http://0rz.tw/3040N How are free agent deals determined? 自由球員合約是怎麼簽訂的? 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. 洛杉磯天使隊將會付給中外野手Torii Hunter五年九千萬美金的支票，而另一個中外野 手Andruw Jones則是跟道奇隊簽下了兩年三千六百二十萬美金的合約。 辛辛那提紅人隊跟終結者Francisco Cordero簽下一份四年總額四千六百萬美金的合約， 至於另一個終結者Eric Gagne則從密爾瓦基釀酒人隊手中拿到了一份一年一千萬美金的 合約。 西雅圖水手隊以四年四千八百萬美金的價格簽下了先發投手Carlos Silva，而他也是08 年自由球員當中唯一獲得複數年合約的先發投手。 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? 是哪些要素影響到了這些合約和其他合約之間的差異?為了找出答案，我應用統計學的工 具--主要回歸分析(是這樣翻的嗎?)來檢驗去年冬季的自由球員市場。 我測試了許多種過往表現的分析標準，來找出這些守備位置的球員是物超所值還是簽了不 符實力的肥約，同時考慮了年紀因素和過去的傷病史。而我在調整過其他可能影響的變數 後也測試了有關於球員的額外價值--這也是大部分明星球員被簽下大合約的因素。而且， 我們要問的是，簽約時機會影響到薪水嗎?在十一月和十二月左右簽下合約的球員如果稍 晚再下決定會拿到比較好的待遇嗎? 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. 對球隊決定簽下自由球員來說，這些結果啟發了一套精確定義的衡量標準。我的分析導出 了一個可以解釋在年度平均薪資標準下的自由球員潮中，百分之九十二的球員間差異模型 。並且指示了一種合理的薪資尺度--而不是一系列的武斷決定做為參考。 我用各種計量方法來測定球員表現而且選定了Win Shares--這種由Bill James發展出來並 且由Hardball Times的分析家們修正過的公制變項，被設計用來提煉球員的統計資料來換 算出球員對他所屬球隊的勝利總數做出了多少貢獻。 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. 有一個關鍵的發現是薪資傾向反映出球員在最近一到四年當中最好球季的水準。 這些例子包括了Paul Lo Duca，Gagne，還有Geoff Jenkins。只要有一個表現傑出的球季 --儘管那可能是三或四年前的事情，就能讓球隊總管們冀望魔力有再次發生的可能。這種 希望讓球員的口袋飽飽。如果你把Lo Duca穩定發揮的04年球季略過不提的話，他的表現 看起來就像是薪資比他便宜百分之三十的Michael Barrett。Gagne的薪資很明顯是依照他 過去02到04年在道奇隊總共一百五十五次救援的成績來擬定，而不是他上季在紅襪隊經常 砸鍋的後援表現。而從費城人隊獲得兩年總共一千三百萬美金合約的Jenkins不僅是因為 他去年的兩成五五打擊率和二十一支全壘打才拿到這份合約，主要是因為他在05年有二十 五支全壘打還有兩成九二的打擊率。 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. 這項分析也證實了一項很多人認為的觀點，那就是投手通常比其他位置的球員更容易獲得 大合約，儘管在調整過後的win shares呈現下，前段輪值的先發投手是在食物鏈的頂端， 接著是終結者，後段先發和剩下的後援投手。但在可比較的追蹤記錄下，我們還是可以發 現就貢獻度來說，後援投手明顯的比打者拿了更多的薪資。 把二號捕手Jose Molina和後援投手David Riske做比較就可以顯示這個觀點。過去三年當 中兩位選手的win shares幾乎相同，也就是說他們的薪資應該也差不多。不過Riske的三 年一千三百萬合約以單季來算幾乎是Molina兩年四百萬合約的兩倍，總額更是有將近三倍 的差距。