THE BOOK--Playing The Percentages In Baseball

On the other thread, I said this:

On that basis, some team will overspend to get him for 5/65 to 5/70, when he’s really worth closer to 4/45.

He signed for 4/56 (and if he is traded, 5/75). 

My salary calculator (after you add 10% for the 2008 season) says that a 5/65 deal for 4 years is 4/55:
http://www.tangotiger.net/salary.html

A starting pitcher who pitches 190 IP at age 28 has a very bleak future.  Here is what happens to all of them, on the average:

Age # still pitching average IP ERA

28 171 200 3.97
29 154 143 4.15
30 131 115 4.10
31 117 96 4.17
32 107 83 4.16

The average IP includes zero for those who are no longer pitching.  The ERA’s stay around the same only because the better ones survive (the first year it is low because we are sampling pitchers with at least 150 IP, i.e., the lucky ones).  Each pitcher actually gets worse with each passing year.

The future is pretty bleak because it includes ALL starting pitchers.  What if we only include the good ones, like Buehrle?  This time I will only include pitchers who had at least 150 IP in year 1 and an ERA less than 4.20 in the NL and less than 4.50 in the AL.  I am going back to around 1980 or so.  Of course we are going to have big jump in ERA from year 1 to year 2 as year 1 pitchers are now very lucky because of our ERA requirement.

Age # still pitching average IP ERA

28 122 204 3.64
29 113 155 4.00
30 99 130 4.04
31 89 106 4.09
32 80 91 4.13

These are the good pitchers.  Basically, 1/3 of all good 28 yo starting pitchers with lots of innings will not be pitching at all in 4 years.  And the ones who do pitch, only throw 140 IP!

I had been quoting 10% for the IP attrition rate, but it is more like 20%!

Of course, Buehrle has a history of non-injury and several years of lots of IP under his belt.  Then again, he has thrown to a lot of BF per year, which may portend injury.

O.K., let’s look at pitchers who have had at least 3 consecutive years of 150+ IP in their 25, 26, and 27 age seasons (and then again in their 28 age season).  We’ll also use the same good ERA threshold.  Now we have some good, durable (at least in the past) pitchers:

Age # still pitching average IP ERA

28 39 216 3.38
29 36 170 3.77
30 35 155 3.79
31 33 125 3.98
32 29 107 3.75

These are the Buehrle-like pitchers.  Still, more than 25% are not pitching at all in 4 years.  You also lose half your innings by year 4.  So you expect that on average Buehrle will pitch only 100 IP or so in 4 years (albeit quality innings) including the times he does not pitch at all.

Because of the attrition, the pitchers you are left with are about the same quality as the ones you started with the year before, even though each pitcher is a year older and a little worse.

So even with good, historically durable pitchers, you still can expect to lose 10-15% in quality/quantity per year.  Perhaps that almost makes up for salary inflation.

Interestingly, if we increase the number of years of 150+ pitching before age 28, we increase (slightly) the number of pitchers remaining at age 32 and the number of IP thrown and vice versa if we decrease the number of 150+ years prior to age 28.

Now whether that is because the ones with more experience are better pitchers or because they have a longer injury-free track record is hard to say.  If we make an ERA threshold for those years prior to age 28, e.g., 3 years of 150+ IP AND an ERA less than 4.2 in the NL and 4.5 in the AL, then we still get around a 25% attrition rate after 4 years, but we get slightly more IP after 4 years.  Actually if we limit our pitchers to at least 2 years of 150+ IP in their age 26 and age 27 seasons (and then 150+ in their age 28 season) with no ERA requirement in any season, we still get around the same results, a 25% drop-out rate after 4 years and around 50-55% average IP after 4 years (again, counting zero for those pitchers who do not pitch - if you do pitch, you will pitch around 150 IP as opposed to 210 or so in your age 28 season).

Interesting stuff, MGL. Maybe this is a perfect example of “optimism bias” that was talked about on the Wages of Win blog a little while back. The White Sox are probably not thinking about (or weighting properly) the chance of Buehrle’s innings declining significantly or performance declining. I could see them conveniently forgetting about his 4.99 era last year and saying “what if he’s a 3 era, 200+ innings pitcher going forward...we can’t pass this up”.

Anyway, good stuff as always.

