THE BOOK--Playing The Percentages In Baseball

Joe Sheehan says something stupid.  In other news, sky still blue and chickens are unable to fly.

And that is why I will never, ever, publicly express an opinion regarding whether a batter should have bunted or not. 

damn, that does seem a little harsh.

Joe Sheehan says something stupid.  In other news, sky still blue and chickens are unable to fly.

And Dave Cameron, the so-called “Christian,” says something petty, nasty, and inaccurate about someone who dares to disagree with him. Sky still blue, etc., etc.

"And that is why I will never, ever, publicly express an opinion regarding whether a batter should have bunted or not.”

Except in the case where Adam Dunn decides to bunt. Someone with his ISO / AVG ratio should probably never bunt (well, perhaps not never, but somewhere close to) ...

Or Adam Laroche.

***

As for Dave’s comment, he could just as well have said “Tango said something stupid”, meaning that everyone says something stupid, so who cares.  It doesn’t necessarily mean that everything Joe or Tango says is stupid, just not a reason to be in a huff.

As well, Joe writes that he gets lots of emails where people disagree with him, much like callers on WFAN.  They let them have their peace.  No caller than tells the “Mad Dog” that the previous caller is wrong about “Mad Dog”, which makes the other caller call back.

Anyway, let’s err on the side of caution, and presume that the discussion happening is face-to-face. 

Resuming firing…

So Jeter’s not a real .340 hitter.  He’s a .315 hitter.  Against Verlander, he’s still a pretty good hitter, probably .300 or so.

Lets not get blinded by Verlander’s velocity.  His BA allowed (.266) is just a little better than the league.  He strikes out barely over 6 per game, and the Yankees were quite able to get baserunners on against him.

I’ll have to watch the replay to see where they were playing Jeter.  Nobody’s commented on exactly where Inge was playing him.

Now I read the excellent chapter on the bunt, and I understand game theory, and reasons behind why even good hitters should bunt now and then.  But that should not make Jeter immune from criticism.  He bunts far more often than any comparable hitter that I know of.  Either he bunts too much, or most of the top hitters in the game aren’t bunting nearly enough.

Re: the quality of pitcher that Verlander is. Every batter on that team will be facing him. 

I don’t remember what MGL said about the run environment for bunting.  I’m pretty sure the breakeven rate goes down the lower the run environment. 

MGL’s comment #1 above therefore is misplaced.  We have a quality of hitter against a RHP, and we have a separate parameter to consider, and that is the run environment (which affects all hitters).

If Pedro in his heydey pulled everyone’s stats down 35%, I’m still comfortable saying that Jeter is .315, if I also say that A-Rod is .280, etc, *and* I say the run environment is 2.00 RPG.  That is, we care about the relative quality of hitter to the other hitters, whether you set the baseline to .260, 100, or Pedro’s average, *and* we care about the run environment.

Joe Sheehan says something stupid.  In other news, sky still blue and chickens are unable to fly.

Chickens can fly. Sort of. Just not very high or very far.

Just so we are clear, the relative value of Jeter to ARod is not static, of course.  They each have a unique skillset that can be leveraged.  In some run environment, Jeter would be superior, and in others ARod would be.  Calling someone “.315” is just a shorthand, like league average would be “100”.

My problem with the criticism of Sheehan here, that “it’s unfounded and has no basis in fact or evidence,” is that MGL uses the phrase “my guess is” three times. Ordinarily that’s fine, but if you’re taking a guy to task for a lack of supporting evidence or fact, you can’t just come back with more conjecture (largely) of your own. It’s just not fair.

According to fangraphs, Jeter’s BUH% was 36.4% (24/66) for 2002-06. He also had 36 sacrifices over the period. So I’m guessing he was successful 60/66?

For the record, there is a comment by Dave over at USSM stating:

“Dave Sheehan is an idiot.”

Just sayin’.

In the BTF entry linking to this blog, some fans are talking about the Yanks, and Cano and ARod specifically.

A couple of people are debating what kind of range Cano has.  Now, stop here.  Why?  Why are they debating, especially when one says he’s barely seen him?  I have dozens of Yankee fans who took the time to tell us how they look.

http://www.tangotiger.net/scouting/scoutResults2006_NYA.html

So, if you want to know, “how does Cano look out there”, go to the above link.  Yank fans think he’s an ordinary 2B.  It doesn’t matter what one single random fan thinks, or even you out there reading this.  Your opinion, on its own, is highly suspect.  Fans still think that Jeter is an average SS.  What is interesting is how far they flung ARod down this year. 

When you see forecasts based on UZR or other PBP metrics, it now becomes necessary to add a “skills-degraded” component.  Fans see ARod as having dropped terribly fielding-wise.  ARod now has no top-comp.  David Wright is just about his closest, and he’s not that close. 

In contrast, last year, ARod’s top comps had alot of SS (Tejada, Cabrera, Uribe, Gonzalez).  How the mighty have fallen.

As I state/imply in The Book, bunting/not bunting is a complicated manner.  Unfortunately, it is one of the few things that the “analysts” have completely bungled over the years.

Basically it involves the interaction of the speed/bunting ability of the batter and where the defense is playing VERSUS the expected hitting ability (and specific components) of the batter also given the position of the defense.

On top of that, because the run scoring distribution after the bunt is different than that of the non-bunt, even for the same RE, you have to consider the overall run environment in order to nail the WE for bunting or non-bunting.

On top of that, because the distribution of bases/outs also is different for the bunt/non-bunt, you have to consider the profiles of the following batters.

While it is indeed very complicated, you can use some very good rules of thumb, such as the following:

Unless the bunter is a decent bunter with decent speed, it is rarely correct to attempt a sac.  This is one of the most prevalent mistakes by managers.  The reason this is so is that without enough ROE’s and base hits, the sac bunt is almost never correct, no matter how “successful” (advance the runner with an out) you are.  We know this from the RE and WE charts, right?

And the reason why this is the area where managers make the most mistakes is that they consider it a resounding success to advance the runner regardless of how few the ROE’s and base hits.  As I say in The Book, EVERY manager will gladly accept an offer to advance the runner in exchange for an out (when he is going to bunt), yet we can use the WE charts to show that that almost always would be a terrible decision.

If the defense is playing completely back, almost any batter can attempt a sac bunt, even great hitters and sluggers, because there are so many extra ROE’s and singles.  There is still a requisite minimum level of bunting ability and speed though, of course.

Don’t forget (this is often overlooked) that when a good hitter attempts a bunt, he gets an added advantage over the poor hitter, in that a significant percentage of time, the count goes to two strikes and the batter has to swing away.  IOW, the 2-strike swinging is factored into the RE/WE of the bunt attempt, and obviously it is higher for good hitters than for poor ones.

With the infield playing way up, it is usually not correct to bunt, no matter how bad of a batter you are (unless you are a poor hitting pitcher) or how good of a bunter (and fast) you are.  In addition, you must make the defense “pay” for playing up by sometimes hitting away and you also must make the defense “pay” for playing back by having your sluggers bunt every once in a while (of course that is rarely going to happen just like sluggers rarely bunt when the IF plays a shift on them, even though they should).

Finally, almost all batters (other than the worst bunmters/slow runners) need to bunt some percentage of the time in order to force the defense into playing somewhere in between up and back.  This is how you use game theory to optimize your RE/WE in a bunt situation.

I can easily add 1 win onto a team’s season w/l simply by giving a few rules of thumb to managers.  And they are welcome to tweak and adjust those rules of thumb using their wisdom, experience, and scouting.  Actually all of those rules of thunb are in “The Book.”

