http://0rz.tw/3040N How are free agent deals determined? 自由球员合约是怎麽签订的? By Vince Gennaro, Special to Yahoo! Sports 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. 洛杉矶天使队将会付给中外野手Torii Hunter五年九千万美金的支票，而另一个中外野 手Andruw Jones则是跟道奇队签下了两年三千六百二十万美金的合约。 辛辛那提红人队跟终结者Francisco Cordero签下一份四年总额四千六百万美金的合约， 至於另一个终结者Eric Gagne则从密尔瓦基酿酒人队手中拿到了一份一年一千万美金的 合约。 西雅图水手队以四年四千八百万美金的价格签下了先发投手Carlos Silva，而他也是08 年自由球员当中唯一获得复数年合约的先发投手。 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? 是哪些要素影响到了这些合约和其他合约之间的差异?为了找出答案，我应用统计学的工 具--主要回归分析(是这样翻的吗?)来检验去年冬季的自由球员市场。 我测试了许多种过往表现的分析标准，来找出这些守备位置的球员是物超所值还是签了不 符实力的肥约，同时考虑了年纪因素和过去的伤病史。而我在调整过其他可能影响的变数 後也测试了有关於球员的额外价值--这也是大部分明星球员被签下大合约的因素。而且， 我们要问的是，签约时机会影响到薪水吗?在十一月和十二月左右签下合约的球员如果稍 晚再下决定会拿到比较好的待遇吗? 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. 对球队决定签下自由球员来说，这些结果启发了一套精确定义的衡量标准。我的分析导出 了一个可以解释在年度平均薪资标准下的自由球员潮中，百分之九十二的球员间差异模型 。并且指示了一种合理的薪资尺度--而不是一系列的武断决定做为参考。 我用各种计量方法来测定球员表现而且选定了Win Shares--这种由Bill James发展出来并 且由Hardball Times的分析家们修正过的公制变项，被设计用来提炼球员的统计资料来换 算出球员对他所属球队的胜利总数做出了多少贡献。 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. 有一个关键的发现是薪资倾向反映出球员在最近一到四年当中最好球季的水准。 这些例子包括了Paul Lo Duca，Gagne，还有Geoff Jenkins。只要有一个表现杰出的球季 --尽管那可能是三或四年前的事情，就能让球队总管们冀望魔力有再次发生的可能。这种 希望让球员的口袋饱饱。如果你把Lo Duca稳定发挥的04年球季略过不提的话，他的表现 看起来就像是薪资比他便宜百分之三十的Michael Barrett。Gagne的薪资很明显是依照他 过去02到04年在道奇队总共一百五十五次救援的成绩来拟定，而不是他上季在红袜队经常 砸锅的後援表现。而从费城人队获得两年总共一千三百万美金合约的Jenkins不仅是因为 他去年的两成五五打击率和二十一支全垒打才拿到这份合约，主要是因为他在05年有二十 五支全垒打还有两成九二的打击率。 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. 这项分析也证实了一项很多人认为的观点，那就是投手通常比其他位置的球员更容易获得 大合约，尽管在调整过後的win shares呈现下，前段轮值的先发投手是在食物链的顶端， 接着是终结者，後段先发和剩下的後援投手。但在可比较的追踪记录下，我们还是可以发 现就贡献度来说，後援投手明显的比打者拿了更多的薪资。 把二号捕手Jose Molina和後援投手David Riske做比较就可以显示这个观点。过去三年当 中两位选手的win shares几乎相同，也就是说他们的薪资应该也差不多。不过Riske的三 年一千三百万合约以单季来算几乎是Molina两年四百万合约的两倍，总额更是有将近三倍 的差距。一种付给投手更多薪水的解释是球队总是想要加强他们的三号先发并且为牛棚买 保险，而打者就不适用这种解释。也就是说三十队中有二十多队已经有固定先发的游击手 ，而不是在市场中寻找，所以跟投手比起来，打者比较少队参与竞标，需求较少价格自然 比较低。 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. 今年投手市场里的其中一条头条新闻就是洋基队决定以三年四千五百万的薪资跟终结者 Mariano Rivera续约，而这也替MO加了百分之五十的薪水。拥有充沛现金的洋基队无疑是 奖励MO长久且稳定的生涯表现，不过更重要的是他们也提早把充满终结者的自由市场的盖 子给盖上了。而这个合约的决定可能也明显暗示了现代的终结者可能要比以往拿更多的薪 水，之後红人跟Cordero的巨大合约可能只是个开始而已。 在今年的市场中，另外一个唯一跟其他位置不同的就是二游位置的野手。在调整过各种要 素之後我们发现，跟其他位置比起来二垒手和游击手是比较便宜就能签到的。 年龄对自由球员薪资的影响 球员 每年平均薪资 年龄 假设球员为28岁时可能得到的薪资 Tom Glavine 八百万 42岁 三百八十万 Mariano Rivera 一千五百万 38岁 两百七十万 Andy Pettitte 一千六百万 35岁 两百六十万 Mike Lowell 一千两百五十万 34岁 三百二十万 Torri Hunter 一千八百万 32岁 两百万 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. 年龄很明显的是决定自由球员薪资的重要因素，较老的球员所得的合约长度较短而且每年 平均薪资也较低，如果Tom Glavine在28岁时的过去几年成绩跟现在42岁时一样的话，模 型显示他将会拿到比现在的平均每年八百万美金再多出三百八十万。上面的图表秀出了今 年自由市场里五个球员的年龄对薪资的影响。 另一个重要的要素是健康。