I see this as an ok trade for the next two years based on more of a information asymmetry perspective.  Let’s suppose that Ken Williams perfectly understands that Buehrle isn’t quite worth what he just paid for him.  But, he also knows that most other GMs overvalue established pitching and undervalue inexperienced pitching. (See Zito signing, Milwood signings, Mulder/Haren trade, and Danks/McCarthy trade, etc.) Williams also knows that the next couple of years look bleak for the White Sox as the Tigers and Indians look to be strong for at least a couple of years.  So, Kenny’s looking at a losing team, and high draft picks.  Why not lie in wait, gather the draft picks, take college players that will hopefully be ready for the majors on a relatively quick time table and then trade Buehrle for an undervalued inexperienced pitcher when the trade window opens, when the White Sox will hoepfully be ready to strike.

The added bonus of this strategy is that your fan base will not be in revolt during the dark period because you threw them a bone and kept a fan favorite through the dark period.

So, as long as Buehrle doesn’t fall off a cliff until the trade window opens, this move might pay off in a couple of years.  If Buehrle happens to buck the odds and remain an excellent pitcher, so much the better.

Buehrle is likely to remain the good, but not great pitcher he is.  It is the injuries that do a pitcher in as far as future IP and attrition and to some extent talent/performance are concerned.

To sign a pitcher to an inflated long-term contract in order to trade him at some future time is a risky strategy at best.  I doubt that the WS and Williams are that creative in any case.  Of course to trade any signed FA who is making too much money to start with and get ANYTHING in return is always a coup.  As Tango likes to say it is like trading a 200,000 house with a 250,000 mortgage for something of value.  Really stupid (for the other person - the one getting the house).

I am not a big fan of Williams.  My guess is that they simply overvalued Buehrle because of his fine year this year, and that they, like most teams, grossly overalue starting pitching.  There is no way you are going to convince almost any GM that a pitcher like Buehrle is worth the same as some halfway decent position player who is also worth 2.5 wins above replacement (I could name a dozen that most GM’s would laugh at), not to mention the fact that the position players is going to have better long-term value as you don’t have the same attrition rate with position players.

I tried doing what MGL did, but with 200+ IP in their age 26,27 & 28 seasons, and an ERA under 4.00 at 28, since 1950.

Age--#--IP--ERA
28--60--257--3.01
29--58--224--3.26
30--58--200--3.47
31--54--191--3.38
32--49--160--3.28

That’s an 18% drop rate and 62% as many innings at 32 than at 28. Not quite as bleak for pitchers with excellent durability.

Anthony, good job.  There does not seem to be a greater risk of injury when a pitcher, at least for those ages and other parameters, pitches a lot of innings.  In fact, it might be the opposite, as suggested by your and my data, although we do have selective sampling issues and a confluence of quality and quantity.

In almost any case, I think that the attrition for pitchers is quite a bit higher than that for batters, but I have not looked at the batter data in a while.

In light of this, how would one go about actually building a pitching staff?  It appears that, because of the risk involved and the presence of optimum outcome bias in the marketplace, it is virtually impossible to sign a pitcher for a “reasonable” contract, that accounts for the likely outcomes of his career.

Are we to avoid giving any FA starters contracts?  Are we to build a rotation on arb guys alone?  I buy in to the idea that Mark Buehrle is overvalued.  However, by that logic, I have to imagine that 95% of all pitchers are.  At the end of the day, bottom line performance is more important than cost efficiency.  How does a GM go about building a staff in light of this?

Virtually every free agent starting pitcher is overvalued.  I’d close my eyes to every single one of them.  If teams are overvaluing there, they’re undervaluing somewhere else. 

It will be very interesting to see what happens with Johan Santana.  I think he’s a free agent after the 2008 season (so are Sheets, Peavy, CC, I think).

Dude is a .700 pitcher, meaning he’s an insane +7.0 to +7.5 WAR pitcher.

Add 20% to this chart for players entering 2009 on a new contract:
http://www.tangotiger.net/salary.html

And he’s going to be worth 7/250, without the starting pitcher premium.

Don’t forget that all free agents get almost twice what they are worth in terms of wins.  So, free agents, to start with, are overvalued.  Then, add in the standard starting pitcher premium, and forgetaboutit.

However, I have to believe that Santana will not get a premium, simply because of the sticker shock.

Back to your question: I’d make all my starting pitchers under 30.  If they are over 30, I’d make sure they are there only to round out the rotation. 

Me?  I’d trade Johan for… I dunno… a team’s entire farm system?  Would that be a fair trade?  Johan has, what, about 20 MM left on his contract, where a free agent of his caliber would be worth about 40 - 45 MM for 1.5 years?  How much is a farm system worth?

"Dude is a .700 pitcher, meaning he’s an insane +7.0 to +7.5 WAR pitcher.

Add 20% to this chart...And he’s going to be worth 7/250.”