BTW, Joe wrote me a nice e-mail thanking me for the “critique” and saying that he was “probably wrong” about that bunt, or something like that, although he still thinks that Jeter bunts too often.  As I said, Joe is a real nice guy and very reasonable, as far as I can tell.

Who is David Sheehan?

A 36.4 bunt hit % is a pretty decent percentage I think.  Most good/great bunters are around 40-45%, IIRC.  Of course, the more you attempt a bunt, the more that % should go down (just like with stealing), as you are bunting in “tougher” situations and you are forcing the third baseman to play in even more.

As far as whether Jeter is in fact bunting too much in sacrifice situations, that can easily be determined, within the bounds of sample error of course.  Simply look at the distribution of results after he does bunt and compare that to what he would do if he hit away (using a Markov model of course).  If it is anywhere close, then he is bunting around the correct perdentage of times.

Given that he is apparently a good bunter (36.4 is good, not great), and smart enough to realize that “bunting for a hit” (more or less) is probably better than simply “giving yourself up” in a sac situation (for good bunters at least), my guess is that he is NOT bunting too much in sac situations.  A good hitter and good bunter (and fast runner) should probably bunt around 25-50% of the time in a sac situation.  I doubt that Jeter bunts even that often.

Game theory is a really tricky concept as it applies to baseball strategies and it is hard to get your arms around.

Consider this, with regard to sac bunting and game theory:

If when the IF is playing completely back in a sac bunt situation (whether they are or are not in reality), a sac bunt by a particular batter is “better” (higher WE) than hitting away, which as I said, is true for most batters, good or bad, as long as they can bunt a little and are not slow as dirt, that batter MUST bunt some percentage of the time, assuming the defense are not complete idiots (e.g., they play in even when the batter NEVER bunts).

BTW, A-Rod’s defense really has degraded over the years (not unexpected, although we don’t “expect” more than 1-2 runs per year in degradation).  Of course, it could be that he was never as good as his earlier UZR’s (or even observation) suggested that he was.  Or somewhere in between.

2002 +12 (SS)
2003 0 (SS)
2004 +7 (3B)
2005 -5 (3B)
2006 -9 (3B)

His projection at 3B is now in the “red.” Of course he is still better than Jeter, according to UZR.

Jeter’s career regular season SH per 534 PA is 4.4.  In the post-season, in 534 PA, he’s had 8.

Other semi-random players’ bunt hit % (2002-2006):
48% Ichiro (29/61)
43% Lofton (38/88)
39% Pierre (128/332) !!! Sure bunts alot!
38% A gonzalez (17/45)
36% Jeter (24/66)
36% Reyes (27/75)
35% Damon (17/48)
33% Endy (40/120)
33% Podsednik (43/132)
33% Castillo (38/115)
31% Crisp (34/110)
29% Crawford (21/72)
26% Vizquel (28/108)
25% Figgins (25/101)
23% Vizquel (25/107)

This is not a comprehensive list, but it seems to me that the league average would likely be in the low 30s, and the range would be 20% to 40%.  So, Jeter is likely one of the best bunters in the league.  We already know he’s one of the best baserunners, and a great percentage basestealer (career 80%, 34/39 this year).  He’s probably well-built, physically, mentally to be a good bunter.  He just happens to be well-built to be a great hitter too.

Ichiro is really the tough one to figure out, as to how often he should bunt.  He’s got a 48% success rate, which means it’s “too high”, meaning he doesn’t take enough chances.  But, because he’s such a good hitter overall, it needs to be rather high.

So, the bunt success rates should actually be in the same order of a player’s wOBA.

If we use this chart here:
http://www.tangotiger.net/RE9902event.html

And assume all “bunt for a hit” occur with bases empty, we see the run value of a single with 0 outs is +.39, while the run value of the out is -.26 runs.  So, the breakeven point is 40%.  With 1 out, the breakeven point is also 40%.  With 2 outs, the breakeven point is almost 50%.

However, that’s for a league average hitter.  Say you have a poor hitter, someone who is -.03 runs per PA with bases empty?  If you get 35% bunt singles, and 65% outs, the run value of the bunt is -.03 runs.  On the other hand, if you have a great hitter, say one who is +.03 runs per PA with bases empty, the breakeven point is 45%.

So, for the Ichiro/Jeters of the world, they need to be successful 45% of the time.  Ichiro, in this respect, is probably much smarter than Jeter.

Don’t forget game theory with respect to bunting for a hit!  Most players should probably be around the BE point, otherwise the third baseman is probably not playing in enough.  One reason their non-bunt averages are as high as they are is that they force the third baseman to play in.  For most batters, the third baseman should be playing such that it does not matter whether the batter bunts or not (and he should be at the BE point with respect to his bunt hit %) and the batter must bunt a percentage of time such that it does not matter where the third baseman plays!

Dave Sheehan may exist somewhere as a human being, but here he is a typo. Obviously, I meant Joe Sheehan. Here’s the USSM comment, OK?

*snip*
217. Dave said:
October 2nd, 2006 at 4:51 pm

Joe Sheehan is an idiot.
*snip*

Click the link and scroll down to comment #217, if you want to look it up yourself. Happy?

I am not commenting about the DC comment on his blog, just about statements “out of context” in general.

People, even smart ones, and this is especially salient in politics and the media, do not realize how much context can change the meaning of a statement or situation, even when it is not evident at first glance.

Here is a fictitious example:

Here are the facts:

Media (and Democrats) reports that a CIA person walked into a meeting of the Bush administration shortly before 9-11, and told them that they have credible (in their opinion) evidence that there is going to be an attack in/on the U.S. sometime soon.  Bush administration does virtually nothing about it and it even appears thatr they all but ignore the warning.

Reaction:

Wow, the Bush administration must be incompetent, bordering on reckless, right?

Let’s think about that. Unless they are incredibly stupid, like IQ of 85 stupid, not just “stupid” in the sense of “This is a stupid administration and President,” or they are in cahoots with Al Queda, there must be a reasonable explantion.

Remember that this is fictitious, but here is the extenuating and mitigating circumstance:

It turns out that the CIA comes into these meetings on a regular basis with the same kind of warning and that up until now, they have never been correct.  In fact, this is the 43rd such “warning” in the last 2 years, and while the administration does certainly “look into” this warrning as they did all the other ones, and does take them all seriously, it makes no sense to do any more than that, given the history of these warnings.

Context, context, context!

While I don’t think very highly of Joe Sheehan, MGL’s right, context is important.  That quote is in response to someone asking me what I think about Joe’s following comment in his last BP chat:

“Joe Sheehan: If you’d rather have Adrian Beltre and his contract rather than Pat Burrell’s and his, you’re too far gone to mention. Beltre has been awful, while Burrell is productive, just not as much as Phillies fans want him to be. The Phillies would be helped if they’d bat him between Utley and Howard, instead of giving away the platoon advantage late in close games.

Beltre is one of the worst FA contracts in recent memory, and I said so at the time.” (emphasis mine)

This comment is classic Sheehan; simultaneously ignorant and condescending, concluded with a ridiculous statement that can’t be backed up with any kind of evidence to support it.  Joe characterizes a totally defensible position as “being too far gone to mention”, because he’s made up his mind on the issue long ago, and he’s not interested in revisiting one of his favorite talking points. 

He’s not an idiot in the “unable to comprehend basic knowledge” kind of way, but his combination of ignorance and arrogance are enough to classify him as such in my mind. 

And that’s enough from me about Joe Sheehan.  I won’t waste any more of Tango’s bandwidth on such a silly issue.

**And that’s enough from me about Joe Sheehan. I won’t waste any more of Tango’s bandwidth on such a silly issue.**

And the crowd roared!

"This comment is classic Sheehan; simultaneously ignorant and condescending, concluded with a ridiculous statement that can’t be backed up with any kind of evidence to support it.”

