Extra Points －A new way to understand the NBA's best scorers
分數剩餘－了解NBA最佳得分手的新方法
LeBron James is the best player in the world. That may be obvious to anyone who has watched basketball over the past few years, but for some reason it's hard to find many statistics to support this claim. Back when Michael Jordan ruled the NBA, he would commonly lead the league in points per game; Chamberlain and Russell put up insane rebounding numbers; Kareem Abdul-Jabbar is the league's all-time leading scorer.
LeBron James是現役地表最強球員。對任何近年有在看籃球的人來說這是理所當然的事，但奇怪的是很難找到很多數據來支持這項論點。在過去Michael Jordan統治NBA時，他一直都是聯盟得分王；Chamberlain和Russell往往抓下誇張的籃板數；Kareem Abdul-Jabbar是聯盟史上累積得分紀錄保持者。
James recently joined those giants as one of the five NBA players to win four MVP awards. Despite that impressive feat, his dominance is not reflected in conventional basketball stats. Somehow a vast majority of the game's most oft-cited statistics obscure the greatness of the game's greatest player. James shines in terms of Win Shares and PER, but those stats only vaguely describe what makes him so good. They fail to highlight any particular element of James's performance. In fact, many of our most common metrics imply that other players are more effective or more efficient than James.
James最近成為聯盟第五位獲得第四座MVP的球員，使自己成為和這些神獸平起平坐。除了這項傲人的事蹟，他的統治力並沒有反應在傳統數據上。不知為何，絕大多數最常被引用的數據掩飾了當今球場最優秀的球員的統治力。James在WinShares和PER（譯按：WS為球員為球隊的貢獻值；PER為球員的效率值）的表現相當耀眼，但這些數據只有模糊的解釋James厲害之處。它們無法標明任何James表現內容的明確要素。事實上，相當多常見的衡量標準顯示其他球員比James來的更有效率及更有影響力。
Last season, DeAndre Jordan led the NBA in field goal percentage. However, consider the following ridiculous statistical couplet:
上一季，DeAndre Jordan在投籃命中率上領先全聯盟。然而，思考一下下面兩個誇張的數據。
No player scored more points close to the basket than LeBron James last season.
上一季LeBron James的籃下得分是全聯盟最多。
No player converted a higher percentage of his shots near the basket than LeBron James last year.
上一季LeBron James的籃下命中率是聯盟最佳。
Think about that. Not only did he outscore every player in the entire league within the NBA's most sacred real estate, he converted his shots at the highest rate, too. As a whole, the NBA made 56 percent of its shots in that area last season; James made a staggering 72 percent of his 637 attempts there. Despite this unreal scoring prowess, James trails inferior interior scorers in field goal percentage.
動腦想想吧。他不但在NBA最神聖的禁區得到比聯盟中的任何球員更多的分數，而且還保有聯盟最高的命中率。整體而言，聯盟上一季的籃下命中率是56%；在James 637次的籃下出手中，他的命中率是驚人的72%。儘管有這電動般的得分本領，James的命中率比較差的禁區球員還更低。
Few people would argue that Jordan is a more efficient scorer than James, but according to field goal percentage, that's exactly what he is. Jordan led the NBA in that category, shooting 64 percent, while James managed only 57 percent. Although it can be useful to know which players convert field goal attempts at the highest and lowest rates, that doesn't really tell us much about scoring effectiveness.
很少有人去主張Jordan（譯按：指的是快艇隊DJ，不是MJ）是個比James更有效率的得分手，但從命中率籃看這卻是事實。Jordan的64%命中率領先全聯盟，而James只有57%。雖然了解球員們的命中率是高是低是有用的，但這無法告訴我們真正的得分效率。
Some players, like Steve Novak, shoot lots of 3s; others, like Kevin Garnett, rely on 18-footers; DeAndre Jordan works almost exclusively in the paint. Players like Jordan almost always lead the league in field goal percentage. The problem is that while NBA players have different roles and different shooting habitats, almost all of our shooting evaluations ignore that.