有洋洋洒洒伤病史的球员在自由市场里是较不受欢迎的。为了 取代伤病史我用过去五年的总出场数来做为变项，像是双城队的Livan Hernandez还有白 袜队的Scott Linebrink，或是道奇队的Jones从过去的纪录来说都算是能够稳定出赛的球 员。 耐力对自由球员薪资的影响 球员 每年平均薪资 耐力对薪资的影响 耐力影响的百分比 Alex Rodriguez 两千七百五十万 两百六十万 9% Jorge Posada 一千三百一十万 一百八十万 14% Andrew Jones 一千八百万 一百四十万 8% Livan Hernandez 五百万 九十万 18% Tom Glavine 八百万 八十万 10% 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. 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. 就另一方面来说，以芝加哥小熊队经常受伤的後援投手Kerry Wood为例，如果他能维持同 样的投球威力并且能像Linebrink一样稳定出赛的话(他在过去四季分别出赛了73, 73, 73 和71场比赛)，他的价值会比现在一年平均四百五十万多出两百二十万。这个理论同样可 以应用在打者身上。如果游骑兵的Milton Bradley的耐战度跟Jones差不多的话，他的价 值就值一年平均七百八十万，比现在他签下的一年五百万多得多。上面的图表显示了今年 自由市场中球员耐力对薪资的影响。 时机也会对合约价值产生一定的影响，在春训开始之後才签下的合约通常会获得一定的折 扣。一个似乎可信的解释认为高获益的球队总是在休季没多久就急於补强他们最迫切需要 的位置。当月历走到了一月末二月初时，很多球队都对他们的关键需求感到满意而剩下的 球队就开始寻找折扣。红雀队最近以一年四百二十五万的价格签下了先发投手Kyle Lohse ，以模型的估计来看，这个较晚的签约为球队省下了大约二十万。不过，根据Lohse和他 的经纪人--Scott Boras在休季期间稍早的谈判认为以Lohse的资历，过往表现，年纪和耐 力等，应该能转换成一年平均六百二十万美金。 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. 而统计分析中最後一个被揭露出来的变项是可量化的明星魅力。在明星的额外价值背後的 理论其实相当简单，如果行销大公司像是百事或耐吉愿意付给明星运动员大量的金钱来推 销他们的品牌，那同样的理由，球员也能因为每天穿着球队的球衣上场而创造类似的效应 。 不过衡量额外价值并不太容易，虽然分析可以提供一些洞察的角度，在对球员表现，年龄 ，耐力和位置价值作出调整後，我们可以发现一个明显的图像来呈现未经解释的自由球员 市场薪资的比例分布。根据包含变项来测量明星球员的额外效应，像是Hunter,Jones还有 A-Rod，我们可以看到自由球员市场如何衡量"非表现面"的球员面向，也就是额外价值。这 个分析指出A-Rod因为他的额外效应每年多得到九百七十万的津贴，而不只是因为他的球 场表现，年龄，位置和耐力。而Hunter的额外价值是每年六百万，Jones则是每年五百一 十万。 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. 这个分析其中一个重要的结论是每一个要素的影响--球场表现，年龄，位置和耐力都和球 员的表现等级成比例。举例来说，A-Rod有能力打155场比赛隔年就替他的所值多增加了三 百万，以同样的标准衡量Jones的话产值则是一百五十万。 根据这个模型，Silva和太空人队的二垒手Kaz Matsui是最不符身价的自由球员，Matsui 每年平均值五百五十万，但分析显示他只值三百万，Silva被认为只值一年平均八百七十 万，但他比这个数字还多拿了两百三十万。在尺度的另外一边则是光芒队的外野手Floyd ，他的薪资应该有四百九十万，但分析指出他其实只拿到符合他身价百分之六十的薪水-- 三百万。 而没被签下的自由球员价值又如何呢?模式认为三十九岁的Mike Piazza值一年三百二十万 ，四十岁的Kenny Lofton值两百四十万，而四十三岁的全垒打王Barry Bonds则价值一千 两百八十万，不过这个估计忽略了他据传的类固醇使用和大陪审团起诉所带来的负面包袱 。 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. 图三单独呈现了各个关键要素对这些球员薪资的影响。 我对合约的长度执行了类似的分析，发现这五个关键要素也指示了合约的长度。毫无意外 的，球场表现和合约长度有正相关，球员表现的越好，合约长度就越长。也可以说明星球 员运用他们的力量来让他们的价值得到保障。 年龄和耐力是另外的要素。年纪较大和有伤病史的选手总是得到较短，风险也较低的合约 ，唯一对位置有影响的是後援投手。在调整过各个其他变项之後，後援投手还是相对来说 会得到较长的合约。最後一个决定合约长度的要素是一个球员是否为A型自由球员。球队 放弃了一个高顺位选秀可以签下其他队的高等级自由球员。为了保证交易有价值，球队会 倾向给A型自由球员较长的合约。 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. 这个分析也能用在呈现最近Johan Santana的延长合约的另一种观点。虽然他并未接触自 由球员市场，考虑到Santana最近的投球表现，年龄，耐力和身为最有威力的先发投手之 一的额外价值，模式认为他值一年平均两千两百一十万，跟他和大都会的六年总额一亿三 千七百五十万的合约做比较，球队每年大概平均多付了他八十万。 这个统计分析指出了数个警讯，包含了资料只限制为去年的休季，事实上相关性和因果关 系仍未被证实，而且有些变项--像是额外球员价值的命名跟定义也有点主观。不过这个分 析对於提供对自由球员市场运作的洞察和照亮自由球员薪资是如何签订上还是很有帮助的 。 -- http://www.wretch.cc/blog/randyorton 无聊碎碎念 --

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