## On \$-per-Win Estimates of Baseball Players’ Worth

Frequently, I receive a comment or e-mail that brings up the dollar-value estimates at Fangraphs.com. Fangraphs is a fine site with lots of interesting numbers, but I don’t think the dollar-value estimates listed on the site (or any simple wins-to-dollars conversion) properly value players. Here’s why.

1) The derived estimates are based on the assumption that there is a constant linear relationship between wins and dollars. This assumption is incorrect: there are clear increasing returns to winning. This is the revenue function I estimated for my book, converted to wins instead of runs.

2) By dividing the total value of free-agent contracts (Y) by total “wins” added by the signed free agents (X), this method assumes the y-intercept (b) is 0, which biases the estimates. Y = mX + b, when you assume b is zero when it’s not, bad things happen to slope m. The graph below from the popular econometrics textbook Understanding Econometrics: A Practical Guide by A.H. Studenmund demonstrates why this assumption biases the estimates.

Due to the thinness of the free-agent market and the potential for market mistakes, I prefer a fundamental-value approach to valuing players as opposed to a market-valuation approach. However, if I want to use the free-agent market to value talent, I prefer Anthony Krautmann’s “free-market returns” approach, which can be implemented in ways to avoid the problems mentioned above.

In Chapter 4 of my book, I explain why I prefer the Gerald Scully inspired approach to the free market returns approach. This is not to say that market prices are not useful for valuing free agents. In my book explain where free market returns helped me shape my estimates. Also, here is a working paper in which I discuss the pros and cons of the Scully and Krautmann methods.

## 2010 Most Valuable Players (Pitchers)

Here are the most valuable position players in the leagues, according to my estimates. Position players here.

```AL
Rank	Player			Team	\$-Value (MRP)
1	Cliff  Lee		SEA/TEX	\$18.94
2	Felix  Hernandez	SEA	\$17.13
3	Justin  Verlander	DET	\$15.71
4	Francisco  Liriano	MIN	\$14.79
5	Jered  Weaver		LAA	\$13.73
6	CC  Sabathia		NYY	\$13.57
7	Zack  Greinke		KCR	\$13.17
8	Jon  Lester		BOS	\$13.06
9	John  Lackey		BOS	\$10.94
10	John  Danks		CHW	\$10.80
11	Colby  Lewis		TEX	\$10.56
12	Carl  Pavano		MIN	\$10.43
13	Ricky  Romero		TOR	\$10.29
14	Mark  Buehrle		CHW	\$10.26
15	Gavin  Floyd		CHW	\$10.23
16	Joba  Chamberlain	NYY	\$10.18
17	David  Price		TBR	\$10.14
18	Joakim  Soria		KCR	\$10.03
19	Matt  Thornton		CHW	\$10.00
20	C.J.  Wilson		TEX	\$9.88

```
```NL
Rank	Player			Team	\$-Value (MRP)
3	Ubaldo  Jimenez		COL	\$15.84
4	Josh  Johnson		FLA	\$15.67
5	Matt  Belisle		COL	\$15.40
6	Carlos  Marmol		CHC	\$13.87
7	Tim  Lincecum		SFG	\$13.05
8	Brian  Wilson		SFG	\$12.65
9	Jonny  Venters		ATL	\$12.62
10	Sean  Marshall		CHC	\$12.52
11	Chris  Carpenter	STL	\$11.91
12	Billy  Wagner		ATL	\$11.60
13	Tommy  Hanson		ATL	\$11.46
14	Heath  Bell		SDP	\$11.42
17	Anibal  Sanchez		FLA	\$11.19
18	Brett  Myers		HOU	\$11.12
19	Matt  Cain		SFG	\$11.09