有些像Steve Novak的球員，投一堆三分球；又其他的像Kevin Garnett主打18呎中距離跳投；DeAndre Jordan則主要在禁區裡討生活。像Jordan這類球員幾乎都是聯盟的命中率領先者。問題在於當每位NBA球員的角色且投籃習慣不同時，我們的投籃數據大多都忽略它。
Anybody who has ever played H-O-R-S-E can tell you that some shots are easier than others; a layup is easier than a free throw, which is easier than a corner 3. This basic tenet is almost entirely overlooked by our most popular shooting metrics. Similarly, NBA players are all special, and over the course of a season each player generates his own unique "constellation" of shot locations. This is also overlooked; the graphic above demonstrates that the LeBron James constellation is considerably different from the DeAndre Jordan constellation.
有玩過H-O-R-S-E的人都會告訴你有些投籃當然比其他的容易。上籃比罰球容易，而罰球比角落三分簡單。這個基本原則幾乎完全被我們最依賴的投籃數據給忽略。同樣的，NBA球員們都是特殊的，而整個球季下來每位球員都有他的「特有投籃區域」。這點當然也被忽略了。上面的圖表顯示出LeBron的投籃區域和DeAndre Jordan的投籃區域有著巨大的差異。
We can improve our shooting metrics by accounting for court space and the unique natures of players' shot constellations.
我們可以藉由展示球場不同區塊和每位球員的獨特投籃區域，將投籃數據再進化。
At the end of the season, James's average shot distance was 11 feet; Jordan's was 2.8 feet. Essentially, through the hazy lens of FG percentage, James is penalized for having a jump shot, while Jordan is rewarded for not having one. Despite being a very good 3-point shooter, a good midrange shooter, and the most dominant interior scorer in the game, James trailed players like DeAndre Jordan and JaVale McGee in a crucial scoring metric.
上一季結束，James的平均投籃距離是11呎；Jordan的則是2.8呎。基本上，透過投籃命中率這不清不楚的數據，James因跳投而得利，反之，Jordan因沒有投任何跳投而有利。儘管他是個優質三分射手、好的中距離射手和球場上最優秀的禁區得分手，James在這個重要的命中率數據上輸給DeAndre Jordan和JaVale McGee。
What the hell?
搞屁阿！
While it's tempting to claim that our stats are "advanced" now, think about these two basic questions:
- 1. Who is the best shooter in the NBA?
- 2. What metrics would you use to justify your answer to this question?
雖然稱呼我們的數據為「進階數據」是件誘人的事，先想想這兩個基本問題：
1. 誰是NBA現役最強得分手？
2. 你用什麼去來證明你的答案是對的？
When it comes to shooting stats, one would think there would be a spreadsheet somewhere on the Internet that delineates "great shooters" like Stephen Curry and Kevin Durant near its top, and "bad shooters" like Monta Ellis and Josh Smith at the bottom. But there's not. We still rely on hunches and vague reputations to make our assertions about "pure shooting" skill in the NBA. Amid the chatter of an ongoing revolution in basketball statistics, the notion that we still can't effectively measure shooting ability is troubling — but it's also correctable.
當提及投籃數據時，人人都可能想有某個網路上找到的表格描述著「優質射手」像Stephen Curry和Kevin Durant和「劣質射手」像Monta Ellis和Josh Smith。但沒有這東西。我們依然依靠著直覺和曖昧不清的名聲來主張NBA中「純粹的投籃」技巧。在籃球數據進化的爭論中，我們依然無法有效的衡量投籃能力這個概念，進而造成許多困難。但這也是可以修正的。
The issue is, almost every NBA player's overall FG percentage will always have more to do with where he shoots than how well he shoots.
問題在於幾乎所有NBA球員的投籃命中率和投籃位置的關聯強於投得多好。
The inconvenient truth is that every NBA field goal attempt has its own level of difficulty that's determined by several factors, including the shooter's location on the court. Even though previous approaches have mostly ignored this thorny reality, thanks to relatively new forms of NBA data we can now begin to understand it.
不願面對的真相是每個NBA的投籃出手有著屬於其的難度，其受射手的位置等幾個因素影響。即使前面幾個方法都忽略這個麻煩的事實，由於相對來說更新的NBA數據，我們現在可以開始去理解它。
Last year, NBA players took just about 200,000 shots. The league's collective shot chart reveals the spatial nature of the NBA's average shooting efficiency. By itself, the chart shows the stark relationship between court space and expected points per shot — that's why 3-point shots are rapidly increasing in popularity while midrange shots are diminishing.