What a very strange thing to say about a columnist.  Seems likely he could back it up.  So I checked.  Sheehan, BP, 12/17/04:

“....despite the convictions of those around me that the deal is a bargain in this market, I’m not convinced that it’s going to work out well for the Mariners.

Beltre is being paid as if his 2004 performance represents a new established level; I don’t think that’s a realistic assessment. While not minimizing what he did, there was no change in his walk rate, not much change in his strike-zone judgment, and he continued to show a loss of speed. He’s 26, but he has already lost almost all of the speed he came into the league with. What he did last year was add 40 singles and 25 home runs to what he normally does. I don’t think all of that is real; I expect him to level off at around .290/.340/.490, a line that will look a bit worse thanks to Safeco Field. If his defensive improvement is real, he can be a five-win player over the life of the deal.

There’s almost no way that this contract isn’t going to end up disappointing Mariners fans. The Mariners are paying Beltre to have ‘04 over and over again, and that’s not going to happen. Park factors will make his numbers look even worse, adding to the perception of failure. Come 2007 and 2008, the Mariners will be paying $27 million a year to two corner infielders, which is a hard way to build a team unless you’re George Steinbrenner. Unless they can develop a lot of inexpensive talent at premium positions, the Mariners will have a hard time assembling a complete team.

Beltre has been overvalued based on one big year at the right time, and the Mariners find themselves stuck with the winner’s curse. Given the competition in the division, I would be surprised if Beltre made the postseason as a Mariner, or finished out his contract in the Pacific Northwest.”

Beltre is being paid as if his 2004 performance represents a new established level...

No, he’s not.  The Mariners didn’t expect him to repeat his ‘04 performance, and if he did, he’d be the biggest bargain in baseball.  $13 million a year is not the going rate for an 26-year-old MVP candidate.  His 2004 season was worth something like $22 or $23 million.  The M’s weren’t expecting anything close to that, and they aren’t paying him like they were. 

He’s 26, but he has already lost almost all of the speed he came into the league with.

I disagree.  When he wasn’t hitting in April and May, he was running the bases like a madman in order to try to produce some value.  He was 9 for 9 on steals the first two months of the year.  He stopped running when he started hitting again. 

I expect him to level off at around .290/.340/.490, a line that will look a bit worse thanks to Safeco Field. If his defensive improvement is real, he can be a five-win player over the life of the deal.

Yea, that’s the same neighborhood that I’m thinking.  I’d probably go .280/.330/.475, but basically the same player.  Depending on his defensive performances and his overall streakiness, I’d expect him to be between a 4-7 win player for the rest of the contract.

Based on the $2-$2.5 million per marginal win number that is commonly accepted, that means his actual value, as we see it, is somewhere in the neighborhood of $8-$14 million or $10-$17.5 million, depending on which marginal win number you want to use.  In a Bad Beltre year, he’s overpaid by about $5 million.  In a Good Beltre year (assuming ‘04 was Fluke Beltre, never to be seen again), he’s underpaid by about $3 million.  There’s certainly no way the contract is “one of the worst in recent history.”

I’d argue that you’d have a hard time proving that Eric Chavez is demonstrably better than Adrian Beltre, yet I don’t think I’ve ever seen an article written decrying the “albatross” that is the 6 year, $66 million deal Beane gave to Chavez. 

Unless they can develop a lot of inexpensive talent at premium positions, the Mariners will have a hard time assembling a complete team.

I’d suggest that Yuniesky Betancourt, Jose Lopez, Felix Hernandez, J.J. Putz, and Rafael Soriano qualify as five of the best inexpensive players at their positions.  You could easily argue for the inclusion of Chris Snelling, George Sherrill, Mark Lowe, and potentially Adam Jones and Jeff Clement as well.

Beltre has been overvalued based on one big year at the right time, and the Mariners find themselves stuck with the winner’s curse. Given the competition in the division, I would be surprised if Beltre made the postseason as a Mariner, or finished out his contract in the Pacific Northwest.”

I doubt I’d trade the Mariners 25 man roster for any other 25 man roster in the division.  There’s warts, to be sure, but the basis of a very good baseball team is in place.  Adrian Beltre isn’t holding the Mariners back from winning the division.  He’s overpaid by a couple million per season, but paying $13 million for a $10 million third baseman who plays every day isn’t going to cost anyone a playoff berth.

Interesting, I had Beltre projected for this year at +8 in offensive lwts and +9 in UZR, for a total of +17.  His offensive lwts was actually 6.4 this year (a little higher than an average 3B) and +12 in UZR, for a total of +18.  His baserunning is a tad negative (due to GDP), so total is around +14 predicted and +17 actual for 2006.  2007 will be a little worse of course, by around 2 runs.

At +15 to +18, a third baseman is around 16 runs above an average third baseman, which is around 3.5 wins above a replacement third baseman.  These numbers are all per 150 games of course.

Using David’s 2 to 2.5 mil per win, that makes him worth in 06 and going into 06, around 7-9 mil.

Given that his 06 performance was almost exactly his 06 Slwts projection, I don’t think any of these numbers can be argued with.

So I think that David’s 10 mil is a little too high, but this is nowhere near the worst FA contract in recent years.  It is and was definitely a bad contract, especially for a team that cannot overpay for talent like the Yankees (I assume, but I don’t know enough about the M’s finances to know). Contracts like Konerko’s are infinitely worse.

Sexson was projected at -6 in UZR and was in fact -7.  His offensive lwts was projected at +26 and was +18.  So again, not too bad a projection (as much as I hate using the actual results of a couple of players to validate a projection).

His baserunning is worth another -2 runs, which puts him at a total 06 projection of +18, which is only 7 runs above an average first baseman and 2.5 wins above replacement.  That is worth 5-6 mil as a FA.  How much is he paid?  11.5 mil I think in 06 and 14 mil in 07 and 08.  Now that is a BAD contract!  A horrible one!  Atrocious!

As I have stated for a long time, slugging first basemen are way overpaid.  Most teams would be better off putting a replacement payer at first (and there is evidence that replacement level at first is one of the highest replacement levels of all the positions) and spending their money on other positions…

Also, just for fun, here’s a list of the current major league regular third baseman who have more than six years of service time, so they’re being paid what someone believed their “market value” was at the time of their contract. 

Alex Rodriguez, $25.2 million per season
Adrian Beltre, $13 million
Chipper Jones, $12.5 million
Scott Rolen, $11.25 million
Troy Glaus, $11.25 million
Eric Chavez, $11 million
Aramis Ramirez, $10.5 million (and opting out of the deal to get more money)
Mike Lowell, $8 million
Corey Koskie, $6 million

Beltre is in the Ramirez/Chavez/Glaus group of non-elite third baseman who are still valuable players.  The going rate for those guys is clearly $11-$13 million per season on the open market.  Beltre’s obviously the highest paid of that group, but he’s not so egregiously overpaid compared to his peers that Sheehan’s characterization of the contract as “one of the worst in recent history” is anything close to being true. 

That’s the statement that I was referring to that he couldn’t defend, not the idea that he had claimed it was a bad contract up front.  I know Sheehan hated the contract from day one, and he’ll hate the contract until it expires, no matter how well Adrian Beltre plays.

2007 will be a little worse of course, by around 2 runs.

Selective Sample Alert! Selective Sample Alert!

I know you’re going to hate this, MGL, but just for kicks:

Beltre, April-May: .230/.296/.300, 200 AB
Beltre, rest of year: .284/.340/.543, 420 AB

He was so godawful in April and May that his season numbers disguise the fact that he was the best third baseman in the AL the last four months of the season.  I’m not suggesting his June-September performance is his true talent level, but I think he’ll be hard pressed to have another month as unbelievably awful as he was in April. 

