[外電] 總教練應該保留挑戰權嗎

[kobec (水桶工程師)]

Should Managers Save Their Challenges?
MAY 30, 2017 BY KOLYA ILLARIONOV
文章來源：https://goo.gl/BmZZyZ

<懶人摘要>
這是一篇差不多半年前在The Hardball Times 的文章，討論總教練使用挑戰權的時機。
作者利用Leverage index(LI)的概念，提出一個修正後的統計因子LI-7，這個統計量
主要著重於單場比賽中每個Play的重要性，與傳統的LI是衡量每個Play相對於許多比賽
類似條件下的重要性有些差異。

根據MLB給予總教練挑戰權後獲得的數據分析後發現，MLB裁判誤判的機率其實不高，
當比賽接近尾聲時，誤判率與前幾局的差異也不大。因此作者的結論是認為，只要總教練
認為有誤判的可能，就要盡可能的挑戰，挑戰越多次越好。




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In the seventh inning of an otherwise unremarkable May 9, 2015 game against
the Texas Rangers, Tampa Bay Rays manager Kevin Cash received a standing
ovation, a gesture of appreciation usually reserved for managers ejected
after a colorful, face-to-face tirade against a vilified umpire. But Cash had
done no such thing. He had just challenged a call, and for the first time in
12 attempts that year, he succeeded in having the call overturned.

2015年五月九號，一場平淡無奇的比賽到了第七局，光芒隊的總教練Kevin Cash 
獲得全場觀眾起立歡呼致敬。一般來說，總教練要能獲得這樣的殊榮，多半得與 
執法裁判面對面激烈爭執並被驅逐出場才行。但Cash並未這麼做，他只是挑戰了 
裁判的判決並成功使裁判改判。之所以能獲得全場起立全因這次挑戰成功是他該年
十二次挑戰裁判判決以來首次成功。








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A refresher on the rules: Both teams’ managers start the game with one
challenge, and receive another if their first challenge is successful.
Beginning in the eighth inning, a manager out of challenges can prompt the
umpire crew chief to initiate a review of a call. As a result, the final few
innings see, on average, 39 percent more challenges than the first seven,
though the number of overturned calls increases only marginally.

讓我們複習一下規則：兩隊的總教練在比賽開打後都有一次挑戰的權利，當第一次
挑戰成功後將可獲得第二次挑戰的權利。八局開打後，若某隊總教練已經用盡挑戰
權，則可以提醒裁判長能否重新檢視判決。這項規定導致平均而言，最後幾局的挑戰
次數比前七局多出了39%，但改判的次數卻沒有多出多少。

https://imgur.com/a/B7tMd







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Until 2014, there was no way to overturn bad calls. Once manager challenges
and instant replay were introduced, teams had a way to appeal those. The
strategy behind deploying challenges hasn’t been scrutinized–except when it
goes wrong. In replay’s inaugural month, Giants skipper Bruce Bochy lost a
challenge on a close play at first base, and was then unable to challenge a
not-so-close play at the plate later that inning. Cash made (small) waves for
challenging any call that looked close, without consulting a bench coach
looking at video, and lost his first 11 challenges of the 2015 season.

2014年之前，並沒有任何方法可以更改裁判錯誤的判決。自從挑戰權規定上路後，
一旦總教練發起挑戰，就會即時重播關鍵判決，這制度使得球隊有機會能針對這些
有疑慮的判決進行申訴。但球隊並未事先研究提出挑戰的策略，只能從錯誤中學習。
在重播輔助判決上路的第一個月，巨人隊的教練Bruce Bochy在挑戰一個一壘相當接近
的判決失敗後，使得它們失去挑戰該局後續發生在本壘附近一個顯而易見判決的權利。
Cash 故意不事先諮詢負責看影片的首席教練，直接憑直覺挑戰那些看起來很接近
的判決，這導致他在2015年球季開打後的前十一次挑戰都以失敗收場。




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What’s the optimal strategy? Challenge at the first opportunity, or wait for
a crucial moment?

那怎樣才是最佳的策略呢?
在第一次有機會挑戰時就使用，還是等到關鍵時刻才出手呢?

For the start of the 2017 season, Major League Baseball fine-tuned the rules
for instant replay. The headline was a new 30-second time limit for a manager
to decide whether to challenge a call, and a two-minute limit for umpires to
decide on the call. Not receiving as much attention, but arguably more
strategically significant, was the rule change pushing umpire-initiated
reviews to the eighth inning; in prior years, it had been the start of the
seventh.