去年，NBA球員大約投了200,000球。整合的聯盟出手圖表顯示出NBA平均投籃效率的空間因素。根據圖表顯示球場位置和每次出手的期望分數的顯著關係。這也是為什麼投三分球快速流行而中距離投籃慢慢消失。
But this chart also provides a useful baseline that we can use to evaluate individual shooting performances. By overlaying players' shot constellations, we can estimate the expected total number of points that an average NBA shooter would produce, based on where he took his shots; then we can compare a particular player's actual yield against it.
但這個圖表也提供我們一個可以用來衡量個人投籃表現的有用基準。將球員的投籃區域圖覆蓋於其上，我們可以基於他的投籃位置來估計一位平均的NBA射手所能得到的分數。然後我們可以比較這位球員的真實得分。
For example, last season LeBron James attempted 1,354 shots. Using that league-wide baseline as our guide, if an average NBA shooter attempted this exact same set of 1,354 shots, he would produce a yield of 1,397 total points.
舉例而言，上一季LeBron James出手1,354球。以聯盟基準來看，假如是一位NBA平均的球員出手這1,354球，他總共會得到1,397分。
James actually yielded 1,628 points from that constellation, 231 more than expected. No player accumulated more points than expected than James. By accounting for the fundamental relationship between court space and NBA shooting averages, we can see which players scored the most and least points above expected levels in the NBA. And we can figure out which players are actually the most effective scorers in their native shooting habitats.
James在那些投籃位置實際上得到了1,628分，比期望值要再多231分。沒有球員的期望值以上累積得分比James多。藉由說明球場位置和NBA投籃平均值的重要關係，我們可以看到哪些球員得分和NBA平均得分差值的最高跟最低。也可以依球員的投籃習慣來搞清楚哪位球員是真正的最有效率得分手。
Along with Ashton Shortridge, a professor at Michigan State, I did this analysis for every player who took at least one shot during the 2012-13 regular season. We refer to the difference between a player's actual point yield and his expected yield as ShotScore. For good shooters this number is positive; for bad shooters it is negative.
和一位Michigan州大的教授Ashton Shortridge一起，我作了至少投了一球的每位球員在2012-13的投籃分析。我們將球員實際得分和期望得分的差距值稱為ShotScore。好的得分手的數字會是正值，反之差的得分手是負值。
James came out on top, and is joined in the top three by a pair of elite shooters.
Highest ShotScores in the league:
James最優，和另外兩位優質射手成為排行榜前三位。聯盟最佳ShotScore：
1. LeBron James, +231
2. Kevin Durant, +204
3. Stephen Curry, +164
These are three very different players with unique scoring strengths. Each accrues point surpluses in different spaces. Unsurprisingly, most of James's gigantic surplus comes close to the basket, where he puts up those freakish numbers.
這三位不同的球員有著獨特的得分特長。每位都能在不同區位產生分數剩餘。不意外的，多數James的大量剩餘來自於他產生變態數據的籃下，
Kevin Durant is also quite good near the basket, but he's more active and even more deadly from the outside than James. In a normal era, Durant would likely be the most effective scorer in the league, but we're not in a normal era — we're in the LeBron era. Still, Durant is an elite shooter from virtually every spot on the floor.
Kevin Durant的籃下得分也相當不錯，但他和James比起來，外圍攻擊更多且更致命。在正常的時代，Durant很有可能是聯盟最有效率得分手，但我們現在不是在正常時代，而是在LeBron的時代。仍然，Durant差不多在球場上每個位置都是優質射手。
He is so good that the weaknesses on his shot chart are the spots where he's only slightly above NBA average. That's crazy. Curry is a better perimeter shooter than both James and Durant, but he can't match their abilities near the basket, where he's actually a below-average NBA scorer. Still, thanks to his insane jump shot, Curry accumulates points at unusually effective rates.
他（Durant）實在好到他在投籃表的較弱的位置依然些微領先聯盟平均。瘋狂吧！Curry和James和Durant相比是位更優秀的外圍射手，但他不能和他們兩位的籃下能力相提並論，而在籃下他甚至是個低於NBA平均水準的得分手。仍然，由於他的瘋狂外線跳投能力，Curry以異常的效率累積分數。
Calculating ShotScore for outside shots only (eliminating the inside shots) reveals the great "pure shooters" in the NBA. It should come as no surprise that Curry comes out on top. Last season, the Warriors guard took 1,120 shots outside of 7.5 feet; these shots resulted in 1,247 points, or 195 more points than expected. League-wide, in terms of ShotScore for outside shots, Curry leads a top five that also includes Kevin Durant, Jose Calderon, Kyle Korver, and Dirk Nowitzki.
