THE BOOK--Playing The Percentages In Baseball

You’re absolutely right that’s what he should be paid, Tango.  $35 million a year.  Does anyone believe that an owner would actually pay that?

Tango, get out of my files! Just this morning, I asked myself this question and put it on the to-do list. I don’t think Pujols would get what he deserves relative to the market.

Remember, I always stick to and agree to a linear marginal $ per win.  Most of the posters here look for an ever rising dollar value per win.  In that case, my estimate is conservative.

As for any owner paying that, no they wouldn’t.  However, they would sign him for a 5/181 deal.  That is, while they’d love to give him a lifetime contract, there’s probably a maximum dollar value that a team will pay.  I think a team will not go over 200 million$.  Jeter’s 189 is probably the ceiling, as ARod’s 252 carries such a sick feeling.

So, Pujols would be offered just 5 years.  And, he’ll still be in his early 30s when that contract would expire.

Studes, the Yankees might, after all, they’re looking for a right handed first baseman.

I agree that the Yankees might, but they’ve become more conservative recently.  I personally don’t think they’d approach those numbers.  I think that Pujols would break the $20 million mark and maybe break $25 million, but I don’t think he’d break $30 million.  Of course, that’s just my opinion.

There’s a psychological limit to prices.  That’s the theory, for instance, behind splitting stocks.

When was the last the time a player of Pujols’ quality came on the market? Probably A-Rod, and look at the contract he got! True, that was in the heady days of new millenium but the market this year is at least as crazy.

There is little doubt that Pujols would redefine the market were he available. No-one expected A-Rod to for $25M but he did. Execs aren’t stupid (ok, they might be a little) but I reckon they’d be smart enough to recognise the value of Pujols relative to some of the FA dross. I reckon he’d surge through the $30M mark quite comfortably. Compared to Soriano 181/5 would be a steal.

When someone in the class of Pujols comes on to the market any psychological price limit tends to go out of the window ...

Problem was, Bobby Orr supposedly never *knew* he was offered that.  If he did, we never would have had to see him in a Blackhawks jersey.

I think the only way that Pujols would have gotten 30 would have been if the Sox traded Manny for prospects and had some salary to play with.

Right, Bobby Orr didn’t know.  He has as much class as his agent (and at the same time head of the NHLPA!), the unmentionable, had crass.

My question is how do you make the calculation?  Assume Pujols will earn say 300 million$ over the next 8 years.  Assume the Cards are worth say 500 million$ today, and in 8 years they will be worth 1 billion$.  Do you simply take the present value of the 1 billion$ (say 4% inflation rate), and give Pujols a 300/730, or 40%, stake in the Cards in exchange for no contract?

Hmmmm… that 300 million needs to be present-valued as well (annuity really), so say that would come out to 250.  So, 250/730, or about 35%?

Tango,

That is one option. The problem with that is that Pujols then has his money locked up in an asset that appreciates at 10% per annum (assuming baseball value continue to grow at that rate). Perhaps in a different asset class he’d more likely get five percent, not ten percent.

What you’d need to do to rectify that is to assume that the contract had a life of say 12 years and then in the perpetuity caclulation assume a 5% growth in Pujols’ stake and a 10% growth in club value.

Given the time frame we are talking about here I suspect that will still amount to ~30-32% stake in the Cards.

The question is would the Busch organisation be prepared to cede that sort of control?

What would/should the pitching equivalent of Pujols (namely, Johan) be worth on the open market? If he hadn’t signed that 4yr/$40M deal after ‘04, I think this would be his first year as a free agent.

Maybe after ‘05 he would’ve been a FA, but the question stands.

I am sure Tango can enlighten us, but I have Santana as about 5 wins above average, or 7 above replacement.

According to Tango’s little chart that is a 140/5 contract, or $28M a year, which is a heck of a lot more money than he is currently making. Factor in a decline, and possible pitcher risk and it would probably be less. If you think that Clemens earned $22M last year (pro rated over the whole season), then $28M a year for Santana isn’t outlandish.

"There’s a psychological limit to prices.  That’s the theory, for instance, behind splitting stocks.”

I agree that there is probably an upper limit on what teams would pay any one player.  But it may not just be psychological.  I can see at least three reasons teams would be reluctant to pay $35M to Pujols, even if that’s his true expected value:

1) it commits your team to paying full price (FA price) for a lot of wins for a long time.  For a few very wealthy teams that may not be a problem, as they will always devote much more than $35M to FAs.  But even for a team like StL, this would greatly limit future flexibility.  It basically requires you go find value in pre-arb and arb players, and if those don’t materialize you’re out of luck. 

2) This is a very illiquid asset.  The trade market will always be extremely limited, and at times may be non-existent. 

