This is a guest post by Adam Bernfeld. He is trained as an engineer and likes
to apply his analytical nature to baseball to differentiate 「what seems」
vs. 「what is」. His interests include PITCHf/x, DIPS, the concept of
clutch, and Laura Posada.
這篇是來自Adam Bernfeld的文章。他是一名工程師，並且喜歡利用自己的專長來區分「
似乎是」與「肯定是」。他關注於PITCHf/x，DIPS，concept of clutch與Laura
Posada(Posada的老婆)。
「Statistics are like women: mirrors of purest virtue and truth, or like
whores to use as one pleases.」
-Theodor Billroth
「統計數據有時可以反映出真實性，有時卻可依照個人觀點來使用。」- Theodor
Billroth
It is true that in a vacuum, statistics are almost entirely useless. One can
manipulate the numbers to prove any side of an argument. They can however
provide illumination in instances where what seems may differ from what is.
For example, a few years ago before John Dewan wrote the Fielding Bible, a
lot of Yankee fans truly did believe that Derek Jeter was a good defensive
shortstop because he both seemed like a good fielder, and our broadcasters
told us that he was a good fielder. Similarly, watching a Yankee game, one
could be led to believe that Chien-Ming Wang possesses the best sinker in all
of baseball. After all, it is 94 miles-per-hour and looks like it is dropping
off a cliff. Surely no one's could be better, right? Well, using PITCHf/x
data, I hope to crown the true 「Sultan of Sink.」
事 實上在個案中，統計數據幾乎是完全沒有用的。任何人都可以巧妙的運用數字，甚至
舉例子來解釋似是而非的論點。例如，幾年前在John Dewan的著作Fielding Bible完成之
前，許多洋基迷確信Derek Jeter是一名防守優異的游擊手，因為他看起來似乎是個好的
守備員，播報員也告訴我們他是一個好的防守者。同樣地，觀賞洋基隊的比賽時，任何人
都可能認 為王建民是大聯盟中最棒的伸卡球投手。畢竟他的伸卡球有94英哩的速度，而
且看起來就像從懸崖掉下來似的。肯定沒有人能投的更棒，對吧?好吧，運用 PITCHf/x的
資料，我希望能找出真正的「伸卡球之王」。
For those new to PITCHf/x, it is a system developed by Sportsvision in use by
Major League Baseball that uses two cameras to measure the position of the
baseball between the pitcher's hand and home plate, which can be used to
determine various parameters about each pitch including velocity and break
(for a more thorough introduction to PITCHf/x, refer here and here).
對於PITCHf/x不熟悉的人，它是一套由Sportsvision所發展的系統，並且被大聯盟所採用
，這套系統使用了兩部攝影機測量球從投手出手到本壘版之間的位置，可以測定出每一球
的速度與變化量等等數值(詳細介紹請參考這裡和這裡)。
Using PITHf/x data compiled by Josh Kalk of The Hardball Times, detailed
pitch information can be seen for individual players or in a searchable
database. For this study, I will compare the speed, horizontal break and
vertical break of the average signature pitch of baseball's prominent
sinkerballers from the 2007 season. Based on reputation and ground ball
rates, I have chosen a test group that includes: Chien-Ming Wang, Fausto
Carmona, Aaron Cook, Roy Halladay, Tim Hudson, Derek Lowe, Sergio Mitre,
Brandon Webb and Jake Westbrook.
