Extra Points － A new way to understand the NBA's best scorers
分数剩余－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是现役地表最强球员。对任何近年有在看篮球的人来说这是理所当
然的事，但奇怪的是很难找到很多数据来支持这项论点。在过去Michael Jordan
统治NBA时，他一直都是联盟得分王；Chamberlain和Russell往往抓下夸张的篮板
数；Kareem Abdul-Jabbar是联盟史上累积得分纪录保持者。
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最近成为联盟第五位获得第四座MVP的球员，使自己成为和这些神兽平起平坐
。除了这项傲人的事蹟，他的统治力并没有反应在传统数据上。不知为何，绝大多
数最常被引用的数据掩饰了当今球场最优秀的球员的统治力。James在WinShares和
PER（译按：WS为球员为球队的贡献值；PER为球员的效率值）的表现相当耀眼，但
这些数据只有模糊的解释James厉害之处。它们无法标明任何James表现内容的明确
要素。事实上，相当多常见的衡量标准显示其他球员比James来的更有效率及更有
影响力。
Last season, DeAndre Jordan led the NBA in field goal percentage.
However, consider the following ridiculous statistical couplet:
上一季，DeAndre Jordan在投篮命中率上领先全联盟。然而，思考一下下面两个夸
张的数据。
No player scored more points close to the basket than LeBron James last
season.
上一季LeBron James的篮下得分是全联盟最多。
No player converted a higher percentage of his shots near the basket than
LeBron James last year.
上一季LeBron James的篮下命中率是联盟最佳。
http://ppt.cc/TdTq
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.
动脑想想吧。他不但在NBA最神圣的禁区得到比联盟中的任何球员更多的分数，而
且还保有联盟最高的命中率。整体而言，联盟上一季的篮下命中率是56%；在James
637次的篮下出手中，他的命中率是惊人的72%。尽管有这电动般的得分本领，James
的命中率比较差的禁区球员还更低。
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.1 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.
很少有人去主张Jordan（译按：指的是快艇队DJ，不是MJ）是个比James更有效率
的得分手，但从命中率篮看这却是事实。Jordan的64%命中率领先全联盟，而James
只有57%。虽然了解球员们的命中率是高是低是有用的，但这无法告诉我们真正的
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的球员，投一堆三分球；又其他的像Kevin Garnett主打18呎中
距离跳投；DeAndre Jordan则主要在禁区里讨生活。像Jordan这类球员几乎都是联
盟的命中率领先者。问题在于当每位的NBA球员的角色且投篮习惯不同时， 我们的
投篮数据大多都忽略它。
http://ppt.cc/TKj2
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.
有玩过H-O-R-S-E的人都会告诉你有些投篮当然比其他的容易。上篮比罚球容易，
而罚球比角落三分简单。这个基本原则几乎完全被我们最依赖的投篮数据给忽略。
同样的，NBA球员们都是特殊的，而整个球季下来每位球员都有他的“特有投篮区
域”。这点当然也被忽略了。上面的图表显示出LeBron的投篮区域和DeAndre
Jordan的投篮区域有着巨大的差异。
We can improve our shooting metrics by accounting for court space and the
unique natures of players' shot constellations.
我们可以借由展示球场不同区块和每位球员的独特投篮区域，将投篮数据再进化。
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.
上一季结束，James的平均投篮距离是11呎；Jordan的则是2.8呎。基本上，透过投
篮命中率这不清不楚的数据，James因跳投而不利，反之，Jordan因没有投任何跳
投而得利。尽管他是个优质三分射手、好的中距离射手和球场上最优秀的禁区得分
手，James在这个重要的命中率数据上输给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?
虽然称呼我们的数据为“进阶数据”是件诱人的事，先想想这两个基本问题：
1. 谁是NBA现役最强得分手？
2. 你用什么去来证明你的答案是对的？
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.