只計算外線投射的ShotScore（扣除內線出手）顯示出NBA的優秀「純射手」。不意外的，Curry是第一名。上一季，這位勇士後衛投了1,120球7.5呎外投射。而這些出手產生1,247分，或說比期望得分多195分。聯盟中的外線ShotScore，最佳五位為Curry、Kevin Durant、Jose Calderon、Kyle Kover和Dirk Nowizki。
These are players who already enjoy great reputations as shooters, but to this point there hasn't been a metric that has certified their superior status.
這些球員已經是以射手著名，但至今還未有數據證明他們高人一等的地位。
Controlling for the number of total shots taken helps further refine the idea. Jose Calderon had the highest ShotScore per outside shot. Calderon led the league with a +25 ShotScore per 100 outside shots, indicating that he accumulates 25 percent more points than would an average NBA shooter for every 100 outside shots he takes. This is especially impressive considering Calderon was playing for a pair of middling teams last season.
當控制住投籃總數時更進一步的提升這個概念。Jose Calderon有最高的每一球外線出手的ShotScore。Calderon有優於全聯盟的每100外線出手+25的ShotScore，代表他比起一般NBA得分手每100球外線出手的累積分數多25%。考慮到Calderon上季在兩個普通球隊打球的話，這更是令人敬佩。
As it turns out, of the 162 NBA players who attempted at least 300 outside shots last season, only three of them accrued more than 20 points above expected values per 100 shots: Calderon, Kyle Korver, and Steve Nash, who despite his broken-down body still managed to put together great shooting numbers. Interestingly, many of the names on the list below are not frequent shot creators, but when they do get shots they are extremely accurate relative to their peers.
數據的結果為上季162位至少出手300球外線的NBA球員中，只有3位每一百次出手產出高於期望值20分：Calderon、Kyle Kover和儘管身體受傷依然完成優質投籃數據的Steve Nash。有趣的是，多數下面列出的名字不是大量出手的人，但當他們有機會投籃時，和其他球員相比他們是致命的準。
Top 10 Outside Shooters Per 100 Shot Attempts
每一百次外線出手最佳10位射手
1. Jose Calderon, +25
2. Kyle Korver, +23
3. Steve Nash, +21
4. Stephen Curry, +17
5. Dirk Nowitzki, +16
6. Serge Ibaka, +16
7. Jarrett Jack, +16
8. Shane Battier, +15
9. Danny Green, +15
10. Steve Novak, +14
So does this mean that Jose Calderon is the best shooter in the NBA? No, it means that when Calderon shoots it's a beautiful thing. We all know that the NBA isn't just a catch-and-shoot league; it's also very much a create-your-own shot league. Some NBA players, like Novak, only thrive in those catch-and-shoot scenarios, while others, like Stephen Curry, Dirk Nowitzki, and Kevin Durant, constantly create their own chances off the dribble or in the post. These differences are reflected partly in the volume of shots guys take every year, and relative to players like Curry, Nowitzki, and Durant, Calderon is not a very creative shooter.
這代表Jose Calderon是NBA最佳得分手嗎？不，這代表當Calderon投籃時是件好的事。我們知道NBA並非只是個接球後立即投籃的聯盟，它也是個製造自己投籃機會的聯盟。一些像Novak的NBA球員，只有在接球後立即投籃的情況下有殺傷力，而其他像是Stephen Curry、Dirk Nowitzki和Kevin Durant等則時常在運球後或低位創造自己的投籃機會。這些差距部分反映在球員每年出手的量，而和Curry、Nowitzki和Durant等球員相比，Caldreon並不是個有創造投籃能力的得分手。
I find it interesting that Jeff Van Gundy likes to refer to Novak as the "best pure shooter" in the NBA. The numbers don't back up that claim. Suggesting that a player like Novak is a better shooter than Curry, Durant, or Nowitzki is just as foolish as saying that DeAndre Jordan is a more efficient scorer than LeBron James.
我發覺Jeff Van Gundy喜歡談說Novak是聯盟中「最佳純射手」這件事很有趣。數據並沒有支持這個說法。說Novak是比Curry、Durant或Nowitzki更好的射手和說DeAndre Jordan是比LeBron James更有效率的得分手一樣愚昧。
How efficient would Curry or Durant be if they just camped out on the perimeter and took catch-and-shoot jumpers a few times per night? Unfortunately for their efficiency numbers, these guys also toil inside the arc and take tons of shots off the dribble. Conversely, how bad would Steve Novak be if he tried to do this at the end of a playoff game?
