THE BOOK--Playing The Percentages In Baseball

Friday, November 04, 2011

Contract crowd-sourcing

Here’s what Fangraphs readers say.  Don’t focus on the amount as a fixed number, but rather relative to the whole group. 

Contract Name
$186 Albert Pujols
$136 CC Sabathia
$136 Prince Fielder
$101 Jose Reyes
$78 C.J. Wilson

$42 Jimmy Rollins
$40 Jo. Papelbon
$39 Aramis Ramirez
$38 Carlos Beltran
$34 Edwin Jackson
$30 Mark Buehrle

$27 Heath Bell
$25 Ryan Madson
$25 David Ortiz
$24 Grady Sizemore
$23 Hiroki Kuroda
$22 Michael Cuddyer

$19 Josh Willingham
$16 Rafael Furcal
$16 Kelly Johnson
$14 Carlos Pena
$14 Jason Kubel
$14 Javier Vazquez
$12 Aaron Hill
$11 David DeJesus
$11 Ramon Hernandez

$8 Clint Barmes
$7 Wilson Betemit
$7 Rod Barajas
$7 Derrek Lee
$6 Jamey Carroll
$6 Jerry Hairston
$5 Mark Ellis
$5 Jorge Posada
$5 Jim Thome
$4 Nick Punto

Tuesday, November 01, 2011

Paying CC to terminate his opt-out option

CC Sabathia had an opt-out option following the 2011 season.  That opt-out clause had a certain amount of value when his first signed preceding the 2009 season, and that opt-out option’s value changed pitch by pitch, game by game, year by year, so that when the 2011 concluded, that opt-out option had a certain amount of value.

CC had signed a 7yr/161MM$ deal with the option going into the 2009 season.  Had he not had that option, he would have signed for MORE.  It might have been a 7/180MM$ deal let’s say.  That is, he got some discount in order to have the opt-out option.  This is really a faith in himself, that he knows more than the Yankees about how he would have aged.

In his last 3 years with the Indians, he had a total of 20 fWAR.  Seeing that he was at his (theoretical) peak and had nowhere to go but down, the expectation would have been for him to accumulate something like 16.5 wins for 2009-2011, and then 15 wins for 2012-2015.  Those 31.5 wins, worth a weighted average of 5.7MM$ per win gives us 179MM$.  CC signs for 18MM$ less, in return for the opt-out option.

If CC earns less than 16 wins for 2009-2011, then it’s a wasted option.  If he earns more than 17 wins in 2009-2011, then we have a good chance that he is aging better than expected.  He will then exercise that option.  He had 19 fWAR from 2009-2011.  This means that CC aged better than expected.

Whereas when he signed the deal in 2009, his expected WAR for the 2012 would have been for around 4.5 wins.  Today, knowing what we know with his last three seasons (and his career), his expected WAR for 2012 is closer to 5.5 wins.  Because he is better today than we expected him to be, he exercices his opt-out option.  This is no different than any stock option.  CC Sabathia Properties is just like your Microsoft or Oracle stock options.

Had the economy not tanked, CC would have gotten a much better deal than the one he got.  This is how it looked like in 2009:

(We need to subtract 6MM$ for each of 2009, 2010, 2011, in return for the opt-out option.  The 6MM$ and all the above numbers are just an illustration.  I don’t know what the actual value of the option is, but it would be easy enough to figure out.)

He was paid for delivering 16.5 wins, but he delivered almost 19 wins.  He was undervalued, and therefore, he wants to be properly valued.

This is what he looks like today:

That’s 5 years and 123 million$.

The two key differences is that he’s more talented today than we expected him to be.  But, with the economy tanking, he doesn’t get the larger multiplier effect.  Hence, the fairly mild extension he got.

