a player’s use is.  A team has to account for the difference in a player and his theoretical replacement by a replacement (league min salary) player.  That difference in wins is the player’s intrinsic value - period.  Look at it this way:  I don’t pay my players until they perform in whatever role (and average LI) they happen to perform in.  If one of my pitchers (a closer, for example) happens to pitch in high leverage situations in the 9th, and by virtue of that is 4 wins better than a theoretical replacement pitcher in that same role, then I must pay him 4 times the value of a marginal win, by definition, using whatever I want for the value of a marginal win.  If that same pitcher happened to have pitched in middle relief where his average LI was 1.0 then his win value over a replacement pitcher was only 2.0 wins, so I pay him less.  One call, that’s all.

Say you are Tony Soprano, and you have 5 henchmen, of varying degree of bank-robbing skills.  Do you randomly assign each robber to banks, or, do you make sure to put your most effective robbers at the banks where he can get the most money?  (Maybe one guy is a great safe-cracker, let’s say.)

If the safe-cracker goes to a bank where the safe is empty most of the time, well, you won’t get much money out of the deal.

All 5 henchmen come back, and they have money in their bags.  Won’t you have more money by deploying the top safe-cracker at a bank that’s got their safe filled most of the time?

The question is how much commission to pay out on your henchmen.  They didn’t have anything to do with putting the money into the safe.  They didn’t even choose which banks to go to.  Tony did.  He decided who goes where.

Who gets the money?

In terms of the chaining process, if the top safe-cracker was shacked up with some babe, Tony would have relied on his second-best guy.  So, there’s no reason for Tony to believe that how much money he would end up with, overall, is the difference between the top guy, and putting in his 6th guy who is a novice.  Tony would have redeployed his henchmen optimally.

So, the chaining process will, in effective, be equivalent to giving half the credit to the henchman, and the other half to the “timing” that would go into a general bucket.

Tango (and anyone), do you use actual LI to value past performance by relievers?  Or the LI determined by chaining?

Let me ask it a different way: forgetting about the irrationality of the marketplace, and presume that the market moves on the fundamentals, what should be the average annual salary for the following players at their peak: Hoffman, Wagner, Percival, Nathan?  (I excluded Mo because he stands above these guys.) Just give me an average number for the group.

Presume that a .500 starter with 180 IP makes $10MM.

I use chaining, meaning, in effective, halfway between 1 and LI.

Ouch.  That’s twice I’ve said “in effective”.  My brain was stuck between “in effect” and “effectively”.

MGL/27 —The implication there seems to be that the run distribution for a reliever impacts games more so they should get more credit.  I have qualms with valuing 9th inning runs more than 6th inning runs so that’s not a terribly convincing argument for me.  I also question whether or not a reliever can consciously affect their run distribution patterns.

If we’re going to discuss it simply in terms of wins, I’d have to take a simulator w/ probabilities and see if having a 2.30 true talent level closer in a 4.60 run environment would produce more than 2 wins over 81 innings.  I can’t answer that question realistically without running a sim.  If the answer is that they’d be worth 4 wins, then that would be a valid reason for me to “buy into” leverage.

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Tango/28

“In terms of the chaining process, if the top safe-cracker was shacked up with some babe, Tony would have relied on his second-best guy.  So, there’s no reason for Tony to believe that how much money he would end up with, overall, is the difference between the top guy, and putting in his 6th guy who is a novice.  Tony would have redeployed his henchmen optimally. “

This is an all-or-nothing kind of scenario though.  If he sends his 2nd best henchman against the best bank and he got only 95% of the returns he was expecting, and for the 3rd best against the 2nd best back gets only 90% of his expected return, etc. Wouldn’t the difference in returns on an incremental level be the same as the difference between the 1st and the 6th henchman. Or am I misunderstanding the analogy?

Aside—I’ve never watched the Sopranos.

The difference though is that the larger bank has more payout.  So, if he sends the 6th guy to the 5th bank and the 5th guy to the 4th bank, there’s not much money lost.  But, sending the 2nd guy to the 1st bank, while the 1st guy sits out will be huge.  And the difference will be MORE than the difference between the 1st and 6th guy.

***

I’d have to take a simulator w/ probabilities and see if having a 2.30 true talent level closer in a 4.60 run environment would produce more than 2 wins over 81 innings

...if you can make the closer pitch in the close games.

And, this has been done already:
http://www.baseballthinkfactory.org/files/primate_studies/discussion/robw_ood_2003-02-04_0/

It’s one of the best pieces of sabermetrics out there.

Remember, we are NEVER presuming that he will pitch better in tight games.

I say that it doesn’t matter whose “responsibility” a player’s use is.  A team has to account for the difference in a player and his theoretical replacement by a replacement (league min salary) player.  That difference in wins is the player’s intrinsic value - period.