```

## 2010 Most Valuable Players (Position Players)

Here are the most valuable position players in the leagues, according to my estimates. Pitchers here.

```AL
Rank	Player		Team	\$-Value (MRP)
1	Jose  Bautista	TOR	\$21.11
2	Josh  Hamilton	TEX	\$19.43
3	Miguel  Cabrera	DET	\$18.65
4	Shin-Soo  Choo	CLE	\$18.00
5	Evan  Longoria	TBR	\$17.67
6	Robinson  Cano	NYY	\$17.03
8	Daric  Barton	OAK	\$15.28
9	Carl  Crawford	TBR	\$15.11
10	Ichiro  Suzuki	SEA	\$13.48
11	Austin  Jackson	DET	\$12.48
12	Joe  Mauer	MIN	\$12.38
13	Nick  Swisher	NYY	\$12.35
14	Nelson  Cruz	TEX	\$12.04
15	Vernon  Wells	TOR	\$11.98
16	Justin  Morneau	MIN	\$11.93
17	Nick  Markakis	BAL	\$11.93
18	Billy  Butler	KCR	\$11.93
19	Paul  Konerko	CHW	\$11.91
20	Torii  Hunter	LAA	\$11.83
```
```NL
Rank	Player		Team	\$-Value (MRP)
1	Albert  Pujols	STL	\$21.61
2	Joey  Votto	CIN	\$20.17
3	Matt  Holliday	STL	\$18.04
4	Ryan  Zimmerman	WSN	\$17.99
6	Jayson  Werth	PHI	\$16.13
7	Aubrey  Huff	SFG	\$15.95
8	Troy  TulowitzkiCOL	\$14.83
9	Carlos  GonzalezCOL	\$14.02
10	Jason  Heyward	ATL	\$13.97
11	Ryan  Braun	MIL	\$13.81
12	Jay  Bruce	CIN	\$13.15
13	Kelly  Johnson	ARI	\$13.05
15	Rickie  Weeks	MIL	\$12.14
16	Prince  Fielder	MIL	\$11.94
17	Hunter  Pence	HOU	\$11.80
18	Chris  Young	ARI	\$11.76
19	Chase  Utley	PHI	\$11.71
20	Angel  Pagan	NYM	\$11.70
```

## Valuing Free Agents for 2011

Here is a list of some top free agents, and what I project them to be worth in 2011.

— These values are projected based on recent past performance.
— The estimates account for aging and league revenue growth.
— These values are just for 2011. Over a longer term, value will diminish with age, but increase with revenue growth. Revenue growth is stronger than aging decline; therefore, even as players age their value tends to increase. If a player signs a five-year contract, he will typically get more than five-times the value projected in 2011.
— Values assume the player signs with an average team. Players who sign with winning teams are worth considerably more than their value to an average team. Example: Clill Lee is worth nearly \$10 million/year more to a top team than an average team.

```First	Last		Last Team	2011 Value (in millions)
Lance	Berkman		NYY		\$9.8
Pat	Burrell		SFG		\$7.0
David	Bush		MIL		\$4.5
Carl	Crawford	TBR		\$15.0
Johnny	Damon		DET		\$9.5
Jorge	de la Rosa	COL		\$6.5
Jon	Garland		SDP		\$8.5
Orlando	Hudson		MIN		\$10.0
Aubrey	Huff		SFG		\$11.0
Derek	Jeter		NYY		\$9.0
Paul	Konerko		CHW		\$9.5
Cliff	Lee		TEX		\$18.5
Victor	Martinez	BOS		\$10.0
Kevin  	Millwood	BAL		\$6.5
Carl	Pavano		MIN		\$9.5
Carlos	Pena		TBR		\$10.0
Andy	Pettitte	NYY		\$6.0
J.J.	Putz		CHW		\$5.0
Manny	Ramirez		CHW		\$7.0
Jon	Rauch		MIN		\$6.0
Edgar	Renteria	SFG		\$5.0
Mariano	Rivera		NYY		\$9.5
Rafael	Soriano		TBR		\$8.6
Jim	Thome		MIN		\$9.5
Juan	Uribe		SFG		\$7.0
Jayson	Werth		PHI		\$14.0
Jake	Westbrook	STL		\$7.0
```

## Why Would Dan Uggla Reject a Four-Year, \$48 Million Contract?

That’s the question Ken Rosenthal tries to answer. The Florida Marlins supposedly offered Dan Uggla a four-year, \$48 million extension that he turned down. Like the team, I am a bit surprised that Uggla didn’t accept. I estimate Uggla to be worth approximately \$51 million over the next four years (\$12.75 million per year). That’s in the same ballpark as the Marlins’ offer, plus Uggla still has another year of arbitration, when he will likely get a little less than his market value.

Uggla, the only second baseman in history with four 30-homer seasons, has slightly lower rate stats than outfielder Jayson Werth over the past three years, but more home runs, extra-base hits and RBI. Werth, a free agent, almost certainly will command more than four years, \$48 million.

I have Werth valued at \$4–5 million more per year than Uggla. If this is what Uggla is waiting for, he probably shouldn’t hold his breath.

A four-year deal for Uggla would amount to a three-year extension on top of his final year of arbitration, making him a free agent at 34. Uggla likely would seek at least a five-year contract as a free agent after next season, delaying his next deal to 36.

That’s true, but the future market will account for his depreciated value as he ages. Also, he risks having an awful season in 2011 that could raise uncertainty about his future performance. That’s an awfully big gamble to take for a few more million dollars. This contract would be more than triple his current lifetime earning as a baseball player.