So I think that David’s 10 mil is a little too high, but this is nowhere near the worst FA contract in recent years.  It is and was definitely a bad contract, especially for a team that cannot overpay for talent like the Yankees (I assume, but I don’t know enough about the M’s finances to know). Contracts like Konerko’s are infinitely worse.

Right.  No one’s arguing that Beltre has earned his paycheck the first two years of the deal.  But I can name 15 contracts off the top of my head that are much, much worse.  The Tigers are about to carry Magglio Ordonez’s $15 million carcass into the ALCS, for instance.

His baserunning is worth another -2 runs, which puts him at a total 06 projection of +18, which is only 7 runs above an average first baseman and 2.5 wins above replacement.  That is worth 5-6 mil as a FA.  How much is he paid?  11.5 mil I think in 06 and 14 mil in 07 and 08.  Now that is a BAD contract!  A horrible one!  Atrocious!

Totally agree.  The M’s owe Sexson $14 mil each of the next two years.  I’ve done several posts at USSM in the last month advocating the team deal him just to clear the money off the payroll.

Beltre, April-May: .230/.296/.300, 200 AB
Beltre, rest of year: .284/.340/.543, 420 AB

He was so godawful in April and May that his season numbers disguise the fact that he was the best third baseman in the AL the last four months of the season.  I’m not suggesting his June-September performance is his true talent level, but I think he’ll be hard pressed to have another month as unbelievably awful as he was in April.

Come on!  I just ate (a late) dinner!

Let me see if I understand David’s position.  Saying that Beltre’s contract is ONE of the worst in recent memory is “a ridiculous statement,” one “that can’t be backed up with any kind of evidence.”

MGL has Beltre worth 3.5 wins or about $8m, while the Mariners are paying him $13M, so they’re giving away $15M over the next three seasons if he does what we expect (plus the 2005 shortfall).  David points out—to support his case, I think—that Beltre is paid more than Rolen, Chipper, Glaus, Chavez, and Ramirez. 

Sheehan probably overstated his case, but it’s hardly “ridiculous.” I think most of us would be pretty happy if this were the dumbest thing we’d ever written....

MGL has Beltre worth 3.5 wins or about $8m, while the Mariners are paying him $13M, so they’re giving away $15M over the next three seasons if he does what we expect (plus the 2005 shortfall).  David points out—to support his case, I think—that Beltre is paid more than Rolen, Chipper, Glaus, Chavez, and Ramirez.

3.5x2.5 = 8.75.  So, really, if you accept MGL’s projection, Beltre’s a $9 million player going into his age 28, 29, and 30 seasons.  I’d suggest that 3.5 wins is the low-end of what to expect from Adrian the next three years, and I’d peg him as closer to a $10 million player. 

And unless you want to pick nits, he’s not paid substantially more than Glaus, Chavez, or Ramirez.  His paycheck is essentially in line with theirs, and he’s a comparable player.  Considering he’s the youngest of the group and by far the most healthy of the trio, I’d argue he’s also the best bet of the four going forward, and I wouldn’t trade him straight up for any of those three. 

Sheehan probably overstated his case, but it’s hardly “ridiculous.” I think most of us would be pretty happy if this were the dumbest thing we’d ever written....

That’s far from the dumbest thing Joe’s ever written, but the comment that I took issue was that if you didn’t agree with Joe on an issue that I see a very strong case against that “you are too far gone to mention.”

Why are my estimates of a player’s value (projection of course) akways the “lowest” that someone will accept (Beltre, Jeter, Konerko, etc.)?  As far as I know, my Slwts projections are the most accurate projections known to man.  Seriously.  Please don’t say that my projections are low or high without at least a modicum or an iota or even a scoche of evidence that they are not as accurate as one can possibly get.  Some players are extremely easy to project.  Beltre is one of those.  In fact, almost any veteran is easy to project.  You really can’t do any better than to say that Beltre projects to be 3.5.  Why is that a “low end?” Because otherwise your argument about his contract not being ridiculous holds less water?  Because you “think” that he is better than that?  You have a projection methodology that is better than mine?  He “looks” like a batter player than that?  A lot of people “think” he is better than that?  At least give me a respected projection (e.g, Pecota) that is substabtially higher than mine.  One that includes a defensive projection based on PBP data.  While I have respect for Pecota’s offensive projections, and in fact, they may be better than mine, you can only use their offensive projections - their defensive ones are not particularly good, and you can’t use their silly “replacement level” which is like 40 runs below average, offense and defense combined.

Beltre, from 2002-2006, was +2 wins cumulative in WPA (he was neutral in clutch).  Essentially, a shade above league average hitter.

He’s a great fielder of course, and that’s worth about +1.5 wins.  3B is a “neutral” position, so we don’t need further adjustments.  So, Beltre is +2 wins per seaons.

***

Chavez in the same time period was +7 wins hitting (and also neutral in clutch). 

He’s likely a bit better fielder than Beltre, let’s say +2 wins.  So, +1.5 for hitting and +2 for fielding, and he’s +3.5 wins.

***

RElative to replacement, Beltre is +4 and Chavez is +5.5, making Beltre 10 million a season, and Chavez 13 million a season.  They are in the same ballpark, though Chavez is a little higher.

I think Chavez signed 66/6, but that included pre-FA years I believe.

Within the context of a FA contract, you’d probably want to multiply by 3.5 instead of 2.5, putting Beltre at 14 million a year in “market value”, as opposed to “intrinsic value”.

***

The Beltre contract was a typical FA contract, meaning it was a bad move to begin with.  The same would apply to just about every 40+ million$ contract signed.  It definitely wasn’t a great contract, but neither was it a horrible one.

Crisitan Guzman on the other hand…

Some players are extremely easy to project.  Beltre is one of those.

I disagree. I doubt you’ll find this convincing, but that’s okay.

I don’t believe that all player performance over a certain time period is indicative of the true talent level of a particular player.  I believe MLB has underachievers and overachievers, guys whose past performance is some percentage greater or less than what they actually should be achieving, based on their baseball skills.

Adrian Beltre, in my opinion, is an underachiever, much like Javier Vazquez, Freddy Garcia, Eric Chavez, Hank Blalock, Corey Patterson, Austin Kearns, and Travis Lee, among others.  They have more talent than their performances indicate, and for whatever reason (work ethic is the likely cause, in my opinion), they have yet to live up to the inherent abilities they have.

My view is that these underachievers represent a sample of players where the spread of projections will fail to incorporate the correct possibility that the player will have some kind of epiphany and become the player that he could be. 

I don’t have a thorough study to back this up, and I’m completely willing to agree that slwts+uzr is a very effective projection system for a great majority of major leaguers.  Even you are aware of its limitations, however, and I believe this kind of player is one of them.

PECOTA backs me up on this to some extent.  Even coming off his poor 2005 season, it had Beltre projected at 29.8 VORP (again, offense only, no defensive projection included) with a .282 EqA for 2006, and it projected absolutely no decline from that performance over the next four years. 

PECOTA’s projected EqA’s for Beltre, prior to the season, were .282, .284, .284., .286, and .284 from 2006 through 2010.  Obviously, I can’t give you its slwts projection, since I don’t know how EqA or VORP convert to slwts, but a .285ish EqA from a great defensive third baseman who is one of the most durable players in the league is a borderline all-star, and worth significantly more than 3.5 wins over replacement. 

PECOTA’s picking up on some of the talent that Beltre hasn’t put to use in his career thus far.  It’s finding other comparable players, such as Brooks Robinson, who had tremendous physical abilities, underachieved at the beginning of their careers, and then became stars in their late 20s and early 30s. 