一種付給投手更多薪水的解釋是球隊總是想要加強他們的三號先發並且為牛棚買 保險，而打者就不適用這種解釋。也就是說三十隊中有二十多隊已經有固定先發的游擊手 ，而不是在市場中尋找，所以跟投手比起來，打者比較少隊參與競標，需求較少價格自然 比較低。 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. 今年投手市場裡的其中一條頭條新聞就是洋基隊決定以三年四千五百萬的薪資跟終結者 Mariano Rivera續約，而這也替MO加了百分之五十的薪水。擁有充沛現金的洋基隊無疑是 獎勵MO長久且穩定的生涯表現，不過更重要的是他們也提早把充滿終結者的自由市場的蓋 子給蓋上了。而這個合約的決定可能也明顯暗示了現代的終結者可能要比以往拿更多的薪 水，之後紅人跟Cordero的巨大合約可能只是個開始而已。 在今年的市場中，另外一個唯一跟其他位置不同的就是二游位置的野手。在調整過各種要 素之後我們發現，跟其他位置比起來二壘手和游擊手是比較便宜就能簽到的。 年齡對自由球員薪資的影響 球員 每年平均薪資 年齡 假設球員為28歲時可能得到的薪資 Tom Glavine 八百萬 42歲 三百八十萬 Mariano Rivera 一千五百萬 38歲 兩百七十萬 Andy Pettitte 一千六百萬 35歲 兩百六十萬 Mike Lowell 一千兩百五十萬 34歲 三百二十萬 Torri Hunter 一千八百萬 32歲 兩百萬 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. 年齡很明顯的是決定自由球員薪資的重要因素，較老的球員所得的合約長度較短而且每年 平均薪資也較低，如果Tom Glavine在28歲時的過去幾年成績跟現在42歲時一樣的話，模 型顯示他將會拿到比現在的平均每年八百萬美金再多出三百八十萬。上面的圖表秀出了今 年自由市場裡五個球員的年齡對薪資的影響。 另一個重要的要素是健康。有洋洋灑灑傷病史的球員在自由市場裡是較不受歡迎的。為了 取代傷病史我用過去五年的總出場數來做為變項，像是雙城隊的Livan Hernandez還有白 襪隊的Scott Linebrink，或是道奇隊的Jones從過去的紀錄來說都算是能夠穩定出賽的球 員。 耐力對自由球員薪資的影響 球員 每年平均薪資 耐力對薪資的影響 耐力影響的百分比 Alex Rodriguez 兩千七百五十萬 兩百六十萬 9% Jorge Posada 一千三百一十萬 一百八十萬 14% Andrew Jones 一千八百萬 一百四十萬 8% Livan Hernandez 五百萬 九十萬 18% Tom Glavine 八百萬 八十萬 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. 就另一方面來說，以芝加哥小熊隊經常受傷的後援投手Kerry Wood為例，如果他能維持同 樣的投球威力並且能像Linebrink一樣穩定出賽的話(他在過去四季分別出賽了73, 73, 73 和71場比賽)，他的價值會比現在一年平均四百五十萬多出兩百二十萬。這個理論同樣可 以應用在打者身上。如果遊騎兵的Milton Bradley的耐戰度跟Jones差不多的話，他的價 值就值一年平均七百八十萬，比現在他簽下的一年五百萬多得多。上面的圖表顯示了今年 自由市場中球員耐力對薪資的影響。 時機也會對合約價值產生一定的影響，在春訓開始之後才簽下的合約通常會獲得一定的折 扣。一個似乎可信的解釋認為高獲益的球隊總是在休季沒多久就急於補強他們最迫切需要 的位置。當月曆走到了一月末二月初時，很多球隊都對他們的關鍵需求感到滿意而剩下的 球隊就開始尋找折扣。紅雀隊最近以一年四百二十五萬的價格簽下了先發投手Kyle Lohse ，以模型的估計來看，這個較晚的簽約為球隊省下了大約二十萬。不過，根據Lohse和他 的經紀人--Scott Boras在休季期間稍早的談判認為以Lohse的資歷，過往表現，年紀和耐 力等，應該能轉換成一年平均六百二十萬美金。 