I’m a bit confused: if we assume Santana is a 7 WAR pitcher, shouldn’t we go to the 7 WAR row, go across to 9 years, then subtract the first two years?

That is, 7 WAR equates to a 9/255 deal. Remove the first two years since he’s under contract until 2009, and we’re left with 7/198.

If we just add 20% to the chart...doesn’t that assume that Santana remains a 7 WAR player through 2009?

That seems to go against MGL’s findings in post #2.

I’m assuming that, because of his age, he will be a +7.0 WAR pitcher entering 2009 season.

The adding the 21% is because the value of a free agent win, I presume, increases by 10% every year.  For the 2007 season, it’s 4MM.  For the 2008, it’s 4.4, and for the 2009, it’s 4.84MM.

Entering the 2009 season, he will be 30 years, 19 days old, meaning he’s still at his peak, or on a fairly gentle slope off his peak.  If the standard improvement/decline across all ages is .020 wins per 9 IP, it will be fairly faint at the 28-30 yr old level (and much harsher in the 36-40 age level).

In any case, this is really just a rough guideline, which works surprisingly well.  You start off with what you think he will be as of Apr 1, 2009 (I say .700, but if you want to say .650, that’s ok).

You figure how many IP he’s due to pitch in 2009 (including injuries).  I think I said 23 full games, but if you want to make it 21, that’s ok too.

I give a standard 0.5 wins decline per year (for both loss of effectiveness and loss of playing time).

The repl level pitcher as a starter is .380.

.700 minus .380 all times 23 = 7.4 WAR
.650 minus .380 all times 21 = 5.7 WAR

I nicked him down from 7.4 to 7.0 for my possible overenthusiasm.

Assuming he’ll get 7 years (Zito level), then the 7.0 WAR line comes in at 202 MM.  Add 21% and that gives us 244 MM for 7 years.  Nick him up to 250.

I have the advantage of living in Chicago and the response has been pretty positive.  What Williams is (over)paying for is the certainty of having a “good but not great” pitcher around, as opposed to letting him walk.  Buehrle is the type of pitcher who’s not exactly common, but not exactly rare.

Consider: If MB goes, then Williams is the “guy who let Buehrle go.” It’s even worse if Buehrle goes out and posts a 20-4 season with a 2.00 ERA somewhere else.  He’d also run the chance that no one else would come along to fill the void from the farm system or a cheap signing from elsewhere.  Look at Oakland.  They didn’t sign Hudson, Zito, or Mulder to long-term deals and they’ve been having a lot of trouble finding decent starting pitching lately (yes, that little puddle under your monitor is fresh sarcasm.  I hope.)

Signing MB to an over-priced contract will hamstring Williams on other signings, but then he can blame “the market” or the owners being stingy.

I’m convinced that 95% of the inefficiencies and bad decisions in baseball are the product of the deep human need to pass the buck.

All pitchers born since 1960, through age 28, here are their “Mulholland Starts %” ... you know it as “Quality” not “Mulholland”:

http://www.bb-ref.com/pi/shareit/ryPa

98 pitchers qualify for the list.  Buehrle is 20th.

This is OPS+
http://www.bb-ref.com/pi/shareit/8KWE

He’s 23rd here.

And ERA+
http://www.bb-ref.com/pi/shareit/mpKY

He’s 14th.

You know, right off the bat, without any analysis and without looking at the numbers, this looked like a pretty good deal for me. I’ll tell you why:

(1) Mark Buehrle has proven himself to be as durable as any pitcher in the major leagues. He’s had six consecutive seasons with 200+ IP, and I can’t remember ever hearing about him having any kind of arm problems. If you want to measure his expected drop-off in innings, I think you have to look at 28 year-olds who had six consecutive years of 200+ IP. I bet you won’t find many…

(2) That’s another one. Buehrle is only 28. The White Sox won’t be on the hook for his mid-30s, which is really when most pitchers’ arms start to fall apart. It’s not very realistic to believe that Barry Zito (another durable pitcher) won’t have any injury problems over the duration of his contract; I think it is believable that Buehrle will not.

(3) It’s only a four-year deal. There’s a lot less risk involved, and the contract is easier to trade.

(4) The White Sox play in a big market. Buehrle is worth more to them than he is to the average team.

Also, for people doing consecutive years studies, two reminders: (1) Remember to combine years in the Lahman DB where the pitcher played for more than one team, and (2) Make sure all the pitchers you’re looking at have had a chance to pitch in the years after their base season. Pitchers who threw 200 innings in 2006 obviously are not going to have thrown any innings the year after (well, according to the database) or two years after, etc.