在2017年球季，大聯盟調整了即時重播的規則，其中的要點是總教練只有三十秒
決定是否提出挑戰，以避免過去經常看到總教練慢條斯理地走入場中似乎要提出
挑戰，但實際上卻是等待其他教練觀看重播來確定是否為誤判。同時也規定裁判
必須在兩分鐘內決定判決結果。
雖然這次調整沒有獲得太多關注，但新規則同時也將裁判可以主動提出重播判決
的時間從原本的第七局改成第八局後，這項更動將會改變總教練提出挑戰時的策略。
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While subtle, this inning change should shift manager strategy a bit,
increasing the value of their challenge. As described by Oliver Roeder at
FiveThirtyEight, the challenge is similar to an American-style financial
option that now expires at the conclusion of the seventh inning, rather than
the sixth. In theory, managers should now be slightly more hesitant to use
their challenges, for fear of needing them later. In practice, challengeable
calls occur so rarely (though perhaps Earl Weaver disagrees) that any call
with a decent chance of being overturned deserves a challenge.

這次調整讓總教練提出挑戰的策略出現微妙的變化，也讓挑戰權更有價值。
如同Oliver Roeder在538網所提到的，挑戰權就像美式期權*一樣，到期日訂在七局
，而非第六局。理論上在新規定上路後，總教練隊挑戰權的使用應該會稍稍變得猶豫，
避免在之後遇到更關鍵的判決時已經沒有挑戰權可供使用。實際上，能被挑戰的
判決次數並不多(雖然Earl Weaver未必會同意)，所以只要任何判決有機會被推翻
都值得提出挑戰。

*:美式期權是金融商品的一種，指在過期日前都可任意使用的期權。
  還有一種稱作歐式期權，只能在到期日當天行使。


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Since 2014, there have been 4,090 challenges in 14,574 games, of which 2,029
have led to overturned calls, a 49.6 percent overturn rate. A look at the
situations in which calls were overturned during the 2014 season showed that
of the successful challenges, the average gain for the challenging team was
0.65 runs, or roughly a 6.5 percent increase in win expectancy on average.
However, this change can be leveraged if it comes at a particularly impactful
moment in the game. An overturned call at first base with two outs and the
bases loaded in the seventh will matter a whole lot more than for instance,
the same call with the bases empty.

2014年至今，在14574場比賽中共出現4090次挑戰，其中有2029次改判成功，改判率
為49.6%。仔細分析2014年一整年出現改判的判決中，挑戰成功的球隊平均獲益0.65分，
或是多了大約6.5%的獲勝機率。我們還可以將這些挑戰依照比賽當下的關鍵程度
更進一步的細分，例如同樣是發生在一壘的改判，若發生在第七局兩出局滿壘的
情況，其重要性就遠高於壘上無人時。





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The leverage index (LI) attempts to quantify the importance of such a play by
looking at the change in win probability given the range of outcomes for a
play relative to the average situation. For example, a scenario with a 3.0 LI
will have thrice the impact on a game as an average scenario. Jesse
Wolfersberger’s terrific analysis here at THT of challenge situations used
LI as a proxy for importance. Wolfersberger set up the framework of how to
evaluate challenge decisions, but his article was written before we had any
actual data. Now that we have data, we can figure out how managers can
optimize their challenging strategy. Leverage Index is still a great lens to
look through for this endeavor, but it doesn’t consider how likely another
important situation is to arise.

關鍵性指數(LI)試圖比較每一個Play發生後，相對於一般情況下，對於獲勝機率
的影響，藉此定量描述每一個Play的重要程度。例如在3.0 LI的情況下，該Play
對於比賽的影響是一般情況下的三倍。Jesse Wolfersberger在THT有一篇相當好的
分析，他是利用LI來討論使用挑戰權的時機。他的文章著重於評估何時該使用挑戰權，
但當他在撰寫文章時，並沒有真實資料可供使用。而本篇文章因為已經有了挑戰制度
上路後的數據，因此我們可以釐清總教練該如何制訂最佳的挑戰策略。
針對這個議題，LI仍然是個很好的工具，可惜的是LI並未考慮發生另一個同樣關鍵
Play的機率。
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A Modified Leverage Index
A more useful measure of the importance of a situation for the purpose of
replay requires a new concept of leverage index. Rather than compare the
variability of a situation relative to the average situation in any game, it
makes more sense to compare it to the average situation from that point
onward in that game. To do this, I’ve created a modified leverage index — I
’ll call it LI-7 — which measures the variability of a situation relative
to all those that follow it, up through the bottom of the seventh (the last
play where a challenge holds any value).