当提及投篮数据时，人人都可能想有某个网络上找到的表格描述著“优质射手”像
Stephen Curry和Kevin Durant和“劣质射手”像Monta Ellis和Josh Smith。但没
有这东西。我们依然依靠着直觉和暧昧不清的名声来主张NBA中“纯粹的投篮”技
巧。在篮球数据进化的争论中，我们依然无法有效的衡量投篮能力这个概念，进而
造成许多困难。但这也是可以修正的。
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.
问题在于几乎所有NBA球员的投篮命中率和投篮位置的关联强于投得多好。
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.
不愿面对的真相是每个NBA的投篮出手有着属于其的难度，其受射手的位置等几个
因素影响。即使前面几个方法都忽略这个麻烦的事实，由于相对来说更新的NBA数
据，我们现在可以开始去理解它。
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球员大约投了200,000球。整合的联盟出手图表显示出NBA平均投篮效率
的空间因素。根据图表显示球场位置和每次出手的期望分数的显著关系。这也是
为什么投三分球快速流行而中距离投篮慢慢消失。
http://ppt.cc/O8ms
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.
但这个图表也提供我们一个可以用来衡量个人投篮表现的有用基准。将球员的投篮
区域图覆蓋于其上，我们可以基于他的投篮位置来估计一位平均的NBA射手所能得
到的分数。然后我们可以比较这位球员的真实得分。
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.
举例而言，上一季LeBron James出手1,354球。以联盟基准来看，假如是一位NBA平
均的球员出手这1,354球，他总共会得到1,397分。
http://ppt.cc/PatG
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在那些投篮位置实际上得到了1,628分，比期望值要再多231分。没有球员的
期望值以上累积得分比James多。借由说明球场位置和NBA投篮平均值的重要关系，
我们可以看到哪些球员得分和NBA平均得分差值的最高跟最低。也可以依球员的投
篮习惯来搞清楚哪位球员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
球员在2012-13的投篮分析。我们将球员实际得分和期望得分的差距值称为ShotScore
。好的得分手的数字会是正值，反之差的得分手是负值。
James came out on top, and is joined in the top three by a pair of elite
shooters.Highest ShotScores in the league:
James最优，和另外两位优质射手成为排行榜前三位。联盟最佳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.
这三位不同的球员有着独特的得分特长。每位都能在不同区位产生分数剩余。不意
外的，多数James的大量剩余来自于他产生变态数据的篮下，
http://ppt.cc/XGdW
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的篮下得分也相当不错，但他和James比起来，外围攻击更多且更致
命。在正常的时代，Durant很有可能是联盟最有效率得分手，但我们现在不是在正
常时代，而是在LeBron的时代。仍然，Durant差不多在球场上每个位置都是优质射
手。
http://ppt.cc/TpSu
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）实在好到他在投篮表的较弱的位置依然些微领先联盟平均。疯狂吧！
Curry和James和Durant相比是位更优秀的外围射手，但他不能和他们两位的篮下能
力相提并论，而在篮下他甚至是个低于NBA平均水准的得分手。仍然，由于他的疯狂
外线跳投能力，Curry以异常的效率累积分数。
http://ppt.cc/RBUz
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.
只计算外线投射的ShotScore（扣除内线出手）显示出NBA的优秀“纯射手”。不
意外的，Curry是第一名。上一季，这位勇士后卫投了1,120球7.5呎外投射。而这
些出手产生1,247分，或说比期望得分多195分。联盟中的外线ShotScore，最佳五
位为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.
这些球员已经是以射手著名，但至今还未有数据证明他们高人一等的地位。
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.
当控制住投篮总数时更进一步的提升这个概念。Jose Calderon有最高的每一球外
线出手的ShotScore。Calderon有优于全联盟的每100外线出手+25的ShotScore，代
表他比起一般NBA得分手每100球外线出手的累积分数多25%。考虑到Calderon上季
在两个普通球队打球的话，这更是令人敬佩。
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.
数据的结果为上季162位至少出手300球外线的NBA球员中，只有3位每一百次出手产
出高于期望值20分：Calderon、Kyle Kover和尽管身体受伤依然完成优质投篮数据
的Steve Nash。有趣的是，多数下面列出的名字不是大量出手的人，但当他们有机
会投篮时，和其他球员相比他们是致命的准。
Top 10 Outside Shooters Per 100 Shot Attempts
每一百次外线出手最佳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.