3) The Albert Belle problem:  suppose Pujols sustains serious injury/illness, greatly reducing his productivity.  It’s not likely, but if it happens you’ve just taken your team out of contention for the duration of the contract.  Hiring 3 $12M players diversifies your risk, just like the investment advisers recommend.  (Insurance may mitigate this, I’m not sure.  Is it just as easy/cheap to insure a $35M contract?  In any case, this only helps if the injury forces him to the DL or retirement. )

Guy,

I’d rather pay Pujols full price for his wins than pay Soriano over the odds for whatever contibution he provides!

I think that your second point is probably the most relevant. If, for whatever reason, you want to get out of the contract then there are only a few teams that could take the asset off your hands. Given that only three teams can really afford him that means it would be impossible to dump the salary if you really wanted to do so. Saying that, it wouldn’t be an issue if you were to give equity in leiu of cash.

I actually think your third point poses an interesting question. From a risk diversification perspective should a GM take one $36M contract of three $12M? DSG showed that balance of the line up appears unimportant so it comes down to risk diversification. You’d intuitively think that the 3x12 is the better option but I’d like to see research to back that up. From a value point of view you could argue that the $36M player could bring in more revenue from superstar status—this would not be reflected in the original price because that is base on WAR only.

If all of your player values are equivalent, 3x12 definitely carries less risk.  I don’t see how it could be different.

You could probably explore the concept of a price ceiling by thinking of the present value of the total commitment as a percent of franchise value.

Guy is basically right, though he’s kind of skirting around the main issue, which is that even if Pujols’ mean projection is 7 WAR, that’s actually near his limit. This is where a system like PECOTA, that gives you both the weighted mean and the median (which we can assume is the same thing as the mean projection of Marcel) really works better. For example, maybe Pujols’ distribution looks something like this:

90th percentile = 10.00 WAR
80th percentile = 9.65 WAR
70th percentile = 9.30 WAR
60th percentile = 8.90 WAR
50th percentile = 8.50 WAR
40th percentile = 7.50 WAR
30th percentile = 6.50 WAR
20th percentile = 5.00 WAR
10th percentile = 3.50 WAR

Weighted Mean = 6.89 WAR

Therefore, Pujols gets more like 5/$140 million, which I could see happening. Moreover, if you actually did the math (I believe this is Poisson stuff) for every possible percentile, that would push the weighted mean down even further, maybe making Pujols’ deal an even-more-manageable 5 years/$130 million or something.

If all of your player values are equivalent, 3x12 definitely carries less risk.  I don’t see how it could be different.

Agreed, but does the impact of having 1 $36M superstar on your team bring in enough additional revenue to mitigate the risk.

It is like saying what value did Bonds add to the Giants over and above three players each a third as good? Can anyone answer that question?

Therefore, Pujols gets more like 5/$140 million, which I could see happening. Moreover, if you actually did the math (I believe this is Poisson stuff) for every possible percentile, that would push the weighted mean down even further, maybe making Pujols’ deal an even-more-manageable 5 years/$130 million or something.

David, why would it be a Poisson distribution? A Poisson distribution is used when you are calculating an event per that occurs x times in a given unit of time. Are you saying that in this case the unit of time is the season?? I’d imagine over that duration it’d equate fairly close to a normal distribution.

John,

This is why I’m not qualified to talk about math I thought you could fit it under a Poisson distribution by using wOBA (which approximates a binomial) and a ZR-type stat (which is also a probability). But I might be totally wrong—this honestly is not my area of expertise. I’m simply saying that the distribution isn’t normal—the probability of Pujols losing 4 wins is much higher than the probability of Pujols gaining four wins.

David,

Interesting. Is the distribution not normal? If not, is it because of injury risk? In otherwords if we were to take out injuries then we’d get a normal distribution.

If it is injury related then I can see how you *might* get a Poisson distribution because I suspect that time on the DL possibly follows a Poisson curve, but I could be wrong.

Injury mostly, and some for general decline. I.e., the chances that Pujols turns into 01-04 Bonds are about one-in-a-million, the chances that he turns into Nomar (though that was an injury-related problem, but I’m sure you can come up with plenty of players who just declined for no apparent reason) or has an injury bug that eventually saps his effectiveness like Griffey is much greater than that.

I agree with David that the distribution is probably not normal.  Its not about his performance.  Lets say Pujol’s mean SLG is .650 and he’s equally likely to slug .750 or .550 in a full season.  I don’t know if its true but for sake of argument.

His playing time affects his value over replacement big time though.  If his mean projected games played is 145, then with bad luck it could be only 35, or even zero if he rips his ACL in spring training.  But it can’t go much higher than 162.

Great point, David.  That’s why I’m a big fan of PECOTA-like output.

John, you asked this…

Agreed, but does the impact of having 1 $36M superstar on your team bring in enough additional revenue to mitigate the risk.