Friday, October 14, 2011

Chance of making playoffs, based on payroll

Back in April 2010, I had a quick indicator to determine the chance a team of making the playoffs (or, more accurately, having a playoff-level team, i.e., winning at least 89 games):

Chance of Playoffs = (Payroll Index / 2) - 23

I figured I’d check to see how it worked out for 2011.  Payroll Index is simply the team payroll divided by the league average.  Anyway, let’s see what we get (doing this as we speak):

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Tuesday, October 11, 2011

Remaining value of contracts

Poz looks at the contracts that need to be foreclosed on.  These are contracts where the mortage owed is far higher than the equity remaining. 

He correctly notes the following:

In the end, it evens out I suppose. The system works so that players get paid later in their career for what they did earlier in the career

Let’s say you have a guy in his early 30s, on the down side of his career.  He’s still a star, but he’s going down.  Let’s say he has this trajectory left:

Wins
4.0
3.5
2.9
2.2
1.4
0.5

That’s 14.5 wins left over the next 6 years, and a team would pay 78MM$ for that.  The standard payment structure is just like your mortgage: 13MM$ per year.  As we know, your mortgage payment is mostly interest payments in the beginning, and only near the end are you paying down mostly equity. 

If you were to pay for performance, this player’s contract would look like this:

His first year, he earns the most, and his last year, he earns the least.  If it’s 4 years later, and he’s got 2 years left, he’d have 26MM$ owed to him, but only 12MM$ of value.  It would look like it’s a horrible contract.  But the reality is that the player gave his team a discount the first 3 years, only to get the deferred payments in the last two years.

So, I get what Poz is saying, and I agree with it under the specific lens of how untradable these players are.  But for the teams that own them in the middle of the contract, you have to evaluate the contract in its entirety.

Monday, October 10, 2011

Does it make any sense for a player to be “untouchable?”

You hear this kind of thing all time:

“I’m tired of talking about it,” he said. “We’re not shopping him. We’re not entertaining offers. It’s frustrating. He’s one of the best players in the game. Why would we trade him? I wish people would stop writing about it.”

That was by Walt Jocketty, the GM of the Reds, and it is in reference to Votto.

Now, some of it is posturing, but you hear it so often, that surely it can’t be posturing all the time.  Personally, I think that most of the time it is sincere.

It makes no sense.  What is the difference how good a player is?  One, someone could always offer you a better player or combination of players.

Two, and MUCH more importantly, who cares how good a player is?  It’s not like you own him for free, like if I had one of the best cars in the world, say a Bugatti Veyron (worth 2.5 mil and one of the most expensive cars in the world), in which case I could reasonably say that I wouldn’t trade him for any other car in the world (of course, someone could offer me 2 cars or 10).  You have to pay all your players a salary, which is like a mortgage, as Tango likes to say (and it is a great analogy).  What you own of course, is the equity on that player, which is roughly the difference between the win value of that player and his salary.

If someone offers you a deal that has more equity, you should consider it.  Obviously there is more to it than that, but to say or think that any player on your team is “untouchable” seems ridiculous and irresponsible to me…

Friday, October 07, 2011

Free agents and BMW’s

As only Phil can link them.

***

I agree that if all players were made free agents, the cost of free agents would be driven down.  That number, I believe, is going to be 2.5MM$ per win.

Thursday, September 29, 2011

Payroll v Wins, in the Moneyball era (2002-2011)

The chart below shows the total team payroll over the ten year period of 2002-2011, in millions of dollars, from the Yankees’ 1.875 billion dollars to the Rays 393 million dollars.  It is plotted against the total number of wins in that time period, from the Royals’ 668 wins to the Yankees 975 wins.

The data shows an r=0.70 correlation, signifying that there’s a great deal of relationship between payroll and wins. 

This is particularly strong, considering that service time is not included as a variable.  As any baseball fan would know, the performance from Evan Longoria’s first four years generated as much win impact as Chase Utley in 2008-2011.  But the cost for Longoria was just a fraction of what Utley earned, due to MLB’s salary being heavily tied to a player’s service time.  If we include service time as a variable, then the correlation would naturally increase.