利用Hardball Times網站的Josh Kalk所蒐集的PITHf/x資料，詳細的投球資料可以從個別
球員或檢索數據庫中 查看。在本次的研究中，我將比較2007年球季大聯盟中主要的伸卡
球投手的球速，水平變化與垂直變化的平均值。基於名氣與滾地球比例，我挑選了包含王
建 民，Fausto Carmona，Aaron Cook，Roy Halladay，Tim Hudson，Derek Lowe，
Sergio Mitre，Brandon Webb與Jake Westbrook。
http://gary711.tw.googlepages.com/20080515_table1.png
Note in the chart above that the values for break represent the number of
inches that the pitch moves compared to a pitch thrown without spin, or,
compared to a straight pitch under only the influence of gravity. The
negative numbers for horizontal break indicate that the pitch moves inside to
right-handed hitters. The positive values for vertical break indicate that
the pitch crosses the plate higher than a pitch without spin would have. This
may seem counterintuitive as we are talking about sinkers, but in reality
sinkers are thrown with backspin and do rise (resist dropping actually),
albeit much less than a 4-seam fastball, so they do in fact appear to sink. A
4-seam fastball is gripped across the seams resulting in more backspin than a
sinker (or 2-seam fastball) which is gripped along the seams; the more
backspin, the larger the positive vertical break. For comparison, Joba
Chamberlain's fastball has a vertical break of 11.42 inches, compared to the
average vertical break of 4.66 for our sinkerballer group.
注 意到上圖中的變化量(break)是指與沒有旋轉的球或是只受重力影響的直球比較之下的
移動量。水平變化中的負數代表球往右打者移動。垂直變化的正數則代 表伸卡球經過本
壘版時的高度比沒有旋轉的球來的高。這似乎和我們所談論的伸卡球相反，但是事實上伸
卡球是反轉的而且會上飄(實際上是抵抗落下)，儘管跟四 縫線速球相比少得多，所以看
起來會下沉。由於四縫線快速球的握法跨過縫線，所以與沿著縫線握球的伸卡球(或是二
縫線速球)相比會造成較多的反轉;反轉越 多，正向的垂直變化越大。相較之下，Joba
Chamberlain的快速球有11.42吋的垂直變化，而我們的伸卡球投手群平均變化量則是4.66
吋。
The chart above can be shown graphically by plotting horizontal break on the
x-axis and vertical break on the y-axis with pitch speed represented by dot
size. In this graph, the lower right hand corner, the point (0,0), represents
a pitch thrown without spin.
上圖以圖形化顯示，X軸代表橫向變化，Y軸代表垂直變化，圓點的大小則代表球速。在這
張圖中，越接近右下角(0,0)這點，表示球的旋轉越少。
http://gary711.tw.googlepages.com/20080515_chart1.png
In hopes to build some sort of consensus as to who possesses the best sinker,
I used the three PITCHf/x values (speed, horizontal break, vertical break) to
create a z-score (also called a 「standard score」) which is a statistical
quantity used to combine multiple values measured on different scales. I then
ordered the average z-score of each pitcher from high to low to rank the
pitcher with the best combination of speed and break. Think of this as an
index of the 「stuff」 on the pitcher's sinker, or a 「sinker-stuff index」.
This value appears on the chart below alongside each pitcher's groundball to
flyball ratio (GB/FB), swing and miss (S&M) percentage, fair ball (FB) hit
percentage, and fair ball extra base hit (XBH) percentage. All of these
values are for sinkers only, except GB/FB which is the rate for all pitches
thrown regardless of type.
為了找出誰是最佳的伸卡球投手，我使用了三個PITCHf/x數值(速度，水平變化，垂直變
化)以建立Z值(又 稱為「標準值」)，這個統計值結合由數個標準測量出來的數據。我將
結合了每位投手的球速與變化量的平均Z值由高到低排列出來。我們可以將之視為「球威
」的 指標。這個值與投手的滾飛比(GB/FB)，揮空(S&M)率，球被有效擊中(FB)的比率，
與球被有效擊中形成長打(XBH)的比率一同列在下 圖中。除了滾飛比(GB/FB)以外，所有
的這些數據都是只統計伸卡球。
http://gary711.tw.googlepages.com/20080515_table2.png
The results of this study are interesting. While throwing one of the harder
sinkers in the league (second only to Fausto Carmona), Chien-Ming Wang's
sinker actually sinks less than any other member of the test group. This is
certainly a surprising observation. In fact, his sinker also has the lowest
horizontal break, causing his sinker to rank 8th out of 9 in my sinker-stuff
index. This certainly manifests itself in his below average groundball to
flyball ratio and sinker swing and miss percentage. Remarkably however,
compared to the test group Wang has the lowest percentage of hits off of
sinkers, and by far the lowest percentage of extra base hits off of sinkers.