I’m not saying Adrian Beltre is going to outperform his slwts+uzr.  I’m saying that I believe the spread of possibilities for a player with his abilities is wider than the slwts+uzr projection will give him credit for.  I think the fact that he has real potential to be a +6-7 win player next year makes the +3.5 median projection a little low.

My projections and any other projection “system” other than Pecota, as far as I am aware, does not give any “spread of possibilities.”

Other than that, I can’t really argue with your comments.

From what I can gather, you think that certain players’ projections are higher than the typical “Marcel-like” projection (and I assume there are a set of players that would be lower, since they have to balance), you think that one (someone) can identify these players, and you think that Beltre is one of those players.

I cannot argue or even discuss that theory since you have no edidence that it is true (as far as I aware), and I have no evidence that it is not true (although I don’t think I have that burden).

You say that you don’t know what EQA converts to in terms of Slwts (and neither do I), yet you say that it is worth significantly more than 3.5 wins above replacement.  Well, if you don’t know how the EQA translates into runs above average or replacement, how can you know or suspect that it is significantly more than 3.5 wins?

Well, Tango seems to think that Beltre is worth 4 wins above replacement, but I think he has his defensive value for Beltre (and Chavez) way too high. He says that 3B is a neutral position, so there is no extra defensive value there.

He says that Beltre is +15 runs and Chavez is +20.  Almost no one projects that high in defense because of regression, and certainly not at 3B because there are so few opps as compared to say 2B, SS, and CF.  Beltre’s UZR was 20, 12, 24, and 3 over the last 4 years, which projects to a +10, after weighting, age adjusting, and regressing.  In fact, his 06 UZR was +12.

Chavez actually had 11, -3, 4, and 6, which projects to a +4, so I don’t know where he gets the idea that Chavez is a much better defender or even a better defender.  This year he was a -4, granted with leg injuries.

Tango also uses 2 wins below average as replacement.  I think that is a tad too high and should be closer to 18 runs (per 150 games) or 1.6 wins in the AL and 1.8 wins in the NL.

To be honest, it doesn’t really matter to a team what the “spread” of a player’s projection is.  The mean or median (I think it is about the same) is really the only thing that matters.

If you want to argue that Beltre’s mean projection is substantially higher than 3.5 wins (per 150), fine.  If you want to argue about the “confidence interval” around that, there is no argument (at least with me), because I don’t know what that interval is and I don’t care what it is.

Now, as always, and I don’t mean this with any hostility or disrepsect - only that I often willing to put my money where my mouth is - if you think that Beltre’s expected performance next year is substantially higher than 3.5 wins (I assume that you mean higher than 4.0 wins), I’ll gladly, and I mean gladly, wager any amount you want, under 4.0 and you can take over 4.0, and of course, someone will have to verify the UZR, the baserunning, and the park adjustments, since otherwise you will have to take my word for it.

In 5 years of making these offers, I have yet for someone to take me up on them.  Now, I understand that most people don’t like to bet or bet on things like this, but do you think it might have ANYTHING to do with the fact that they are not so sure that they are smarter than I am (with repsect to these things)?

Just to add one thing.  Anyone can use anthing they want for replacement level and it doesn’t change their projection or the value of a player.  So anytime there is a “discussion” or disagreement about a player projection, it should ALWAYS be based on runs or wins above AVERAGE.  In this case, I am arguing that Beltre’s expected offensive, defnesive, and baserunning performance next year, park and opponent adjusted, is around 1.7 wins or 19 runs above AVERAGE (actually the average third baseman, which is around the same as the average player).  Now, 10 runs of that is in defense and -1 in baserunning, so I’ll even go 10 runs on offense above an average third baseman or an average major league player in the same league.  Your choice.  Again, park and opponent (for the pitchers he faces) adjusted.  I am assuming that you think that 10 runs is way too low.  I am assuming that you think it is more like 20 runs.  So we’ll just use 15 runs as the “over-under” if that is OK with you.

So just a throw a $ figure out there and consider it a deal.  Tango can vouch for me.

MGL, your regression is towards zero as your population.  However, we know something more about Beltre and Chavez (and Rolen) and that they are wonderful 3B.  (Your claim about 3B opps, while true, belies Scott Rolen’s UZR.  Check that out!) Even if Chavez is not wonderful, and you are in the minority, a group of Beltre, Rolen, Chavez, selected based on scouting information, forms a distinct population from one that includes a Butch Hobson.  As you yourself have said many times, if we know, or think we know, that Chavez, Beltre, and Rolen are distinct from Butch, then we need to regress toward that.

Going back to Chavez, some A’s fans are calling his season at 3B perhaps his best season ever.  You give no weight to that, and I give it tremendous weight.  We’ll agree to disagree.

***

I use 2 wins per 162 games, you like to use 1.6 or 1.8 per 150.  So, that’s the same thing.

In any case, if you want to get real technical about it, we should report as per 140 or per 145, since the Marcel forecast will top out at around there.  Again, anyone who doesn’t believe me can verify that themselves. The basic equation for G is whatever you think it is based on recent history, take 60% of that, and add 40-50 games.  So, even if you have a guy who you think will play 162 games means you will forecast him for 140-odd games.

As a convenience, I set all my stats as per 162 games, or per 600 PA (140 games), as the mood strikes me.

From what I can gather, you think that certain players’ projections are higher than the typical “Marcel-like” projection (and I assume there are a set of players that would be lower, since they have to balance), you think that one (someone) can identify these players, and you think that Beltre is one of those players.

Yea, basically.  I think there are varying degrees of potential among players.  In my opinion, Adrian Beltre has a much larger span of possible performances going forward than David Eckstein does.  And yes, I think these players can be identified through scouting. 

You say that you don’t know what EQA converts to in terms of Slwts (and neither do I), yet you say that it is worth significantly more than 3.5 wins above replacement.  Well, if you don’t know how the EQA translates into runs above average or replacement, how can you know or suspect that it is significantly more than 3.5 wins?

Because I understand how EqA is calibrated in terms of player performance, and I’m able to come up with a rough estimate in my head of what the slwts translation should be in the ballpark of. 

Since a .260 EqA is set to league average, a .285 EqA is a 10% better than average offensive performance.  Using any kind of reasonable replacement level, 10% above average + good defense + good health = more 3.5 wins above average. 

To be honest, it doesn’t really matter to a team what the “spread” of a player’s projection is.  The mean or median (I think it is about the same) is really the only thing that matters.

I disagree. The varying possibilities are of significant usefulness, I believe.  Using Eckstein and Beltre again as examples, and pulling these percentages out of thin air, as this is just to make a point, not to try to compare the two players value:

I’m guessing Eckstein’s projection is going to put him at +1 win over replacement level, or something in that neighborhood.  His spread of possible performances would be something like this:

-1 to 0 wins: 10%
0 to +1 wins: 40%
+1 to +2 wins: 40%
+2 to +3 wins: 10%

Meanwhile, Adrian Beltre’s spread of possible performances would look more like this:

0 to +1 wins: 5%
+1 to +2 wins: 10%
+2 to +3 wins: 25%
+3 to +4 wins: 25%
+4 to +5 wins: 20%
+5 to +6 wins: 10%
+6 to +7 wins: 5%

Beltre’s median projection of +3.5 wins will give us a good general idea of where he’s likely to perform, but the fact that there’s real potential to perform at an MVP level enhances his actual value, in my opinion.  A +3.5 win player who has a 15% chance (or whatever) to be a +5 player is a better buy, in my opinion, than a +3.5 win player who has a 5% chance to be a +5 player. 