While the Yankees, Red Sox and Phillies are among the high-revenue teams that wouldn’t pursue a second baseman in the 2011-12 market, Uggla also could play third base and outfield, increasing his options.

While I don’t think a position switch is necessarily in his future, he would be worth more to a winning club. It may be that he’s willing to hold out for free agency in the hope of grabbing on with a perennial winner that will value him more than a merely-decent club like the Marlins. Or maybe, he wants assurances that if he signs, he won’t be traded to somewhere else in an attempt by the Marlins to capture some of his added value to winning clubs.

Who knows what really is going in in these negotiations, but I think the Marlins have a pretty good offer on the table.

## Vlad Guerrero: Did the Rangers Get What They Paid For, and Should They Pick Up His Option?

Congrats to the San Francisco Giants on winning the 2010 World Series. While the winner normally gets a few days to bask in the after-glow of its victory, fans of the loser quickly look to next year, when the runner-up can make tweaks to push the team over the top. The Texas Rangers have a few offseason issues, but right now I want to focus on their aging designated hitter/ outfielder.

There is no sugar-coating it. Vlad Guerrero had an awful World Series (.071 AVG, .125 OBP, .071 SLG), and the rest of his post-season wasn’t much better…well, actually it was, but a .615 OPS in the ALDS and ALCS wasn’t up to Guerrero’s expectations. It’s too bad, because Guerrero had a nice regular season, and was a big part of why the Rangers won their division. After a subpar season with the Angels, the Rangers took a chance that Vlad would bounce back and be a productive hitter in their lineup, offering him a one-year \$5.5 million contract, with a second year option for \$9 million or pay a \$1 million buyout.

How did this deal shake out? I estimate his 2010 regular-season was worth approximately \$8.75 million to an average team, and to a winning team like the Rangers he was certainly worth more. At most, the Rangers will end up paying him \$6.5 million for his 2010 services; so, he was a bargain this season. But the real question comes as to what the Rangers should do with his option. \$8.75 is only a little less than \$9 million. From these numbers, picking up the option ranges from a neutral to a bad idea, but I need to make a few corrections.

First, Vlad is getting older, and he really can’t play the field much at all (as he demonstrated in the World Series). He’s been almost a full-time DH since 2008. But, as he showed this season, he can still hit. Even if we just looked at his 2010 second-half (and I wouldn’t recommend doing so), he had an OPS+ of 107. Yes, he’s getting older, but even into their late-30s, good players continue to be good players.

Also, what about his playoff performance? How much does that tell us about his future performance? Not much information can be drawn from 62 plate appearances. In 2009, he batted a spectacular .370/.393/.593 over 27 plate appearances in the postseason. Were people willing to believe that he would be playing near his peak in 2010 based on this small sample? I doubt it. Several hundred plate appearances over the course of the regular season provide far more information about a player’s ability than a small sample from the playoffs.

I estimate that based on his last three years of performance, adjusting for aging and league revenue growth, Guerrero projects to be worth \$7.5 million in 2011. To pick up their option, the Rangers would have to spend \$8 million more than they would have to pay him if they declined (triggering a \$1 million buyout). On top of this, the Rangers are a winning team, so his play is likely worth more than the option to the team. However, Guerrero isn’t the Rangers’ only option. If they want to re-sign Cliff Lee, or go after free agents like Jayson Werth or Carl Crawford, they may prefer not to pick up the option.

Guerrero may be declining, but baseball talent is quite scarce and valuable. I won’t be surprised if the Rangers pick up his option; and, if they decline, I expect he will sign a comparable deal with another team.

## What Is Jayson Werth Worth?

Phillies fan Joe Munley sent me the following question:

With the Phils season now over I’m trying to evaluate where we stand for next year. Jayson Werth, the only power, right handed hitter in the lineup is a free agent and has hired Scott Boras as his agent. The word on the street up here is that the Phils won’t be brining him back since he’s 31 and they have Dominick Brown waiting in the wings. Based on your model for valuing players what do think Werth’s true value really is and would it actually make sense for the Phillies to re-sign him?

Jayson Werth is a great example of how unique player careers can be. He was first-round draft pick who struggled upon entering the league and was plagued by a wrist injury. He’s been traded multiple times and was released by the Dodgers after the 2006 season. In Philadelphia, he played his way from an outfield sub, to a platoon player, to an everyday player and All-Star. He just had his best season at age 31, in a walk year.