The teams noted below were the three teams that got the most bang for their buck.  The Moneyball A’s were #1, followed closely by the Twins and Cardinals.  The teams that got the least for their buck was a two-team race “won” by the Orioles over the Royals.  The Mets came in third worst.

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Tuesday, September 13, 2011

Chris Carpenter: money on the table?

When I saw the deal, it was interesting.  You have someone who at age 34 was one of the best pitchers, if not the best.  At ages 35-36, he was above average.

How much do you pay this pitcher for ages 37 and 38?  Pavano, a bit younger and somewhat worse signed for 2/16.5.  Pineiro close to that.  Pettitte, a bit older, a bit worse, signed for 1/12.

So, thinking about this for the first time, I’d say a one-year deal would probably be 1/14 or so.  A second year probably worth 11 maybe?  So, 2/25 would have been my quick take without doing any kind of analysis.  He signed 2/21, and Eno is arguing he might have left 10MM on the table.  That’s possible.  Maybe a 16MM the first year and 14MM the second year?  Sure, possible.

I agree that he left something on the table.

Sunday, September 11, 2011

I cut the pie, you choose the slice

Economics has long decided how to split something in half, or otherwise choose sides. 

Whether it’s a question of the potential owner’s character, or whether:

Selig will not appreciate Crane claiming that it’s the switch to the American League holding up the sale. That statement is not true, and it seems unlikely Crane believes it to be true. On the list of things keeping Jim Crane from owning the Astros, switching to the American League is about 83rd.

It’s irrelevant for the purposes of my discussion here.  If you have 16 people on one side, and none of them want to go to the either side, how do you incentivize one of them?  Why, with money of course.  Think of it as if each of the NL team kicks in 100,000$ into the pot.  That’s 1.6MM$ in the pot.  First one to say “I do”, gets the 1.6MM$ and moves to the AL.  No one takes?  Ok, each team kicks in yet another 100,000$.  And on and on it goes, until someone yells out “Bingo!”.

We don’t need autocracy or monarchy here.  All we need is pure free market capitalism.

Thursday, August 25, 2011

Cot’s Contracts Compensation Pages integrated with BPro

Good stuff.

Sunday, August 21, 2011

Did Jered Weaver sell himself short?

When Felix signed for 5/78, it was his two final arb years, and three years of free agency.

When Verlander signed days later for 5/80, it was for the same arb/free agent years.

Jered Weaver, essentially an equal to Felix and Verlander in terms of talent, (reportedly) signed for 5/85, but that was his final year of arbitration, and four years of free agency.

So, does that seem too low?  Let’s see.

Verlander and Felix basically signed for this kind of scale:
7MM$
13MM$

20MM$
20MM$
20MM$

That is, their last two years of arb for 20MM$ total, and their three free agency years for 20MM$ each.

Weaver, if he followed their lead, would sign for this:
13MM$

20MM$
20MM$
20MM$
20MM$

And that’s 93MM$.  Is it an age thing?  Verlander is only 4 months younger.

While Felix signed off a huge year, Verlander signed just before his breakout year.  And Jered Weaver had a breakout year last year, plus a huge year this year.

So, I’m surprised that he signed for only 5/85.  I would have expected something closer to 5/93, if not even higher.

Tuesday, July 19, 2011

Did Jon Heyman fail ECON 101 ?

Beltran is owed about 25MM$ over the next 1.5 years.  How much performance can we expect from him?  I dunno, but probably less than 25MM$.  If it’s more, it’s not that much more.  At best, you are talking about a 30MM$ property, with 25MM$ of mortgage.

Domonic Brown probably has 25MM$ of mortgage over the first 6 years of his contract (that is, the SAME as Beltran).  I expect him to generate alot more than 30MM$ of property value over those 6 years.

UPDATE: Looks like the answer is: “No”.  It’s possible that Heyman was not speaking for himself, but for the Mets.