This is called a lot of things; upside, potential, ceiling.  Whatever you want to refer to it as, it matters.  Players don’t have an equal spread of potential, and given similar projections for a player, a team is better off with the higher potential player than a guy who is already performing near the upper end of his physical capabilities. 

So just a throw a $ figure out there and consider it a deal.  Tango can vouch for me.

Even if I took the bet, Beltre posted a +4.1 season in 2007, and I “won”, it wouldn’t validate my point, because I’m not making an over/under argument. 

If we wanted to test this hypothesis, we’d have to do something more like let me select, say, 30-40 players that I believe have a wide range of performance possibilities, figure out your 2007 projection for them, and then see if my group of scouted players has a wider range of performances (by using std dev or some similar measure) next year than the league average. 

If you’re willing to do something along those lines, I’m in.

Since a .260 EqA is set to league average, a .285 EqA is a 10% better than average offensive performance.  Using any kind of reasonable replacement level, 10% above average + good defense + good health = more 3.5 wins above average replacement.

Dave’s bet of choosing 30 players makes more sense, and that’s exactly the test I did when I took 30 hard-to-forecast players:
http://www.tangotiger.net/forecastFinal2.html

In essence, did fans know more intrinsic about these players than the forecasting systems.  Answer: individually, they were terrible, but as a group they were fanstastic.

Now, Dave is talking about the same thing, but rather the typical fan, he’d rather have a “professional scouting” fan.  I suspect such a fan might do as well as a group of average Tangotiger.net fans, but a group of Daves would do better.  However, would such a group also surpass a forecasting system?

That’s what’s on the table.  So, what superfan wants to take on MGL?  I’ll come up with the names of players, and MGL and the superfans will offer their forecasts.

As for converting a .285 EqA to runs, I’m sure there’s a complex process to do it.  But, EqA seems to scale to BA.  Since wOBA scales to OBP, and I know how to convert that to runs, let me try the same with EqA.

A .285 EqA on a .260 lgBA would be a .362 OBP on a .330 lgOBP.  32 bases in OBP or wOBA is 28 points in runs.  So, +.028 runs per PA.  Give him 600 PA, and that’s +17 runs above average, or +1.5 wins above average.  I guess.  I’m sure the EqA afficianados will chime in if my shortcut works or not.

EQA = (Runs/Out/5)^.4

Or R/O = EQA^2.5*5

So a .285 EQA is .217 r/o, where I think Clay defines an average league as .260 or .172 r/o.  If I we go with Tango’s .362 OBA, then in 600 PA he makes about 383 outs, so (.217-.172)*383 = +17 runs

Thanks for that Patiot. 

Having that information handy, I ran through the runs above average, per 600 PA for levels of EqA from .200 to .350, comparing Clay’s method to my shortcut:

EqA Tango Clay
0.200 -40 -37
0.210 -33 -31
0.220 -27 -25
0.230 -20 -19
0.240 -13 -13
0.250 -7 -7
0.260 0 0
0.270 7 7
0.280 13 14
0.290 20 21
0.300 27 28
0.310 33 35
0.320 40 42
0.330 46 49
0.340 53 56
0.350 60 63

That’s pretty much the same thing, isn’t it?  Unless you are looking at Barry Bonds or a pitcher, the shortcut method works.

So, the shortcut method is:
(EqA - .260) * 1.1 * PA

Actually, I get a correlation of r=0.999, if I make it:

(EqA - .260) * 1.16 * PA

with a restriction of the EqA at .200 to .350.

An r=.995, if the EqA is .100 to .500, and the shortcut is:

(EqA - .260) * 1.09 * PA

So, use whatever you want, but there’s no need to go to exponents.  EqA is for all intents and purposes a purely linear run equation.  And, to that effect, there’s no reason to use it at all then, since, thanks to Ruane at Retrosheet, and David Smyth with BaseRuns, we can come up with the necessary Linear Run estimator.

Beltre’s median projection of +3.5 wins will give us a good general idea of where he’s likely to perform, but the fact that there’s real potential to perform at an MVP level enhances his actual value, in my opinion.  A +3.5 win player who has a 15% chance (or whatever) to be a +5 player is a better buy, in my opinion, than a +3.5 win player who has a 5% chance to be a +5 player.

In order for a +3.5 player to have a 15% chance to be a +5 player, he is also more likely to have a bigger chance to be a less than +3.5 player.

For example, very simplified:

player 1:

+2 : 10%
+3 : 40%
+4 : 40%
+5 : 10%

player 2:

+0 : 5%
+1 : 10%
+2 : 15%
+3 : 20%
+4 : 20%
+5 : 15%
+6 : 10%
+7 : 5%

Dave suggests that he’d rather have the “upside” of the second player, even though he is also more likely to play worse, than the first, more consistent player.

I don’t see why it matters that there’s a wider range of possibilities at all, especially for the purposes of a single-year bet. When you play roulette, you can gamble on a third, or you can bet red, but in the end, you’re always losing money at the same rate. The only argument might be that if the player with more upside DOES figure it out and do well, that will change his projections upward from that point forward. (but at the same time, the reverse is true as well.)

I’m going with MGL on this one.

Let’s take Andy’s example one step further.  Many people (not me) believe that the marginal $/marginal win should rise as the marginal win rises. 

Let’s take a real exaggerated position, and say that the marginal $/marginal win is equal to an average of marginal wins times 1 million.  So, if you are +2 wins, each win is worth 2 million $.  If you are +5 wins, each win is worth 5 million$.

If we apply this to Andy’s two players, the consistent player would earn 12.9 million$, while the guy with the high upside and low downside would be 15.5 million$. 

In order for these two guys to be equals using this spending pattern, the first consistent guy at +3.5 wins would be equal to the inconsistent guy at +3.1 wins.

And, this is an exagerrated look, I think.  If someone wants to argue that +3.5 wins, because of the upside, should be paid as much as a guy with +3.6 or +3.7 wins, who is consistent, ok, maybe.  But, I don’t even think it’s that much.

It seems that there are certain seasons when a team “comes together,” and exceeds expectations, when all the players have career years. Not everyone can pay for consistent superstar talent like the Yankees. Perhaps in order to compete against them, you have to take some of these higher-upside but more inconsistent players and hope everyone has a good year at the same time: the “pray for luck” strategy…

love this blog, btw, tango. quickly becoming my favorite. (but have a ways to go to catch fleshbot )

If we really can identify players with wider ranges of possible performance, it depends what team you have as to who you take.

Beltre would be more likely to lead a below average team like the Mariners to an unexpected playoff berth.  A contender like the A’s or Angels would prefer to fill a hole with a Mr. Consistency (if he truly exists).

I think the scenario that David really had in mind is that Beltre has more potential to be +5 wins than some other +3.5 player does, but NOT that he also has more chance of being a zero to 1 player.  The theory is that Beltre is underperforming his inate physical ability, and therefore could do much better than expected, while the other guy is average or even “maxing out” his physical talents.  There are two problems with that:
1) if Beltre does have more upside, then we’re really saying he’s NOT a +3.5 player.  That value should represent his expected value, including the upside;
2) we have no evidence that Beltre has more upside potential than other players with a similar track record, and to the extent some players’ upside potential is greather than their past performance indicates, I’d have to think the vast majority are much younger than 27 years old. 

* * *

If some players were truly just less consistent in the manner Andy and Tango are talking about (more upside and more downside), then I think teams would pay them LESS, not more.  Stocks and bonds are a good analogy:  stocks have to offer investors a risk premium to accept volatility.  A $15M player who gives you 1 WAR is a disaster few teams can afford, and they will pay to avoid it. 

My theory is this is why pitchers earn about 40% of MLB payroll when they actually deliver 45-50% of the win value—their individual performance is much more volatile than hitters’. 

