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How are free agent deals determined?

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Center fielder Torii Hunter will be paid $90 million over five years by the Los Angeles Angels. Another center fielder, Andruw Jones, will get $36.2 million over two years from the Los Angeles Dodgers.

Closer Francisco Cordero signed a four-year, $46 million deal with the Cincinnati Reds. Another closer, Eric Gagne, got a one-year, $10 million contract from the Milwaukee Brewers.

Starter Carlos Silva will be paid $48 million over four years by the Seattle Mariners. Silva, however, is the only starter from the free-agent class of 2008 to get more than a one-year commitment.

What factors caused the disparity in those contracts, and others? To provide answers, I employed statistical tools – primarily regression analysis – to examine last winter's free-agent market.

I tested various measures of past performance, whether players at certain positions were paid a premium or a discount, and examined the impact of age and injury history. I also tested for evidence of a player’s marquee value – were the most popular stars paid a premium, after adjusting for all other factors? Also, did the timing of the signing impact salary? Did players who inked deals in November and December fare better than late signees?

The results suggest a well-defined set of criteria that teams employ when signing free agents. My analysis resulted in a model that explains 92 percent of the player-by-player variation in average annual salary within the free-agent crop, suggesting there is a rational pay scale, rather than a series of arbitrary decisions.

I experimented with different measures to calibrate player performance and settled on Win Shares – a metric developed by Bill James and modified by the analysts at Hardball Times – designed to distill a player’s statistics down to a bottom-line contribution to his team’s win total.

One key finding is that salaries tend to reflect a combination of a player's most recent season and his best season over the last four years.

Examples include Paul Lo Duca, Gagne, and Geoff Jenkins. A standout season, even if it was three or four years ago, can give a GM hope the magic can be recaptured. That hope puts money in a player’s pocket. If you take away Lo Duca’s stellar 2004 season, he looks a lot more like Michael Barrett, who signed for 30 percent less than Lo Duca. Gagne’s deal was clearly based on the 155 saves he notched with the Dodgers from 2002 to 2004 and not on the blowups he endured down the stretch last year with the Boston Red Sox. Jenkins’ two-year, $13 million deal with the Phillies was boosted by his strong 2005 season, when he batted .292 with 25 home runs, rather than solely on 2007, when he batted .255 with 21 home runs.

The analysis also validates a popularly held view that pitchers are paid a premium over position players, even after adjusting for their win shares. Frontline starters are at the top of the food chain, followed by closers, back of the rotation starters and the rest of the bullpen, but even relievers command significantly more dollars than a position player with a comparable track record.

Comparing backup catcher Jose Molina to reliever David Riske illustrates the point. Both players have accumulated about the same number of win shares over the last three years, meaning they should have similar value. Yet Riske’s three-year, $13 million deal is more than twice the annual value and three times the total value of Molina’s two-year, $4 million contract. One explanation for the higher prices for pitchers is that teams are constantly looking to improve their numbers three and four starters and adding an insurance arm to the bullpen. The same can’t be said for position players. At any point in time, 20 or more teams may be set at shortstop – simply not in the market – thereby reducing the number of teams bidding up the salaries.

One of the headlines in this year’s pitching market was the Yankees move to re-sign closer Mariano Rivera to a three-year, $45 million deal – a 50 percent increase in his salary. The cash-rich Yankees no doubt rewarded Rivera for a stellar career, but more importantly they removed the lid from the simmering market for closers. This contract could have significant implications as the previously modest closer salaries will likely leap higher. The Reds signing of Cordero to a lucrative deal may be just the beginning.

The only other position that exhibited a distinct pay pattern in this year’s market was the middle infield. After adjusting for all other factors, second basemen and shortstops tend to be paid slightly less than other position players.

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Age is clearly a factor in determining free agent salaries, with older players receiving shorter deals and a lower annual value. If Tom Glavine had the same track record over the last several years but was 28 instead of 42, the model says he would have signed for about $3.8 million more than his $8 million deal. Figure 1 shows the age impact for five players in this year’s free agent class.

Another important consideration is health. Players who have a poor injury history are penalized in the free agent market. As a proxy for injury history I used the variation in the number of games played over the last five years. Pitchers such as the Twins’ Livan Hernandez and the White Sox' Scott Linebrink, or position players such as Jones of the Dodgers are bankable in terms of their history of showing up ready to play.