一個改良的關鍵性指數
為了分析重播輔助判決，我們需要一個更有用的統計量來了解每個局面的重要性，
也就是需要一個新的概念來討論關鍵性指數。過去的LI希望突顯某個Play相對於
任何比賽中一般情況的重要性。但針對重播判決這個問題，考慮Play相對於該場
比賽的重要性會比相對所有比賽的重要性還要合理。因此，我們提出了一個修正的
關鍵性指數，稱作LI-7。
這個統計量描述在爭議出現時，該局面相對於接下來到七局結束前的所有比賽內容
的重要性。
(因為七局過後即可促請裁判長使用重播輔助，因此總教練的挑戰權價值就沒了)

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LI-7 should be thought of as a near-sighted, in-game measure of importance,
whereas the traditional leverage index is better equipped to compare
importance over multiple games. LI-7 is defined for a particular situation as
the average change in win probability for the play, divided by the average
change in all subsequent plays up through the last out of the seventh. (For
example, a bases loaded, no-out situation while up two runs in the sixth will
have a LI below 1, as the leading team is very likely to win either way.
However, the LI-7 value will be above 2, as this situation is going to be one
of the most important remaining challengeable situations.)

我們應該將LI-7視作一種測量單場比賽重要性的統計量，傳統的LI則適合描述該
局面相對於許多場比賽的重要性。LI-7的定義是為了某個特定的情況，也就是該球
造成的獲勝機率改變量除以接下來直到七局結束前的獲勝機率改變量。舉例來說，
六局滿壘無人出局的情況，若主隊領先兩分，則LI會小於1，因為不論這個Play的結果
為何，對主隊的獲勝機率改變都不大。但同樣的情況LI-7卻會大於2，代表在這個情況
，挑戰權變得相當有價值。




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For bullpen/pinch-hitting decisions, the analog of LI-9 is more useful (the
denominator being the average change in win probability for all plays until
the end of the game), but that’s a different article. For comparison’s
sake, these are the LI-7 charts for a no-out, nobody on base situation, and a
two-out, bases loaded situation.

若是為了牛棚的使用或更換代打的考量，LI-9會更為有用(分母就改成該Play至整場
比賽結束前，平均獲勝機率的改變量)，但這是另一個課題。
在此處附上無人出局壘上無人以及兩出局滿壘時，LI-7的表以供參考。
https://imgur.com/a/B7tMd

https://imgur.com/a/B7tMd








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Given the LI-7 value of a situation, the inning, and the probability of a
call being overturned, we can determine if a call is worth challenging. Since
the probability is unknown, we’ll express it as the confidence of the
manager in the call being reversed. The inning determines the expected number
of future challenges; the loss of a challenge has a higher opportunity cost
in the first than the seventh. To find the total number of possibly
challengeable calls, we’ll take the average of the seventh inning onward,
where challenges occur upon request.

當知道各情勢下LI-7的數值、剩餘的局數和挑戰判決成功的機率後，我們就可以
估計這個判決是否值得挑戰。由於改判的機率無法被量化，因此我們只能用總教練
對於該判決有無可能改判的信心度來代替。當前的局數表示接下來可能出現挑戰
次數的期望值。若在第一局就失去挑戰權的話，付出的代價會比第七局才失去還大。
為了知道可能出現挑戰的判決次數，我們計算了七局前出現挑戰的平均次數。






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From 2014-16 in the late innings, 7.87 challenges occurred per 100 innings;
they were overturned at a 40.4 percent rate. For a challenge to be
worthwhile, it must therefore have an expected value (probability of being
overturned multiplied by LI-7 plus any future challenges) greater than that
of any future successful challenge. On average, 0.0026 challenges are
overturned per out (for both teams at the plate, with the challenge falling
in favor of the team challenging). Both teams thus start the game expecting
to overturn 0.11 calls, a number that drops linearly over the course of seven
innings to zero. This generates the following cheat chart for challenges,
similar to the one constructed earlier by Wolfsberger, but which uses LI-7
instead of the leverage index.