* * *

“Many people (not me) believe that the marginal $/marginal win should rise as the marginal win rises.”

I don’t see how you can possibly take this position.  The wins we care about most are those between 81 and, let’s say, 96.  That’s what makes teams a success and gets them into the postseason.  Those wins also increase revenue far more than earlier wins, but leave that aside if you want to.  Just in pure baseball terms, those 15 wins matter the most. Truly, all wins are not created equal.

Now that means a team needs about 48 wins from approx 16 players making serious contributions, or 3 WAR each.  You could try to assemble a team of 16 3-win players, but in practice it’s impossible.  And injuries mean some won’t deliver.  To have confidence your team can reach the 96 wins, you MUST have some 4-5 win players, and having a 7-8 win player is even better.  So having some 4+ players is mathematically essential to fielding a winning team. And that makes a 6-win player worth more than 2 3-win players.

The key point is limited playing time.  Without that constraint, a team could hire 48 +1 players and make the playoffs, and all marginal wins would have the same value as Tango suggests.  But that’s not the world we live in.

I think the scenario that David really had in mind is that Beltre has more potential to be +5 wins than some other +3.5 player does, but NOT that he also has more chance of being a zero to 1 player.

Right, and I’m pointing out that that scenario is impossible. If Beltre and another player are both +3.5 players, and Beltre has more potential to be +5, he also necessarily has to have more potential to underperform. It’s simple algebra.

In true talent terms, what we want is to get to about 84-86 wins.  That a playoff team needs 90 or whatever wins is irrelevant, since part of that is timing.  So, we care about true talent.

So, we’re looking to get about +37 wins above replacement.  We have 8 regulars, 5 starters, and 2 relievers, to find that, or say 15 players.  The other 10 players are also above replacement, and say, as a group, they give you +2 wins.  That leaves me with needing +35 wins from my 15 regulars, at about +2.3 wins above replacement.  A team of regulars at pure +2 (average) or +3 (above average) fits the bill. 

The problem I have with paying say ARod + Cristian Guzman more than say Chavez + whoever makes this even is that it doesn’t make sense.  If I have a +7 and a +1, and I have a +4 and a +4, why would I pay these guys differently?

I understand at the team level, I’d want to pay more, depending if I’m in the sweet spot or not, but I don’t see how this can be reflected at the player level, unless you take the team into account.  It doesn’t necessarily follow that ARod at +7 should earn more per win than Chavez.

But regardless of whether a +7 player *should* be paid at a different $/w than a +4 player, you would expect, due to supply and demand, that the +7 player would earn more since there are fewer +7 players available than +4’s.

With that as a given, the question teams face typically is not so much “Should I pay for these four +4 players or should I pay for these two +7 players and two +1 players?” as it is “How can I maximize my payroll, given what’s available on the market?” Since there isn’t yearly free agency, teams are generally carrying over most of their roster, and their opportunities for improvement are very limited when they’ve already got most of the names pencilled in.

So the very high salaries for the highest FA are somewhat offset by the costs accrued in pursuing multiple FA or trying to improve through trade. Those strategies are pretty high-risk in that they can leave you having not made any upgrade or overpaying at the last minute (e.g. Magglio Ordonez). So if a GM has an opportunity to get an overpriced but not astronomical deal signed for a +7 player, the price tag is offset by not having to settle for nothing or overpay down the road. This effect would, I imagine, trickle down, so that it inflates the salaries of the best players more than the good players and then has no effect on the below average players.

Another angle might be trade value; if you acquire a big FA with an overpriced deal but no no-trade clause, they will tend to be way overvalued at the deadline. I don’t know that there’s any wisdom in acquiring marquee names with the intent to trade them, but it merits consideration.

The problems I have with Tango’s scenario are that:
1) it assumes you don’t carry a single below-avg player among your 15 regulars—that’s hard to ensure on a regular basis;
2) it says the team only aspires to be 5 wins above avg in true talent.  That means it will win 92+ games only 16% of the time.  I think a competitive team is looking to be at least a 90-win true talent team, if not more. 

Keeping in mind Tom M’s point that teams are committed to a bunch of players each year and have limited options to improve, I think it’s virtually impossible for most teams in most years to build a strong team without several 4+ win players.  So those players are worth more on a per-win basis.

Is a +8 player also worth more than two +4 players?  I’m not sure.  I would tend to think so given the flexibity it provides the team—allows them to gamble on promising rookie, or survice injuries, or carry a +1 player at a position in a year when no good values were available on FA market.

I’m late to this discussion, but…

While teams will generally (they have to I guess) pay an increasing premium on marginal wins because of supply and demand, that is completely different from whether those increased wins have increased value.  They do not I think and as someone mentioned there is a good argument that after a certain number, the value of a marginal win starts to decrease, assuming that value is proprtional to chances of making the playoffs.  And of course it completely depends on the team’s baseline.

So we are all in agreement that BP’s EQA Pecota for Beltre is +17 runs per around 600 PA, which is exactly my projection (3.5 wins above replacement, which is exactly 17 runs above average by my definition of replacement - for purposes of this discussions doesn’t matter what the definition of replacement is).  Whew!  I thought my projection may have been way too low!

Whether a team wants a player (and how much they are willing to pay) with a wide or narrow range for their projection interval is debatable and it might depend on a number of factors.  I think that no matter what the truth is, it is NOT going to matter much either way.  That is the important thing.  There are some things that are so close, that they are only good as tiebreakers (like 2 players with the same projection, but one may be a better clutch performer than the other).  I think this is one of those things.

There are exactly two ways that a player’s performance in any time period has an “interval” than we can construct a distribution around.  One, is simply the random variance around a certain mean. ALL players will have exactly the same interval in that regard.  I repeat.  ALL players will have exactly the same interval in that regard.  One caveat.  A player’s exact hitting profile (s,d,t,hr,bb,k) will change that interval a little, so ALL players will have ALMOST exactly the same interval in that regard.

The second and ONLY other source of a performance interval is the uncertainty around our projection.  Tango and I have stated this many times, but the MOST significant factor, by far and way, in THAT interval, is the effective (after discounting because of weighting) sample size of the data that goes into the projection.  Certainly small things like age, injury history, etc. can affect this interval in small ways. 

I DON’T see hoe scouting or “fan” information can change this interval.  It can change the projection, but NOT the interval.  So I profess that any player, Ecjstein or Beltre, is going to have almost EXACTLY the same interval in performance given roughly the same sample size of historical data, and roughly the same sample of future performance of course.  Which is why I think that the Pecota intervals are basically hogwash (over and above that they are a function of the two aforementioned things).

So I think that David is completely wrong!  I think that Ecjstein’s and Beltre’s interval (or variance of expected performance) will be EXACTLY the same (obviously centered on the mean of their projection), given the same amount of historical data.

I also want to say that large (or small) variance in the past (like Beltre had a great year and then he had a poor year, etc.) has NOTHING whatsoever to do with the variance of future performance.

So yes, I will take a bet, for any amount of money, that if we take 20 or 30 players who have around the same amoung of historical playing time, they will all have roughly the same variance of performance next year around their projection, as long as we only use those players who have around the same number of PA next year (as I explained), say, around 450-650.

While it SEEMS that big, strong players who have some good years and some bad years, like Beltre, have more “natural” variance, as opposed to “steady” scrappers like an Eckstein, that is a total and complete illusion, and is absolutely NOT true, OTHER THAN the fact that, as I explained earlier, each component has more or less natural variance (more precisely, regression to the mean) than others…

There is also going to be a selective sampling bias when it comes to good versus bad players, when it comes time to measure the variance around their projections.  With the bad players, if they perform a lot less than their projection for some period of time, whether it is because they are truly less talented than we thought, or they were just unlucky, or some combination thereof, they are less likely to accumulate enough PA’s to reach our minimum.