Arbitration rule: 40/60/80

We’re interested in exploring the 40/60/80 rule that many statistical writers use when analyzing contracts for arbitration eligible players. We thought we’d ask you about the rule, since it’s our understanding that you built on research by David Studenmund on the subject. When should the 40/60/80 rule be used in your estimation?

It’s a rule of thumb, and should be used generally speaking.  If you look at specific players, you really should look at “comps” (comparable players).  So, for example, if you look at Verlander, Felix, JJ, Weaver’s first arb-eligible year, they all signed for around 3.5MM$ to 4MM$.  But Lincecum got far more than that (9MM$).

If you consider that they would have received 25MM$ in free agency, then the 40% rule would have said 10MM$.  So, we see that in extreme cases, the 40/60/80 rule doesn’t necessarily apply.  Therefore, in addition to the rule, you need to have a “cap”, based on historical precedent.

Not to mention you have an extreme-rare case like Lincecum, who is really no better or worse than the others I mentioned (and if he is better, then he’s marginally better), but managed to get a Cy Young (two actually).

So, if you are trying to figure something more robust, I would not rely on the rule of thumb.  You’d have to come up with something not so linear.  For example, rather than a hard 40% for expected WAR, it would have a sliding scale that might be 60% for expected WAR for low WAR players down to 15% expected WAR for high WAR players, with bonus points for Cy and MVP (to take care of Ryan Howard, Justin Morneau, etc).  The average will be close to say 40%, but it won’t be so linear.

Or, more likely, you can forget about WAR altogether, and come up with a Arb-based value for a player, that overweights RBI, HR, SV, W, and underweights walks, etc.

Friday, July 15, 2011

K-Rod’s option

K-Rod had an option that would vest at 17.5MM$, if he finished 21 more games this season. 

How much should you pay him to waive that option?  The Brewers and K-Rod agreed on 0.5MM$.  Does that make sense?  Well, with Axford already the closer, it’s very possible K-Rod would not finish many games.  So, the Brewers could have saved themselves 0.5MM$ and rolled the dice that Axford would not get hurt and/or remain effective.

On the other hand, K-Rod would still like to pad his save totals.  If he gives the Brewers flexibility, then he might be able to do that. 

0.5MM$?  I guess.

Monday, July 11, 2011

Market for Japanese pitchers

Michael notes all the Japanese pitchers in MLB:

That’s a total of 75 WARP for 272 MM$, or 3.6MM$ per WARP.  WARP uses a different scale than WAR, and of course, these costs are not timeline-adjusted.

Tuesday, June 21, 2011

Does NFL have more expenses relative to revenue than NBA and NHL?

The NFL pays out 53% of their revenue, and they want that reduced to 48%.  The NBA and NHL pay out above 55%.  It looks something like this:
NHL: 3 billion$ revenue, 1.3 billion$ to owners
NFL: 9 billion$ revenue, 4.7 billion$ to owners

Why does the NFL, with its extra 6 billion$ in revenue need to take 3.4 billion$ of that for themselves?  What is it about the NHL business model that is more efficient than NFL?

Thursday, May 19, 2011

Currency exchange rates

Another driver against the Expos was the currency exchange rate, something that would benefit them greatly these days.  This issue is far more in play in the NHL of course.

It’s not noted by Gabe in that article, but the NHL used to have a “currency matching program” of sorts for the Canadian teams.  When the dollar was at 66 cents, the NHL would guarantee an exchange rate of halfway between that an 1 dollar, and so would bump that up to 83 cents.  (I’m hazy on the details, but they did have something like this in play.)

When you think about what the exchange rate SHOULD BE (based on the fundamentals, and not the technicals), it made good enough sense.  For example, the exchange rate should be based on what Canadians and Americans were purchasing, and so, the conversion rate should be based on that (insofar as to what it means to a sports team anyway).  And I remember at the time reading that the exchange rate based on product purchases should have valued the Canadian dollar at 84 American cents.