這 個研究的結果很有趣。雖然王建民能投出大聯盟中速度最快的伸卡球之一(僅次於
Fausto Carmona)，但是事實上他的伸卡球和其他的研究對象相比下沉幅度的比較小。這
無疑是一個令人感到意外的發現。王建民的伸卡球水平變化量最小，也使得 他的伸卡球
球威在九個人中排名第八。這也顯示在低於平均的滾飛比與伸卡球揮空率。然而與研究對
象的其他投手相比，很顯然的，王建民的伸卡球擁有最低的被有 效擊中率與被長打率。
While some may chalk these low hit percentages up to luck, it appears that
something deeper may be happening here. Finally though, the stats are
pointing towards something that we already believed to be true. What seems
agrees with what is, and that is the fact that Chien-Ming Wang rarely allows
a hard hit ball off of his sinker. Why then, is his sinker so successful in
spite of the fact that it moves so much less than those of his peers? Maybe
my methods are all wrong (I hope not). Maybe pitch speed is more significant
than pitch break (possibly). Maybe the ease of his delivery, which also
includes a pronounced, varied hesitation, has a great effect on hitters'
timing (possible). Maybe Wang's defense is better at turning batted balls
into outs than the others on this list (unlikely). Maybe the DIPS people are
right and hit percentages are no more than statistical variations (possibly,
although I believe that DIPS applies more loosely to sinkerballers). Maybe it
is a combination of all of these factors or even something that I have not
thought of (likely), so please feel free to throw out explanations of your
own.
當有些人將 這些較低的有效擊中率歸因於好運時，也許還有些東西需要討論。最後雖然
統計資料指出某些我們相信的事是確實的。事實上王建民很少備有打有效擊中他的伸卡
球，儘管變化幅度不如其他人，為什麼他伸卡球仍然投的如此成功?也許我的評估方法全
部都錯了(我希望不是)。也許球速比變化幅度更為重要(有可能)。也許 他從容不迫的投
球影響了打者的揮棒時機(有可能)。也許在防守方面，王建民在將被擊出的球轉換成出局
數上比其他人厲害(不大可能)。也許強調DIPS的人 是對的，而被打擊率只是統計變數而
已(有可能，雖然我相信DIPS運用在身卡球投手身上比較不嚴謹)。也許是所有因素的組合
，或是還有我沒有考慮到的地方 (不大可能)，所以請隨意的提出你的見解。
Regardless of the reasons, I am glad that Wang is a Yankee as he gives us a
very good chance to win once every five days. While his low ranking in my
sinker index does not correlate with his outstanding results, at the end of
the day I'll always take the results over the 「stuff」. Though after much
machination, I have not definitively proved where Wang's sinker ranks amongst
his brethren, but I hope that this was interesting and informative, and maybe
allows you to view the game and the sinker in a different light the next time
the Wanger takes the hill.
不 管這些推論如何，我很高興王建民是洋基球員，並且有很大的機會每五天能贏一場球
。雖然他在我的伸卡球指標中排名較低，但是這和他出色的表現一點關係也沒 有，最後
我會以成績取代「球威」。儘管經過了一連串的比較，最後我仍然沒有證明王建民的伸卡
球在眾伸卡球投手中的排名，但是我希望這次的研究是有趣與有益 的，也許能讓你在王
建民下次上場時從不同的角度觀賞比賽。
http://riveraveblues.com/2008/05/12/wang-the-sultan-of-sink-2769/