Based on David’s post, he is supposing that he, or someone, can figure out if a player is playing to his potential or not.  In hockey, for example, Mario Lemieux, one of the 4 greatest hockey players of all time, was pretty good in his first three years in the league, but not other-worldly.  He was not playing to his full potential.

http://www.hockeydb.com/ihdb/stats/pdisplay.php3?pid=3105

However, in the summer of 1987 was the remarkable Canada Cup, where he was paired with the equally talented, but fully-realized-potential of Wayne Gretzky.  It was Mario’s “coming out” moment.  Starting from the 1987/88 season and to the rest of his career, Mario Lemieux was likely the best player in the league.

Now, if you find a group of such players, who are underperforming relative to their intrinsic skills, you may be betting that a few of them will have a watershed moment, and therefore, as a group, you will find greater variance than in a group of guys who are playing to their potential (Eckstein, Pujols).

I don’t disagree with the theory, but, I’m skeptical in someone being able to pick out such players, of guys who are underperforming, of which some may turn it around.  However, I’d lean more toward Dave than MGL.

It must be true, as Tango says, that some players have the physical ability to be better than their early performances indicate.  But surely this is relatively rare, and by the time a hitter is 27 (Beltre) it is extremely unlikely he will establish a new (better) performance level.  For pitchers, my sense is that is not nearly as true—the learning/experience factor, including developing new pitches, is more important. 

I can think of one way we might be able to forecast such an upside, which is looking at peak performance.  Suppose you have two pitchers with identical overall metrics in the minors and first 2 years of MLB, but when you look at the best 20% of their starts one of them performs significantly better.  (This also means his worst games are worse, of course, so this is a high-variance pitcher).  A guy who can put up some 12K/1BB/9IP lines is potentially demonstrating an underlying talent that is obscured in his total stats by his inconsistency.  It might be the case that this high-peak/high-variance pitcher has a better chance of becoming an above-avg MLB pitcher than a consistent pitcher with same stats.

Even if this were true, the problems of small sample size, differences in strength of opposition and league,etc. might make it impractical to use for forecasting individual pitchers.  But it would be interesting to see if including a pitcher’s peak performance level added any power to a Marcel-like projection.

I agree that beyond a certain level, wins have decreasing marginal utility on a team level.  A team that projects to win 110 games is going to win the pennant, and probably won’t have much more revenue by adding yet another +7 superstar.

On the player level, it might be totally different.  I remember an article in baseball prospectus a few years back where they published a stat called “pennants added” I think Sandy Koufax did very well in that, better than some other pitchers who saved more runs over their careers but without the high peak.

Yes, there’s decreasing return at some point, but this is largely a theoretical concern.  If a team’s goal is to get good enough that there is, let’s say, at least a 50% chance of making the postseason then they need to assemble true talent of something like 90-92 wins. And shouldn’t every team really aspire to a 75% or better chance, resources permitting? 

Let’s use a crude estimate of 4+ win players, using BPro data.  If we take 40+ VORP hitters (49) and starters (30), and add 4+ WRX relievers (11), that gives us 90 4+ win players in 2006—3.0 per team.  Ranking teams by wins, they break down this way in terms of avg. # of 4+ players:
Top 6 (90+ wins):  4.5
Next 6 (85-89):  3.7
Bottom 18:  2.3
The 90-win teams had two extra high-value players on average (and twice as many).  These 90+ teams were collectively 82 WAA; their 4+ players were collectively 103 WAA. 

Of course there is selective sampling here:  some players got lucky, and in turn that helped their team win more games.  But it’s also clear that the winningest teams all have a significant number of true high-value players. 

The best cases for the “Tango strategy” are Chi(A)and Oak, each of whom had three 4+ players.  Chicago had three +3 starters, and Oak a bunch of 2-3 win relievers.  But even on these egalitarian teams you needed to have three of the 4+ players (and neither team made the top 4 in wins).  The winningest team with only two 4+ players was St. Louis (83 wins), and of course one of those two was really two 4-win players in one body.

The bottom line is that you cannot generally construct a team that will consistently make the postseason without some 4-6 win players.  And that means these players ARE worth more per marginal win. 

* * *

The discussion of scarcity, I think, is completely off the mark.  The scarcity of a player’s talent is already accounted for when we say he’s a “+4 win player;” if his skills weren’t scarce, he wouldn’t help us win games.  Either marginal wins above average have more value than the first two wins above replacement, or they don’t—I believe they clearly do—but “scarcity” as a distinct issue is irrelevant.

Let’s talk money.  What are you suggesting is the marginal $ / marginal win at these levels:
+1 wins above replacement
+2
+3
+4
+5
+6
+7
+8

Are you suggesting that perhaps that the +1 guy is $1 mill per win, and the +4 guy is 4 mill per win (total of 16 mill), making the +8 guy worth 64 mill?  Or maybe the +1 guy get 1.5 mill per win, and the +3 guy get 2.5 mill/win (total 7.5), and the +4 guy gets 3 mill per win (total 12)… up to the +8 guy who gets 5 mill/win (40 million).

What exactly are the numbers you are proposing? 

And, if you are going to cap the marginal $/win at a certain win level, tell me the reason.

I think scarcity IS an issue if there are fewer than 25% of the 4 win guys than the 1 win guy, which I think is the case.

I’d have to go back and look at some of the analysis of wins and revenue, but it might look something like this:
+1 1
+2 2
+3 2.5
+4 3
+5 3.5
+6 4
+7 4
+8 4
This means a +4 player is worth $8.5M, of course, not $12. And Albert (+8) would be worth $24. 

(Interestingly, I suspect that the handful of 6+ win true talent players are actually underpaid, because A) so few teams can afford them that the market of buyers is limited, and B) concern about having all your eggs in one basket, in terms of what an injury does to your team.)

Ok, so you are taking the marginal wins of the marginal wins.  So, the +4 wins above replacement guy get 1 mill for his first win, 2 for his second, 2.5 for his 3rd, and 3 for his 4th, for a total of 8.5 for 4 wins.  And at the top end, like you said, you have Pujols at 24 mill for 8 wins.

So, if you put it in my scale then:
+1: 1 mill for each win
+2: 1.5 for each win (i.e., 1 mill for the first win, and 2 mill for the 2nd)
+3: 1.8 for each win
+4: 2.1 for each win
+5: 2.4 for each win
+6: 2.7 for each win
+7: 2.9 for each win
+8: 3.0 for each win

So, if you have a +6 and a +2 player, you would pay such a duo a total of 17.5 million$.  The two +4 players, under your scenario, would be paid 17 million$.

In your tiered scenario, you still end up paying virtually the exact same amount as you would under a flat scenario, to get the exact same number of wins.

So, what’s the point of such a tiered scenario?

Oops, that would be 19 million under the tiered scenario and 17 million under the flat scenario.

I still don’t think you are seeing the huge benefit.  How about taking two teams that have wide talent and tight talent, and see how much of a difference the tiered/flat scenario has.

"In your tiered scenario, you still end up paying virtually the exact same amount as you would under a flat scenario, to get the exact same number of wins.”

For example, three 2-win players would cost $9M, two 3-win players cost $11M, and a 6-win player costs $16M.  Seems like a pretty major disparity to me. 

In this scenario, a team obviously wants to have as many +2 and +3 players as possible, because that’s the cheap way to buy wins.  (So playing a replacement player as a regular is a huge mistake.) You don’t want to hire the high-value players because their wins cost more—you only do that because you have to (to build a winning team).