On the other hand, take the case of oft-injured Cubs reliever Kerry Wood. If Wood maintained his same rate of performance but was able to take the ball with the consistency of Linebrink (who appeared in 73, 73, 73, and 71 games over the last four seasons), he would be worth another $2.2 million on top of his $4.5 million salary. The same holds true for position players. If Rangers outfielder Milton Bradley had Jones’ consistency in games played, he likely would have commanded a $7.8 million salary, compared to the $5 million deal he signed. Figure 2 shows durable players in this year’s free-agent class the salary impact of their consistency.

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Timing also made a difference in the value of contracts. Late signees – those coming to terms after spring training camps opened – were obtained at a discount. A plausible explanation is that high-revenue teams strike early in the offseason to fill their most pressing needs. As the calendar moves into late January and February, many teams have satisfied their key needs and the remaining teams are looking for bargains. The Cardinals recently signed starting pitcher Kyle Lohse to a one-year, $4.25 million deal, which is within $200,000 of the model’s estimate of his value as a late signee. However, had Lohse and his agent, Scott Boras, negotiated a deal earlier in the offseason, Lohse’s qualifications – performance history, age, durability, etc. – could have translated into a value of $6.2 million per year.

The last factor revealed by the statistical analysis is the quantifiable value of star power. The theory behind marquee value is simple. If consumer marketers such as Pepsi or Nike are willing to pay star athletes to endorse their products and build their brands, it stands to reason these players can provide similar value for the teams whose uniforms they wear every day.

Measuring marquee value is not easy, although the analysis can provide insights. After adjusting for playing performance, age, durability and positional value, there is a clear pattern to the unexplained portion of free agent salaries. By including a variable to gauge the additional impact of star players such as Hunter, Jones and Alex Rodriguez, we can see how the free agent market values the “non-performance” aspect of a player – his marquee value. The analysis indicates that A-Rod has $9.7 million per year built into his compensation beyond the rate paid for his performance history, age, position and durability. The marquee value estimate for Hunter is $6 million per year and for Jones is $5.1 million per year.

One of the important conclusions of this analysis is that the impact of each factor – durability, age, positional value, etc. – is proportionate to the player's level of performance. For example, Rodriguez’s ability to play 155-plus games year after year contributes nearly $3 million to his annual value, while the same attribute in Jones is worth an estimated $1.5 million per year.

According to the model, Silva and Astros second baseman Kaz Matsui were the most overpaid free agents. Matsui will make $5.5 million per year, but the analysis indicates he's worth $3 million. Silva has a value of $8.7 million per year, $2.3 million less than he will be paid. On the other side of the scale is Rays outfielder Cliff Floyd, whom the model values at $4.9 million, more than 60 percent higher than his $3 million salary.

What are unsigned free agents worth? The model suggests that 39-year old Mike Piazza would be valued at $3.2 million and 40-year old Kenny Lofton at $2.4 million. Barry Bonds, the 43-year old all-time home run king, is valued at $12.8 million, but this estimate ignores negative baggage associated with his alleged steroid usage and grand jury indictment.

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Figure 3 isolates the impact on salary of each of the key factors in the model for selected players.

I performed a similar analysis on the length of contracts awarded and concluded that five key factors dictate term. Not surprisingly, performance is positively correlated with contract length – the better the player, the longer the deal. Think of it as star players using their leverage to convert some of their value into security.

Age and durability are other factors. Older players and those with a history of injuries translate into shorter, lower-risk deals. The only positional effect is for relief pitchers, which after adjusting for all other factors, receive significantly longer deals. The final determinant for contract length is whether the player is a Type A free agent. Teams give up a high draft choice when they sign another team’s top tier free agent. To ensure they make such an exchange worthwhile, teams are inclined to sign a Type A free agent to a somewhat longer deal.

This analysis can also be used provide a perspective for Johan Santana’s recent contract extension, although he never reached the free-agent market. Considering Santana’s recent performance history, age, durability and marquee status as one of the premier starting pitchers in the game, the model places Santana’s annual value at $22.1 million, within $800,000 of his six-year, $137.5 million deal with the Mets.

This statistical analysis has several caveats, including data limited to the 2007-2008 offseason, the fact that correlation does not confirm causality and that some of the variables – such as the designation of marquee players – are somewhat subjective. Yet the analysis is helpful in providing insights into the workings of the free-agent market and sheds light on how free-agent salaries are determined.

Vince Gennaro is a consultant to several Major League Baseball teams and the author of "Diamond Dollars: The Economics of Winning in Baseball," an innovative look at the business of baseball. This followed a 20-year career at PepsiCo, where he was president of a billion-dollar division. Gennaro teaches a graduate course on the business of baseball in the Sports Business Management program at Manhattanville College. Send Vince a question or comment for potential use in a future column or webcast at vgennaro07@yahoo.com.

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