I unfortunately don’t have the time to look into his right now (maybe I will for my THT column), but I have a sneaking suspicion that this will be a better deal than you think.

(And of course, I reserve the right to be wrong.)

"Buehrle is the type of pitcher who’s not exactly common, but not exactly rare.”

Really?  How many pitchers are out there currently who have averaged six years of 225 innings pitched and a 120 ERA+?  I can’t imagine there’s more than ten…

In the past two decades, six pitchers have posted six consecutive seasons with 200+ IP before turning 30: Maddux, Clemens, Radke, Buehrle, Garcia and Zito (the last three being current streaks).

At the same time, is it helpful or hurtful to examine a pitcher’s career more than three years into the past? How much do Buehrle’s 2001-2003 seasons inform his 2008 and beyond?

#2 and #6, could you post the median number of innings pitched for each year? It seems like this is a case where using the mean really skews things because the risk with pitchers isn’t so much the gradually decline but the catastrophic injury that eats up most or all of a season. So my expectation for Buehrle (or any pitcher) going forward is not a steady loss of innings but either near perfect health or basically no production in a given year, with the odds that they provide nothing increasing with each year.

The problem with a Buehrle forecast is his 2006 season. It sticks out like a sore thumb, and, it’s also the most relevant data point… until he pitches 3 more starts, at which point his 2007 season and 2006 season will be equally relevant.

A pitcher’s performance relevancy is based on a 70% scale.  So, you weight his 2007 PA at 100%, his 2006 PA at 70%, his 2005 PA at 50%, his 2004 PA at 35%, etc.... They all count.

If you want to infer his durability, you can use all of the data, but I have found in the past that I only need two years of data for that.  Who knows, maybe in a case like this, you want more.

If we make Buehrle a .550 pitcher, and give him 23 full games, that makes him +3.9 WAR, or 17 MM for 2008 season.  Because he’s so young, maybe you drop him 0.2, 0.3, 0.5 WAR for the following 3 seasons.  You bump up the free agent cost to 5.32, 5.86, 6.44. 

So, 3.7x5.32=19.7
3.4x5.86=19.9
2.9x6.44=18.7

The total is 4/75MM.

This is the problem with these kinds of deals.  Just a little more optimism one way, and all of a sudden a reasonable 4/45 deal becomes a reasonable 4/75 deal, at which point the 4/56 deal looks fantastic.

***

I disagree about the tradeability point.  His deal goes from a 4/56 to 5/75, meaning one extra year is an extra 19MM.  If the Sox are going to trade him, it’s likely on the way down, at which point, the tradee team will want salary relief.

Again, it all boils down to what you mean by a good or bad deal.  Generally I am talking about “as compared to position players” with regard to pitchers.

If you are just comparing pitchers to pitchers that is another story.

And of course, from a team owner’s perspective (assuming they only care about the bottom line), it depends on their marginal revenue per extra win and per extra chance of making the playoffs, as we and many other people have discussed before.

So when I am taking about a good or bad deal for a pitcher, it COULD be compared to other pitchers or it could be compared to a position player with a comparable WAR.  I am usually talking about the latter, unless I say otherwise.  Even if I am talking about comparing Buehrle to other starting pitchers, I don’t think it was a good deal, as I don’t think that 6 mil per marginal win is a good deal for a starting FA pitcher (it may be near average, but not “good").  Other people may debate that 2.5 WAR that I think he is worth, although I think the debate would be what is the ERA of a replacement pitcher.

So, if pitchers are overpriced as compared to comparable position players, how do you build a pitching staff?  Well, you try and build your entire team, pitchers and hitters, with pre-FA players for starters, either from you rown farm system or with trades for other teams’ prospects and young players.  But assuming that you are going to sign some FA, you first exhaust all your position player possibilities and THEN you work on pitching.  It is as simple as that.  Yet how many teams understand that an offensive win is around the same as a pitching win and that decent but not great position players are equivalent to very good pitchers?  Not many.

I mean you start a team from either what you have or you gut it and start with all replacement players. Then you try and add above-replacement players for as little per win as you can.  That almost always means that you start with offense until you can do no more and THEN you work on the pitching, assuming that you have more money to spend or that you have enough revenue to offset the cost of more wins.

For the next hundred years, almost everyone but sabermetricians and their ilk will overvalue pitching in baseball.  It SEEMS like you need good pitching to win but not necessarily good hitting, but that just ain’t the case (although you usually need both to have an excellent team, but not always).

In fact, if I owned a team, I would make sure that my park were an extreme pitcher’s park to give everyone the illusion that I always have good pitching and always need more hitting!