I’m not sure whether the injury caused Werth to reevaluate his commitment to the game, he got better coaching, or he just finally figured things out; but, whatever he did, he has become a much better ballplayer in Philly. With the Blue Jays and Dodgers, he posted a .245/.333/.420 (AVG/OBP/SLG) line. With the Phillies, he’s batted .282/.380/.506. So, when projecting Werth going forward, I believe his Philadelphia performance is most relevant. Werth is also an above average defender and can steal bases.

If Werth was younger, a six- to eight-year deal might be feasible, but at age 32, I think five years is about as long as any team will be willing to go with him. And just because he’s baseball-old doesn’t mean he’s getting ready to head to the bench. Aging tends to be gradual. I’ve estimated that hitters tend to peak around 29-30. If Werth signed a five-year deal, by my estimates he’d be expected to decline by an average of 1.25% per year over the contract term. This lost value from aging will be counterbalanced some by the expected growth in league revenue. Even though his performance will still be diminishing, that diminished performance will be worth more in the future than it is today.

After combining all these factors, I estimate that Werth’s play would be worth approximately \$80 — \$85 million (\$16 — \$17 million per year) over a five-year contract to an average team, and worth even more to a contender. Is this something the Phillies are willing to shell out? I doubt it considering all the chatter seems to indicate that he is gone. But someone is going to give Werth a lot of money, possibly paying him more next year than he has received in his entire career up to now.

## What Is Derek Jeter Worth?

That’s the question Stephen Dubner asked me for a Freakonomics Quorum. Here’s a tease:

I see the problem here as one of gathering information about what each party desires in order to foster agreement where there are strong incentives to hold out. I’d prefer to adjust the bargaining framework rather than directly attempt to reconcile revenue expectations that are largely invisible to the other side and the public.

You can read the rest of my answer, as well as the answers from Dave Berri and Maury Brown, at Freakonomics. Thanks to Stephen for asking my opinion.

## More Evidence for the Three-Man Rotation

Effects of varying recovery periods on muscle enzymes, soreness, and performance in baseball pitchers, by Potteiger, Blessing, and Wilson, Journal of Athletic Training, 1992; 27(1): 27–31.

From the Abstract

Results indicate that muscle damage, as evidenced by CK release, occurs in response to baseball pitching. However CK values, muscle soreness, and pitch velocity are not significantly affected by changes in the amount of recovery time typically scheduled between games.

The authors look at a sample of pitchers and how they recover after pitching different lengths of time. The results show a few things. First, the pattern of recovery indicates most healing occurs soon after pitching, and that further recovery occurs at a diminishing rate. After three days of rest, the measures of skeletal muscle damage were back to baseline values. Second, performance on two days of rest is only slightly worse than, and not statistically distinguishable from, performance on four days of rest. This is good news for the Phillies and Roy Oswalt. The results are also consistent with my analysis (with Sean Forman) of major-league pitchers.

You can get the gist of the results from the graphs in the pages below. The study is short, interesting, and it’s not even new. There a lot of studies in the fields of sports medicine, exercise physiology, and sports science that look at popular sabermetric questions. If you have a sabermetric question, it won’t hurt to do a PubMed search on the topic.

## Gwinnett Commissioner Indicted for Taking \$1 Million in Bribes

Two years ago, I reported that Gwinnett County Commissioner Kevin Kenerly owned a parcel of land near the new Gwinnett Stadium, yet he did not make this public nor did he recuse himself from votes relating to the project. Yesterday, Commissioner Kenerly was indicted for allegedly having much more than a minor conflict of interest in several County land purchases (the stadium plot was not part of this investigation).

A Gwinnett County grand jury on Wednesday indicted the county’s longest-serving commissioner, Kevin Kenerly, on charges of bribery and failure to disclose a financial interest in two properties the county rezoned.

If convicted of all counts, Kenerly faces up to 22 years in prison.

The indictment says that Kenerly “directly or indirectly” accepted or agreed to accept 20 payments of \$50,000 — totaling \$1 million — as bribes for arranging for the county commission to buy a piece of unnamed real estate. The deal benefited developer David Jenkins and settled a lawsuit, although specifics about the purchase were not mentioned in the indictment.

Kenerly also was indicted on two misdemeanor charges for failure to disclose a partnership with D.G. Jenkins Development Corporation, which successfully sought county rezoning on two properties.

“I am going to plead not guilty and I am confident when the jury hears the facts, I will be cleared,” Kenerly told the AJC in a statement after the hearing.

Chairman of the Board of Commissioners Charles Bannister was also questioned by the grand jury. He was not charged, but he abruptly resigned following his testimony.