这代表Jose Calderon是NBA最佳得分手吗？不，这代表当Calderon投篮时是件好的
事。我们知道NBA并非只是个接球后立即投篮的联盟，它也是个制造自己投篮机会
的联盟。一些像Novak的NBA球员，只有在接球后立即投篮的情况下有杀伤力，而其
他像是Stephen Curry、Dirk Nowitzki和Kevin Durant等则时常在运球后或低位创
造自己的投篮机会。这些差距部分反映在球员每年出手的量，而和Curry、Nowitzki
和Durant等球员相比，Caldreon并不是个有创造投篮能力的得分手。
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.
我发觉Jeff Van Gundy喜欢谈说Novak是联盟中“最佳纯射手”这件事很有趣。数
据并没有支持这个说法。说Novak是比Curry、Durant或Nowitzki更好的射手和说
DeAndre Jordan是比LeBron James更有效率的得分手一样愚昧。
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只是驻守外围并每晚只接球后立即跳投几次的话，他们会多么
有效率呢？对于他们的效率数据不利的是，他们也要在三分线内拼命并投一堆运球
后的投篮。相反的，如果Steve Novak试着要在季后赛比赛末端时作他们做的事，
他又会多糟呢？
NBA shooting prowess involves much more than just spotting up.
NBA得分能力并不只有定点跳投。
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.
我们考虑的不单只是投进的球和投不进的球的相对问题。ShotScore的途径借由把
球场位置的重要角色代入计算式中，开启这个新方法，但这绝对不是终点。我并不
是在暗示这个是最重要的NBA新数据，但我的确相信这个能证明哪位球员固定的在
他们的习惯投篮区域中有较高的投进或投失率。更多的资料将使这个方法更进化。
举例来说，SportVU的数据库让我们可以进一步考虑每个出手的空档程度。毕竟一
个空档15呎跳投和被Larry Sanders扑过来的相同投篮比起来可简单多了。
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.
像热火队和马刺队这种NBA好球队的正字标记之一就是经常的制造空档的能力。很
多优质射手没有运气好到在这些战术下打球，他们的数据因此受到伤害。举例来
说，Danny Green毫无疑问的进步神速成为优质定点射手，而他在2013 NBA总冠军
赛的表现相当惊人。但他的突出表现有多少是因为Popovich在圣安东尼奥指挥这
优美交响乐队呢？他过去在Cleveland被释出时可没有这些空档。
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.
这对篮球数据来说是个兴奋的时刻，但很多时候，对于球员表现探索越多，引发的
问题会多过答案。仍然会忍不住想宣称NBA的数据更进一步了，但事实上我们将会
回首看看现况，如同棒球数据呆回首看打击率和RBI的时代。这些球员给了我们很
多，我们至少要回报予更精准的方法来欣赏他们。
原文网址－
http://tinyurl.com/qf3ett4
心得：
相当优质的数据文
前文扑梗的道理其实大家都懂－命中率的谬误
作者提供一个相当棒的方法来更接近真实的比较
里面最让人觉得奇妙的就是Curry
最让人期待也是他
能想像他将三分线内的出手选择和命中率再提升的话
那会是多可怕的事!!!!
不意外的榜上有名的都是知名射手
上季38的Nash还能维持这种手感真令人佩服
必须要再强调说这篇文真的很优质
因为作者很强调出手方式不同会导致这数据被错用
即使可以引用这数据不同进攻模式的球员还是不能一起比较
而不同战术体系的影响亦很重要
但我想这个问题很难用数据解决
除了作者提到的“被防守干扰”与否外
我自己认为这个数据如果能在配上“受助攻”与否来看的话
将会更提升!!!!
身为爱钻研数据的一份子这真的让人兴奋啊
下集预告：以ShotScore分析NBA最差得分手
(欢迎转载，但转至站外请标明原作者和出处，感谢)