The only problem I see with saying stuff like “I wouldnt give him mroe than 3/36” is that its going to be awfully hard to put a pitching staff together, because virtually every big name FA pitcher is overpaid.  You can develop a staff, but thats really hard, and you can go shopping the bargain bin, but the way I see it, those guys have an even larger chance of attrition than the big name guys.  If you find an average guy you think you can sign, well if he loses 20% off his performance he really won’t help you; whereas if you bring in a stud pitcher he can still lose 20% and at least help a team.  I just think its awfully hard to put together a pitching staff without some high paid pitchers.

I count 49 teams (out of 150), from 2002-06, that meet these criteria:
- at least 5 pitchers with at least 14 starts
- group ERA of those pitchers of 4.50 or less

If I add a restriction that a pitcher had to make 6 million$ or less, I get 11 teams (the 2002-04 Marlins, 2002/04 Expos, 2003-04 Padres, 02 Giants, 03 Indians, 03 Pirates, 04 Astros)

***

What if I make the restriction at least 20 starts, an ERA of at most 5.00 for each pitcher, and at least 4 such pitchers?  That gives me 57 teams.

Out of those, how many had each pitcher make 6 MM or less? 21.  The multi-year teams are: 03/05 Indians, 02/03 Expos, 02-04 A’s, 04-06 Padres.

It looks to me that what you need is a smart management team and quality player development.  I suppose that is “awfully hard”, but it sure isn’t impossible.

I think if Billy Beane operates on a principal that he will purposefully handcuff himself to force him not to overpay, and therefore, put the money into player development, that might be an awfully hard yet wise move.  More teams out to be responsible like this.

"In fact, if I owned a team, I would make sure that my park were an extreme pitcher’s park to give everyone the illusion that I always have good pitching and always need more hitting!”

Do you mean to throw off the fans and media so they’d stay off your case?  Or to confuse other GMs?  Or to confound the players in their salary demands, since you’d be amassing a trove of good position players while having more fungible pitchers?

Is this more about the degree to which top pitchers can exceed their brethren versus the degree to which top hitters can exceed theirs?  Or is it a lot about reliability issues?

SK, I don’t understand your last paragraph/questions(s).

It would be to mostly to keep the fans and media (and maybe my own GM and manager) off my back.  To some exent it is wise to fool other GM’s, as that “trickery” can be leveraged.  And it saves a pitching staff, all other things being equal.  The last point is not an unimportant one.

re: 21.  I had a long post in response to 21, but it seems to have been lost.  Basically, in the last 11 years, there have been 11 rotations that fit the criteria you outlined above?  (If I misinterpret the data, I apologize in advance) Thats about 2 teams over 5 years, which doesn’t seem like a whole lot, especially because a few of the rotations you outlined had 3, and in 1 case, 2 pitchers above league average.  That doesnt strike me as a championship type rotation.  I don’t know, it’s possible, as the A’s have shown, but its really hard to consistently develop top of the line pitching, which is what you’re gonna have to do since even when you develop a great arm you are eventually gonna have to pay him.

Conor, I said that 33% of all teams are able to create a quality rotation (49 teams out of 150).  Out of THOSE 49, 11 have done it cheaply.

So, 25% of all quality rotations were done cheaply.

***

In my second part of post 21, I used a looser restriction, so that I had 38% quality rotations (57 teams).  Out of THOSE 57, 21 have done it cheaply.  So, 37% of all quality rotations were done cheaply.

***

The other way to look at it is: given that we want to create an inexpensive rotation, how successful are we?  I’ll come back with those numbers…

In case anyone is interested, here is my official take on the signing:

http://www.hardballtimes.com/main/article/did-buehrle-get-overpaid/

More proof that gut instinct—well, at least mine—doesn’t mean much when it comes to analyzing free agent signings.

"Conor, I said that 33% of all teams are able to create a quality rotation (49 teams out of 150).  Out of THOSE 49, 11 have done it cheaply.

So, 25% of all quality rotations were done cheaply. “

Ok I apologize for the slight misinterpretation of your data.  However, I may disagree with the way you define a quality rotation, and also a few of the teams in there.  I think it was the 04 Pirates who had 2 guys above 100 (neither above 120 I believe) and 3 guys around like 90.  I don’t consider that a quality rotation.  I’m guessing thats an issue with park effects, and there may be some teams in pitchers parks that you left out because of the raw ERA.

I guess it all depends on your definition of a quality rotation; so on average, there are only 10 quality starting rotations a year?  That seems a little low to me, though I guess it all depends on how you define quality obviously. 