I’m not sure what it should be valued at now based on this component.  Indeed, if it’s still 84 cents, then the Canadian teams are really doing well (i.e., lucky that the exchange rate is where it is).

Ensuring K-Rod’s option does not vest, by trading him to a team with an established closer

If we think of K-Rod as a security, like a convertible bond, rather than as a human being, I love the idea here.  If we think of K-Rod as a baseball player, then I hate the idea.

The issue here is that players and owners treat the players as a commodity.  Pedro once said of his contract with the Redsox that they owned his arm for six years, so they could do whatever they want with it.

Anyway, what team would take K-Rod to be their setup guy (with a non-zero chance that he’d be the closer, because closer do get injured)?  And what kind of premium would they want for the non-zero risk that he ends the season with 54 games finished?

Think of him like a security, if you want to have fun with this.

Friday, May 13, 2011

Nomar, Vlad: model for quick signings

After his 0 WAR September call-up year, and his 6 WAR rookie year, Nomar signed a 5 year / 23MM$ deal, that bought out all his arb years.  That was entering 1998.

After his 1 WAR half-rookie year, and 7 WAR full year, Vlad signed a 5 year / 29MM$ deal, that bought out all his arb years.  That was entering 1999.

Back in 1998-1999, the marginal dollar per marginal win was about half what it was today.

But, pre-free agents (slaves and arb-eligible) simply have not kept pace with the overall baseball inflation.  That’s why you are not going to see star players with 1+ years of service (i.e., 1.000 to 1.171) sign 5 year / 50MM$ deals.  For all intents and purposes, the pre-free agents scale has not budged much.

The more interesting cases to discuss is what to pay players with less than 1 year of service, like Longoria did (and Hossmer might).  With Vlad and Nomar, you had one MVP-level season in MLB, so you have a great level of certainty that they were well above-average players.

With Hossmer and Longoria, you didn’t have that.  You have to first decide what are the chances that they were as good after 2 weeks, that Nomar and Vlad showed after a full season.  Let’s say that’s 60% chance of being MVP-level, 30% chance of being above-average, and 10% chance of being close to a bust.  Then you have to decide how much inflation has there been between when Nomar/Vlad signed, and today (among the non-free agents).  It should be 100%, but let’s say it’s actually 50%.

Let’s add it up.  First, let’s turn Vlad/Nomar into today’s dollars, meaning between 35MM$ and 45MM$.  We’ll settle on 40MM$.

Then, we give Hoss/Longo 60% chance of being worth 40MM$, 30% chance of being worth 20MM$, and 10% chance of being worth nothing.

Add it up, and we get 24+6+0 = 30MM$.

So, if Longoria and Hossmer want the quick security after 2 weeks, then they’ll sign for 30MM$. 

(Longoria’s 3rd through 7th seasons were signed for 21MM$, so he signed at a huge discount.  Basically, it would have made sense if it was 1997, not 2008.  In addition, he threw in 2 free agency years at 11MM$ each, which was ridiculous for him to do.  If Longoria told the Rays that he would sign for 21MM$ and buy out all his arb years, they’d have been enthralled, considering it should have been for 30MM$.  To then throw in TWO highly discounted years of free agency will guarantee the Rays front office of accolades for years to come.)

Anyway, if Hossmer is as good as advertised, then 30MM$ to buy out his arb years would seem to be the industry standard (if he signs today).  Of course, if he has an MVP-type year this year, and signs after that (1 year of service time), then it would take close to 40MM$ to buy out his arb years.  If he keeps waiting, then either an injury will knock him out, or he can go year-to-year and look for a Ryan Howard payday and make far more than 40MM$.

That’s why you have to look at this in terms of chances of him performing at a high level or not, and chance of injury.

Paper: Sabermetric and Microeconomic Perspectives on Free Agent Contracts

I’m posting this blind (pdf).  I’ll comment later…