I think you’re mixing up two things.  The $36 million projection for Pujols is based on what the market is currently paying, not marginal revenue.  In fact, that figure blows Pujols’s potential marginal revenue product away.

There may be some inherent marginal revenue impact from having one great player instead of three very good players, but I think it really depends on the player himself, his personality, the characteristics of the surrounding population etc.  Vince Gennaro will publish a nice book about this subject in the spring.

I think you’re mixing up two things.  The $36 million projection for Pujols is based on what the market is currently paying, not marginal revenue.  In fact, that figure blows Pujols’s potential marginal revenue product away.

Yes. That’s is a fair observation, but I think my point still applies in that a $36M player as valued by the market will bring in more revenue that 3x $12M players (hypothesis )! You are probably right in that the marginal revenue a player brings in probably is dependent on personality etc. but Bonds was disliked yet, I’m sure, still added a lot of revenue (but he could well be an outlier because he was incredibly good).

I am keen to get Vince’s book—any idea what it will be called so I can track it on Amazon? Actually I am looking forward to his piece in THT Annual but I am not in the US at the moment so it takes an age to ship the book overseas.

It’s called Diamond Dollars: The Economics of Winning in Baseball.  I don’t see it on Amazon yet.

What is the rationale behind not allowing teams to pay for actual offensive performance?  Is it the fear that players will pad their stats instead of helping the team?  Is it that players will resent being told to hit the ball to the right side to advance the runner?  Is it that players will threaten the official scorer if he calls an error a hit?

Because it seems to me that offering some kind of pay-for-performance contract (not all of it, but maybe base plus bonuses) would be of benefit to both the team and the player.

For players, I’m sure they like the security of guaranteed contracts.

For teams, the examples you mentioned might be part of it.  I’ve seen Juan Gonzalez go crazy on an official scorer because he didn’t get his RBI’s on an error call.

A few years back Jose Guillen went crazy on the Angels after he was removed for a pinch runner.  Imagine how much more of that you’d see when players want to stay in the game as much as possible to pad their stats.

Every player will try and be Cal Ripken too.  They’ll hide any injury they can if their pay depends on being in the lineup and putting up stats.

You’re right, the hiding-an-injury problem would probably be a dealbreaker.

Tango, I tried to apply this to Ichiro as before the offseason started I speculated that the Mariners should extend him after his move to Center Field.

http://www.fanhome.com/forums/showthread.php?t=1805

Here’s my current application of your chart and Ichiro.

Bedir, you are better off continuing the discussion here:
http://www.insidethebook.com/ee/index.php/site/comments/sabermetric_moves_of_the_off_season/#73

At that post (73), I discuss Ichiro, Wells, and Andruw.

I don’t know if everyone knows this, but performance-based contracts are specifically outlawed by the CBA.  That’s why you see so many funky clauses, such as money riding on MVP (which the CBA says is okay) instead of actual performance.

I’ve got Cabrera as +3.5 wins above average as a hitter.

The fielding Bible is low on him, but the Fans’ are a bit above average on him.  Let’s call him even as a fielder.

He is very young.  He qualifies for free agency after the 2009 season, at which point he will be 27 years old entering the 2010 season.  Let’s say that he’ll be +4.5 wins above average when he does so.  He will also have very litle decline in aging. 

What kind of contract will a +6.5 WAR player get at that time?

With modest aging (0.25 decline per year), that’s a 4yr/151 million$ contract (in future dollars).

If the Marlins want to pay for his 3 remaining arb years, and buyout four of his FA years, a fair offer would be 7 year / 180 million$ contract today.  Because of the possibility of injuries, you might want to put in a discount. 

So, a 7/160 offer should be made by Florida today.

Tom,

You know that fans overrate good (especially young) hitters in the field! Cabrera is an atrocious fielder, and should really be at first base or DH (if he goes to the AL). He’s -10 or -15 runs EASILY in the field, which would take him down to +2 or +2.5 wins. I wouldn’t go over 7 years, $100 million, which is not an offer Cabrera would accept. That’s why it probably makes sense to trade him away to a team that has no idea how bad a fielder he is.

Pinto has him pretty much average:
http://www.baseballmusings.com/cgi-bin/DisplayCharts.py?PlayerID=1744&fpos=5&year=2006

If he truly is -1 win as a fielder, that knocks out around 15-20% from his contract, making the reasonable offer 7/130.

I should also note that his 2004, 2005, 2006 Fans Scouting Reports show him as going from a 40 to 50 to 60.  In each case, I had less than 10 ballots. 

I wouldn’t be surprised if the early report is more real, since that’s when a fan is less influenced by media coverage.

The Ryan Howard posts have been moved here:
http://www.insidethebook.com/ee/index.php/site/comments/ryan_howard/

If you call Pujols an 8 WAR player today, then starting in 2011 (as a 31-yr old), the Cardinals should sign him to a 400 million$ lifetime deal.