It was the 03 Pirates, the 5 starters they had had an ERA+ of 129,119,89,85,81.  To put it in raw ERA terms, they had 3/5 of the rotation with an ERA over 4.75.  Do you really consider that to be a quality rotation?  Salomon Torres was the 6th starter, throwing only 20 innings less than the #5, and put up an ERA of 5.51.

I also don’t really buy the 04 Astros, since they benefited from the cheap signing of Clemens, which I guess is ok since I believe it was a one year deal, but they signed Andy Pettitte for 3 years and 30 million, but it was backloaded so he only made 5 million in his first year.  That seems kind of cheap to me.

Its certainly possible I have higher expectations for a quality rotation than I should.

However, I do think the list of teams with multi year runs is pretty interesting.  I would imagine the Marlins and A’s and even the Padres are no surprise.  But i was pretty surprised to see the Indians and Expos up there.

Hey, its possible, like I said, that my standards for a quality rotation were too high.  I am not ruling it out.  Or maybe I am biased because my team, the Mets, hasn’t developed a young stud pitcher in who knows how long (that they have kept around, at least).  Maybe I am also overestimating the amount of big money pitchers that are out there.

All I can say is that you can decide to establish “quality” any way you like (whether that means you have 5, 10, or 20 quality rotations).  And, I would bet you that 20-30% of those rotations are done cheaply.

The Mets DID have Kazmir.

I would imagine you’re right, or close to it, but even so, thats still only 1 out of every 4 or 5 quality rotations thats done cheaply.  I still think that makes it pretty hard, but I could always be wrong.

Kazmir was the reason for the parenthetical comment.

I’ve gotta run, but let me just note what I just did.  I looked for the top pitchers born since 1920, with at least 2700 PA between ages of 25-28, and see how they did at ages 29-32.

As a group, those pitchers has 77% as many PA, and allowed 14% more runs per game.

So, if you have someone who had say 216 IP (24 full games), with an ERA that is 87% of the league average, he will end up, over the 4-yrs to have an average of 166 IP at league-average ERA.

The 216/.87 means that this would be +.07 wins above average (or +.19 wins above replacement) per game, or +4.6 WAR.

In the post group, that becomes +2.2 WAR.

In essence, you lose half your value.

I haven’t looked yet, but if we say that the 25-28 that averaged +4.6 broke down as follows:
+4.3, +4.6, +5.0, +4.5

Then we can continue the chain as:
+4.0, +3.0, +2.0, +1.0

That gives us +2.5, which is still too high.

As you can see when it comes to pitchers, and I selected the best, they come across some devastating injuries.  We all remember Clemens and Maddux, but we forget the others.

***

By the way, Buehrle has a pretty high unearned runs to total runs rate.  His ERA makes him look better than he is.

http://www.baseballthinkfactory.org/files/dialed_in/discussion/landing_buerhle_a_great_move/

Chris Dial follows the same process I have in #30.  His parameters are slightly different.  I agree with him about using more modern pitchers, so I’ll redo my numbers as well.

I also agree with him that we’d like Buehrle to be in the middle-of-the-pack when selecting his comps.  And that is what I did in #30.

Note however that we should be using RA+ not ERA+, for reasons noted in #31.

Finally, he uses total inning from ages 20-28 and ERA+ the same, while I focused on 25-28.  The reason I do so is because you could have a guy with low innings in the 27-28 years if he pumps up his IP in the 20-26 years.  This is corrected if Chris (and I) also put in a 400 IP requirement for ages 27-28.

That said, while I showed they retained 77% of their IP, he shows 82%.  Not something to be worried about.

The “oof” part is that Chris shows that their ERA+ is 130 in the after-years (he doesn’t show what it was in the before years, though presumably it’s around the same). 

Another note: since ERA+ is inversed (it’s lgERA/ERA), you CANNOT simply take the average ERA+ of all pitchers.  You need to first inverse them properly (ERA/lgERA, or do 1/ERA+), then average them, then you can re-inverse them. 

My guess as to what’s happening is that you have those unbelievable Maddux/Pedro years that shoot the ERA+ so high. 

You wouldn’t average PA/HR of Bonds and Neifi and then conclude that the two, on average, stink horribly.  You must always put the opportunities on the bottom and the success on top.  It’s ER/IP.  What Sean Forman does is exactly the same as this:
pitcher IP/ER
divided by
league IP/ER

(The “9” removed since it cancels out.)

A little math shows that this is the same as
lgERA/pitERA

That’s why this is not addable.