This seems a little strict to me.  If a really bad team doesn’t want to spend money on good relievers, they’ll sign mediocre guys to close and set up.  Do those players deserve to be paid like closers and set up guys?  No way.  Most teams won’t offer them more money, because they’re bullpen filler.  And that’s how the crappy team wants to pay them and will probably end up paying them.

I view it like this: The best 30 relievers should be closers (or bullpen aces).  The next 30 should be set up guys.  Say those expected LIs are 1.8 and 1.3, respectively.  Those relievers should be paid using those LIs.  If a team wants a second closer and their set up guy, they’ll need to pay him like a closer.  If a team wants a set up guy as their closer, they should still pay him as a set up guy.

Sky, let’s not confuse issues.  One issue is how many wins a player is worth as compared to any other player, given the role he is placed in.  For a pitcher who pitches in close games in the 9th, that is basically the difference in their RA per inning, times their IP, times 2 (for leverage).

The other issue is how much money a player is “worth.” That is not as cut and dried.  In your example, if a team takes a generic reliever, say league average, and wants to use him in a closer’s role, then while he would be worth the difference in RA per 9 between an average reliever and a replacement reliever times IP/9 times 2 (for closer leverage), the team that uses him as a closer probably does not have to pay a closer price for him, since most other teams will use him as generic, middle reliever.  So this team will actually be getting a bargain. I already said in another post that the value of a player, in this case a reliever, in terms of how much you probably will have to pay for him, depends on how an average team will use him, not how YOU will use him.

Sorry if I’m reviving this thread if others were hoping it’s dead and buried, but I’m working on some stuff with relievers, and was hoping to clarify some things mentioned earlier.

1) I know Sky asked this earlier, but I’m want to make sure I have it straight: the “averaging” of any relief pitcher’s pLI with 1 should always be done when estimating that pitcher’s value over replacement, whether projected or looking back, correct?

2) I assume this is (sort of) what the averaging of a reliever’s WPA and WPA/LI is supposed to do. When looking back on past performance, just to get it straight, I assume that the averaging of WPA and WPA/LI just gives us the reliever’s wins above average, not above replacement. To get wins above replacement, is the best way still to get runs saved about replacement, then multipling it by (pLI+1)/2?

3) One last question, although it has to do with pitching in general, so I’m sorry if this is the wrong place for it. It has to do with how to scale FIP.

In figuring FIP on my own, I use the easy formula from Tango:

(HR*13+(BB+HBP-IBB)*3-K*2)/IP + 3.2

I understand that 3.2 is a generic number that ideally is to be changed to a number so that the lgFIP = lgERA. Even with fague memories of 8th grade Algebra and my rudimentary MySQL skills, I was able to generate table that lists all the league FIP “Scales” to way back when.

Here’s the question: say, like many people, I hate the earned run/run allowed distinction rule,and prefer RA to ERA. In that case, couldn’t the accompanying “FIP” stat be scaled to the lgRA, rather than the lgERA? Would there be anything wrong with that?

I would - and this is just my own intuition - prefer to raise the weights slightly to adjust FIP to an RA scale. It’d be an exceedingly marginal difference either way, and anyone who cares deeply about exceedingly marginal differences should be using something with a little more rigor than FIP to begin with.

Tell me more, Colin! I can’t sleep. I’d prefer something more precise, as well, but for mass data generation of something other than ERA/RA, tRA isn’t always available. (It’s your fault I’m not addicted to MySQL, anyway).

Here’s the formula I use. It’s a modified BaseRuns:

A*B/(B + C) + D

Where:

A = 0.29 * BFP - 0.29 * K + 0.71 * BB - 1.29 * HR

B = 0.31 * BFP - 0.31 * K + 0.2 * BB + 2.55 * HR

C = 3*IP

D = HR

Or for use with the BDB, just use IPOuts for the C term.

And I’ll take that as a compliment, I hope.

Yes, I’m still hung up on this.  I’m looking at the sequence of posts in 6, 9, 17, and 18.  Given an average bullpen and set of LIs, you can find its value via chaining or pitcher-by-pitcher.

ERA LI
3.00 2.0
3.75 1.3
4.25 0.9
4.50 0.8
4.70 0.7
4.80 0.6

Via chaining, the value of the bullpen is worth 42 RAR.  The other route yields 55 RAR.  If you assume a replacement-level team win 48 games, that’s 33 WAR for an average team.  Giving half to pitching and 1/3 of that to the bullpen (which is correct, right?) I get 5.5 WAR for the average bullpen, which is right in line with the second method, not chaining.

What am I missing?  It seems that the average bullpen produces 5.5 WAR above a bullpen of replacement-level pitchers, but chaining wants to pay them like a 4.2 WAR bullpen.

Good summary from sky:
http://www.beyondtheboxscore.com/2009/4/29/856308/bullpen-chaining-and-reliever-war