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. 而統計分析中最後一個被揭露出來的變項是可量化的明星魅力。在明星的額外價值背後的 理論其實相當簡單，如果行銷大公司像是百事或耐吉願意付給明星運動員大量的金錢來推 銷他們的品牌，那同樣的理由，球員也能因為每天穿著球隊的球衣上場而創造類似的效應 。 不過衡量額外價值並不太容易，雖然分析可以提供一些洞察的角度，在對球員表現，年齡 ，耐力和位置價值作出調整後，我們可以發現一個明顯的圖像來呈現未經解釋的自由球員 市場薪資的比例分佈。根據包含變項來測量明星球員的額外效應，像是Hunter,Jones還有 A-Rod，我們可以看到自由球員市場如何衡量"非表現面"的球員面向，也就是額外價值。這 個分析指出A-Rod因為他的額外效應每年多得到九百七十萬的津貼，而不只是因為他的球 場表現，年齡，位置和耐力。而Hunter的額外價值是每年六百萬，Jones則是每年五百一 十萬。 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. 這個分析其中一個重要的結論是每一個要素的影響--球場表現，年齡，位置和耐力都和球 員的表現等級成比例。舉例來說，A-Rod有能力打155場比賽隔年就替他的所值多增加了三 百萬，以同樣的標準衡量Jones的話產值則是一百五十萬。 根據這個模型，Silva和太空人隊的二壘手Kaz Matsui是最不符身價的自由球員，Matsui 每年平均值五百五十萬，但分析顯示他只值三百萬，Silva被認為只值一年平均八百七十 萬，但他比這個數字還多拿了兩百三十萬。在尺度的另外一邊則是光芒隊的外野手Floyd ，他的薪資應該有四百九十萬，但分析指出他其實只拿到符合他身價百分之六十的薪水-- 三百萬。 而沒被簽下的自由球員價值又如何呢?模式認為三十九歲的Mike Piazza值一年三百二十萬 ，四十歲的Kenny Lofton值兩百四十萬，而四十三歲的全壘打王Barry Bonds則價值一千 兩百八十萬，不過這個估計忽略了他據傳的類固醇使用和大陪審團起訴所帶來的負面包袱 。 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. 圖三單獨呈現了各個關鍵要素對這些球員薪資的影響。 我對合約的長度執行了類似的分析，發現這五個關鍵要素也指示了合約的長度。毫無意外 的，球場表現和合約長度有正相關，球員表現的越好，合約長度就越長。也可以說明星球 員運用他們的力量來讓他們的價值得到保障。 年齡和耐力是另外的要素。年紀較大和有傷病史的選手總是得到較短，風險也較低的合約 ，唯一對位置有影響的是後援投手。在調整過各個其他變項之後，後援投手還是相對來說 會得到較長的合約。最後一個決定合約長度的要素是一個球員是否為A型自由球員。球隊 放棄了一個高順位選秀可以簽下其他隊的高等級自由球員。為了保證交易有價值，球隊會 傾向給A型自由球員較長的合約。 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. 這個分析也能用在呈現最近Johan Santana的延長合約的另一種觀點。雖然他並未接觸自 由球員市場，考慮到Santana最近的投球表現，年齡，耐力和身為最有威力的先發投手之 一的額外價值，模式認為他值一年平均兩千兩百一十萬，跟他和大都會的六年總額一億三 千七百五十萬的合約做比較，球隊每年大概平均多付了他八十萬。 這個統計分析指出了數個警訊，包含了資料只限制為去年的休季，事實上相關性和因果關 係仍未被證實，而且有些變項--像是額外球員價值的命名跟定義也有點主觀。不過這個分 析對於提供對自由球員市場運作的洞察和照亮自由球員薪資是如何簽訂上還是很有幫助的 。 -- http://www.wretch.cc/blog/randyorton 無聊碎碎唸 --

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