As you can see, using OPS+ for pitchers (instead of ERA+), Buehrle doesn’t fair as well:

http://www.bb-ref.com/pi/shareit/mpwk

His OPS+ of 89 is pretty much equivalent to 100/.89=112 in ERA+

I think it’s a safe bet to say that Buehrle will post a league average runs per 9IP at ages 29-32, with around 80 full games of innings.  Since a league average starter is +.12 wins above replacement, that makes Buehrle about 9.6 WAR for ages 29-32.  Over that time period, the free agent win will be worth around 5MM each, making him worth around 48MM.  (A bit less since his wins will peak when the cost of those wins will be the least… if you work it out, it’s around 46-47MM).

Here’s another list:
http://www.bb-ref.com/pi/shareit/73KH

The selection criteria is in the header:
- age 25-28
- born since 1957 (i.e., 1982 season and later)
- ERA+ of under 150
- at least 800 IP
- K/BB ratio of at least 2.5

Sorted by OPS+.

There’s a total of 14 pitchers.  Since Sean doesn’t (yet) allow me to limit by OPS+, and since Buehrle has an OPS+ of 89, let’s limit our players to the guys with an OPS+ of 80-98.  Let’s also remove anyone who has not yet played beyond age 32 (Oswalt, Vazquez).  His top 6 comps are:

David Cone
Denny Neagle
Frank Viola
Brad Radke
Dwight Gooden
Erik Hanson

If you want to remove Dwight Gooden for non-baseball related reasons, let’s do so.

So, that’s what you are really left with: Cone, Viola, Radke, Neagle, Hanson.

From age29-32, this is what those 5 did:
Cone, 905 IP, 73 OPS+, 139 ERA+
Viola, 980, 89, 113
Radke, 751, 91, 111
Neagle, 702, 94, 108
Hanson, 539, 91, 102

The OPS+ is 88, and the ERA+ (properly done) is 113.  (In fact, you will typically find that 10000/OPS+ = ERA+). 

The pre and post periods have no change!

Their 25-28 IP is 879, while their 29-32 IP is 775, or a 12% drop.

Now, this is only 5 guys, so obviously, one good or one bad comp throws the whole thing off.  But, this is about as a reasonable optimistic group of pitchers as you’ll find.

An OPS+ of 89 or ERA+ of 113 corresponds to a winning percentage of around .550-.560. 

Buehrle has 802 IP between ages of 25-28, plus whatever he’ll pick up this year, say another 108, to give him 910 total.  And if we forecast a 12% drop in Buehrle IP, that’s 801 IP for ages 29-32, or 89 complete games.

We have what we need.

WAR = (.555-.380)*89 = +15 to +16 wins wins

At 5MM per win over the next 4 years, that’s 75MM to 80MM for the 4 years.  GREAT deal for the Whitesox under this analysis.  That’s about as reasonable an optimistic a case that I can build for him.

There have been 91 pitchers born since 1973 (Buehrle born in 1979) that have at least 700 IP (half of Buehrle’s total).

In terms of unearned runs per total runs, Buehrle ranks 8th highest (at 11%).  Brandon Webb is #1 at 15%.  Derek Lowe is #3.  Jake Westbrook is #15.

Last on the list is Jarrod Washburn with only 5%.  Santana is #80 at 6%.

The median is 8%.

What does this mean?  I think it’s apparent that if you have a severe GB pitcher like Webb, and if you have more errors on IF than OF, that Webb will “induce” errors.  That is, simply by being a GB pitcher, errors will happen, even if you have Ozzie Smith on your team.

As far as I’m concerned, I’d do away with ER and stick with R.

As for Buehrle, since 92% of R are earned in the median group and he’s at 89% of ER to R, then we need to drop his ERA+ down by 3% to compensate.

Brandon Webb’s ERA+ needs to go down 8%.

There were 38 pitchers born between 1958 and 1974 who faced at least 3400 batters between the ages of 24-28.

13 of those pitchers maintained a similar workload (+/- 10%).
13 of those pitchers had a workload of at least a 40% drop (average drop of 57%)
12 of those pitchers had a workload of an average of 19% drop

Overall, these 38 pitchers had an average workload of 3699 PA at ages 25-28, and 2767 at ages 29-32, or an average drop of 25%.

These 38 pitchers allowed 0.60 fewer runs per game at ages 25-28 (close to Buehrle), dropped down to allowed 0.43 fewer runs per game at ages 29-32.

If we expect Buehrle, in his ages 25-28 seasons, to have a total IP of 900, that would mean that’s 100 complete games.  A 25% drop means 75 full games.