如果Curry和Durant只是駐守外圍並每晚只接球後立即跳投幾次的話，他們會多麼有效率呢？對於他們的效率數據不利的是，他們也要在三分線內拼命並投一堆運球後的投籃。相反的，如果Steve Novak試著要在季後賽比賽末端時作他們做的事，他又會多糟呢？
NBA shooting prowess involves much more than just spotting up.
NBA得分能力並不只有定點跳投。
We have to consider more than just field goals made versus field goals missed. The ShotScore approach begins that process by introducing the fundamental role of court space into the equation, but it by no means ends it. I am not suggesting that this is the most important new statistic in the NBA, but I do believe it clarifies which players regularly make or miss baskets at higher rates in their native scoring zones. Emerging data sets will enable this process further. For example, the SportVU data set allows us to additionally consider the openness of a particular shot attempt; after all, a wide-open 15-foot jump shot is a lot easier than that identical shot with Larry Sanders lunging at you.
我們考慮的不單只是投進的球和投不進的球的相對問題。ShotScore的途徑藉由把球場位置的重要角色代入計算式中，開啟這個新方法，但這絕對不是終點。我並不是在暗示這個是最重要的NBA新數據，但我的確相信這個能證明哪位球員固定的在他們的習慣投籃區域中有較高的投進或投失率。更多的資料將使這個方法更進化。舉例來說，SportVU的資料庫讓我們可以進一步考慮每個出手的空檔程度。畢竟一個空檔15呎跳投和被Larry Sanders撲過來的相同投籃比起來可簡單多了。
One of the hallmarks of good NBA teams like the Heat and the Spurs is their ability to regularly create wide-open looks; many great shooters in the league aren't fortunate enough to play in such a scheme, and their numbers suffer as a result. For instance, there's no question that Danny Green has made great strides as a spot-up shooter, and his performance in the 2013 NBA Finals was incredible. But how much of his emergence is due to that beautiful Popovichian orchestra down in San Antonio? He wasn't getting those looks back in Cleveland when he was released.
像熱火隊和馬刺隊這種NBA好球隊的正字標記之一就是經常的製造空檔的能力。很多優質射手沒有運氣好到在這些戰術下打球，他們的數據因此受到傷害。舉例來說，Danny Green毫無疑問的進步神速成為優質定點射手，而他在2013 NBA總冠軍賽的表現相當驚人。但他的突出表現有多少是因為Popovich在聖安東尼奧指揮這優美交響樂隊呢？他過去在Cleveland被釋出時可沒有這些空檔。
This is an exciting time for basketball analytics, but as is often the case, deep explorations into performance often provoke more questions than answers. It's still tempting to assert that NBA analytics are advanced now, but the truth is that we will look back at the current state of affairs the same way baseball nerds look back at the batting average and RBI era. These players give us so much; the least we can do in return is come up with an accurate way of appreciating them.
這對籃球數據來說是個興奮的時刻，但很多時候，對於球員表現探索越多，引發的問題會多過答案。仍然會忍不住想宣稱NBA的數據更進一步了，但事實上我們將會回首看看現況，如同棒球數據呆回首看打擊率和RBI的時代。這些球員給了我們很多，我們至少要回報予更精準的方法來欣賞他們。
心得：
相當優質的數據文。前文撲梗的道理其實大家都懂－命中率的謬誤。
作者提供一個相當棒的方法來更接近真實的比較。
裡面最讓人覺得奇妙的就是Curry。最讓人期待也是他。
能想像他將三分線內的出手選擇和命中率再提升的話，那會是多可怕的事!!!!
不意外的榜上有名的都是知名射手，上季38的Nash還能維持這種手感真令人佩服。
必須要再強調說這篇文真的很優質，因為作者很強調出手方式不同會導致這數據被錯用。
即使可以引用這數據不同進攻模式的球員還是不能一起比較，而不同戰術體系的影響亦很重要。但我想這個問題很難用數據解決。
除了作者提到的「被防守干擾」與否外，我自己認為這個數據如果能在配上「受助攻」與否來看的話，將會更提升!!!!
身為愛鑽研數據的一份子這真的讓人興奮啊!!!!!
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