從2014到2016球季，在比賽後半段平均每100局就會出現7.87次挑戰，而最後的
改判率是40.4。透過期望值的計算，我們可以了解這些挑戰是否值得。
(期望值的計算是改判的機率乘上LI-7加上任何未來的挑戰)
若期望值大於未來任何成功的挑戰，則表示這次的挑戰是值得的。
平均來說，每個出局數會出現0.0026個改判(不論主客隊)，因此兩隊在比賽開始
前，對於挑戰成功的期望值都是0.11(0.0026*42，42是兩隊到七局結束時的總出局數)，
這個數字會隨著比賽開始而線性遞減，直到七局結束時歸零。因此我們得到下面這張
簡易的圖，這張圖和Wolfsberger文中的圖相似，只是這裡使用LI-7而非LI。
https://imgur.com/a/B7tMd
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Given the three years of data available, the chart favors challenging much
more than previously thought. Umpires turn out to be really good at their
job, calling at least 99.6 percent of calls correctly. There is support for
that in this graph, but also in the first graph presented above. In it, we
can see that there is no evidence that calls made later in the game are more
likely to be overturned; there is nothing to suggest any umpire fatigue or
inconsistency. A call made in a late, close game is as likely to be missed as
any other call, implying that, as a whole, umpires aren’t clutch or
unclutch.

當擁有三年的資料後，這張圖對於挑戰情況的描述比之前的想法更為理想。
結果證明了裁判的表現其實相當良好，判決得準確率高達99.6%。不論是這張圖
或是第一張圖都支持這個論述。從第一張圖中我們可以看到不論是比賽前期或後段，
裁判的誤判率都沒有顯著改變，意即裁判並未因疲勞而出現不一致的判決。
在比賽後段或比數相近的比賽，裁判出錯的機率和其他條件下相同，也就是說，
整體而言，裁判的重要性在這些情況下並未特別突出。




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Going back to the initial question, if there is at least a one-in-five chance
of the challenge succeeding (LI-7 rarely falls below 0.4), it will be worth
doing regardless of situation, as there is little chance that a better
opportunity for a challenge will present itself. In short: a manager’s
optimal strategy is to challenge as much as he can. Each one nudges the odds
of victory, just a little bit, in his team’s direction. In other words,
Kevin Cash’s seemingly brazen strategy is right on the money.

回到我們最初的問題。
如果挑戰成功的機率(信心)至少有兩成，由於LI-7很少低於0.4，因此不論在何種
情況，都值得發起挑戰，因為要遇到更好的挑戰機會的機率並不高。
簡單的說，對總教練來說最好的策略就是盡可能的挑戰，越多次越好。每一次的
挑戰都能提高一點點獲勝的機率，換句話說，Kevin Cash表面上厚顏無恥的挑戰策略
其實才是最正確的。







--
※ 發信站: 批踢踢實業坊(ptt.cc), 來自: 140.115.36.223
※ 文章網址: https://www.ptt.cc/bbs/MLB/M.1512440462.A.D31.html
※ 編輯: kobec (140.115.36.223), 12/05/2017 10:21:32
※ 編輯: kobec (140.115.36.223), 12/05/2017 10:21:50
※ 編輯: kobec (140.115.36.223), 12/05/2017 10:23:55
推 KBking: 推
推 re920113: push
推 ACRM2929: 推
推 alpacaHong: 優文推
推 monkeyken: 推……好文
推 bertrend: 美式期權不是經濟學的名詞 是金融商品的一種
感謝指正補充~
推 Aaronko: 反觀膽小吉
推 Kyosuke: 感謝優文分享
推 zzxxcc88: 推
※ 編輯: kobec (140.115.36.223), 12/05/2017 13:13:00
推 vancanucks: 囧拉迪表示
推 pneumo: 推
推 MrNeverDie: 推推
推 Sechslee: 先推再看
噓 corlos: 囧拉迪：不用
推 heacoun: 淚水在戰壕裡，囧拉迪~~~
推 MaxScherzer: 用心推
推 zz8940: 唉吉總
推 aborwang: 推
推 ypw: 既然8局後的接近判決都是關鍵  怎麼不乾脆8局開始兩隊各多1次
推 peter0902: 現在不就是8局之後無限嗎
的確 就我的理解是八局後總教練若有疑慮可以逕行要求裁判進行電視輔助判決
所以相當於有無限次挑戰權 但需要受到裁判判斷是否為接近判決方可挑戰
若只是在八局後兩隊各多一次的話 一方面可能爭議判決太多導致不夠用
或也可能變成總教練恣意的使用挑戰權(反正不用白不用)反而拖累比賽進度

推 Werth28: 好文推
推 jeromeshih: 推
※ 編輯: kobec (140.115.36.223), 12/06/2017 11:04:02
推 ljeff83: 中間插了光芒那段特別好笑