These numbers work out to this:
WAR = (.545 - .380) x 75 = +12.4 wins

At 5MM per win over 4 years, that’s 62 MM for Buehrle.

Under this analysis, the Whitesox got themselves a slightly better than average deal.

***

If I remove the guys outside of Buehrle’s league (Pedro, Clemens, Maddux, Rijo), and the guys at the bottom (Scott Erickson, Kevin Gross, Scott Karl, Bill Gullickson, Mike Moore), I end up with 29 pitchers.

The percentage drop in PA is now 23.5%.

Now, our pitchers go from being 0.55 better than average to 0.29 better than average.  (Essentially, a 50% regression.)

Our new numbers gives us:
WAR = (.530 - .380) x 76.5 = +11.5 wins
That makes him worth 57 MM.  And that’s exactly what he got.

Over the last two years, here are all the unearned runs allowed by Buehrle:

7/21/05—two unearned runs.  infield single, walk, double E-4 scores one, IBB, relieved, SF scores another.

8/1/05—one unearned run.  E-4, single to RF, 5-4, 4-6, blooper scores runner

8/17/05—one unearned run.  Konerko boots a grounder with two out, run scores from second

8/29/05—three unearned runs. E-4 (Iguchi drops popup); 4-6; 1-3; double, walk, E-4 (dropped throw), single

5/14/06—six unearned runs.  single, E-1, single, E-6, single, SF, double… This was the Sunday night game the Sox won anyway.

5/19/06—one unearned run.  Single, E-2 on SH, SF

5/24/06—one unearned run.  single, PB, single

7/2/06—one unearned run.  E-5, single… long chain

7/15/06—one unearned run.  Single, single, E-5, double, single…

So, yeah, he has trouble pitching when Iguchi and Fields don’t catch the ball…

Unearned runs.

Buehrle (Santana in parens)
2002: 7 (5)
2003: 18 (2)
2004: 13 (4)
2005: 17 (3)
2006: 11 (7)
2007: 3 (4)

In that 2003 season, Buehrle’s teammates:
Colon, 3
Loaiza, 2
Garland, 7

In that 2005 season:
Garcia, 4
Contreras, 9
Garland, 6
El Duque+McCarthy, 4

2006:
Garcia, 7
Garland, 6
Vazquez, 7
Contreras, 8

Why does Buehrle get off scott-free here?  His teammates have the same fielders behind him.

For me, I’d do away with ER, and stick to runs allowed.

***

Brandon Webb had 28(!) UER in 2004, otherwise 10 or so every year.

***

GB pitchers allow more unearned runs because they allow more ground balls.  Errors are inevitable.

Here’s Chris Jaffe’s comp-list:
http://www.hardballtimes.com/main/article/looking-for-the-perfect-comp/

As you can see with all these different studies is that you can get a fairly reasonable set of comps based on a fairly reasonable set of criteria.  And those those results can be wildly different.  You can get the IP drop to be 15% or 40%.  You can get the runs/game to increase by 0.10 or by 0.50.  Once you increase your number of years, and the cost/win likewise increases, you can get just about any number.

Right now, I see Buehrle as having, in his next 4 years: .540, .530, .520, .510, with IP totals of 200, 180, 160, 140, on average.  That makes his WAR 3.6, 3.0, 2.5, 2.0.  With the cost/win being 4.4, 4.84, 5.32, 5.86, that gives us a total of: 55 million dollars, with something like a 30% chance that he’ll be worth far more than that, and a 30% chance that he’ll be worth far less than that.

One thing that’s pretty interesting is if you compare the PECOTA comps for Mark Buehrle and Jake Westbrook.  PECOTA foresees a rather stiff decline for Westbrook whereas it has Buehrle aging really quite well for a finesse pitcher (or any pitcher at all for that matter), which is interesting because the only real differences between the two pitchers is that (1) Buehrle is a lefty, and (2) Buehrle became established at 22, Westbrook at 25 or 26. 

Anyway I agree with Tango’s conclusion (?) that the deal is probably about breakeven in terms of Buehrle’s marginal revenue product to the White Sox, before considering off-field considerations, which might be material in this instance since Buehrle is a very popular player.  Clearly the market value for pitchers is a bit higher, so in that sense this deal also provides the White Sox with some trade/option value.  On the other hand, you can certainly argue that Buehrle’s value will never be higher than it is today, and if the White Sox could have gotten say an A-minus and a solid-B prospect for him, they made a mistake by not doing so.

Anthony, great job.  I moved your comment here:
http://www.insidethebook.com/ee/index.php/site/comments/do_pitchers_today_have_it_better_because_of_medicine_and_technology/#25