標題類別想了好久，應該算是外絮，但是引用兩篇文章
反正都是在討論 真實正負值(RPM: real plus minus)
所以用專欄來定義好了 @@
原文：
http://espn.go.com/nba/story/_/id/10740818/introducing-real-plus-minus
數據：
http://espn.go.com/nba/statistics/rpm/_/sort/RPM
Bulls coach Tom Thibodeau recently made the case for Taj Gibson as
the NBA's Sixth Man of the Year. "I think that the biggest thing
for him is what he has contributed to us winning," said Thibs.
"The things that he does for us are all team-oriented. He plays
great defense, challenges shots, guards everybody, runs the floor
hard, sets great screens, does his job."
公牛教頭錫伯杜最近認為手下悍將Taj Gibson應該要被
考慮為最佳第六人。「我認為最重要的是-他做了很多幫我們贏球的事，
大部份的事情都是用整體來看才看得出來的。他防守，干擾投籃，
守五個位置，在場上盡力奔跑，做出漂亮的單檔，做好該做的事。」
So Gibson helps his team win by doing all the little things that
never show up in a box score. But how can we measure the value of
running the floor hard, or making smart defensive rotations, or
setting great screens?
簡單來說，Gibson在場上做了一堆不會在分數盒中列出的小事
幫助球隊贏球。我們要用什麼方式來顯示出這種貢獻呢？
And how can we tell if Gibson has been more valuable to his team
than, let's say, Clippers sixth man Jamal Crawford, who has scored
more points than Gibson (18.6 versus 13.2 PPG) on a higher true
shooting percentage (55.7 versus 52.8) while logging heavier
minutes (30.3 versus 28.8 MPG) for a better team in a tougher
conference?
而且我們要怎樣才能比較出來Gibson比快艇的最佳第六人Jamal Crawford
還更有價值呢？Crawford比Gibson更能得分（18.6ppg vs 13.2ppg），
而且投籃也更精準（真實命中率 55.7% vs 52.8%)，上場時間也更多
（30.3mpg vs 28.8mpg)，並且在比較強的球隊和比較艱難的西區？
Today we're introducing an advanced metric that can help us out:
real plus-minus (RPM).
今天我要向大家介紹ESPN一個新的進階數據來幫助我們：
真實正負值（RPM)。
What is real plus-minus?
什麼是RPM？
As the name suggests, real plus-minus shares a family resemblance
with the +/- stat in the box score, which merely registers the net
change in score (plus or minus) while each player is on the
court.
就如同名字所敘，RPM跟分數盒上的 +/-值是屬於同一家族的。
然而一般+/-值代表的只是單純的該球員在場上球隊的勝分或負分差。
RPM is inspired by the same underlying +/- logic: If a team
outscores its opponents when a player is on the court, he's
probably doing something to help his team, whether or not he's
putting up big numbers.
RPM是利用與此相同的概念-當一個球員在場上時對球隊的整體幫助
而不論他個人表現與否。
But the familiar +/- stat has a serious flaw: Each player's rating
is heavily influenced by the play of his on-court teammates.
但是睿智的鄉民都知道一般+/-值有著嚴重的缺失：
會大幅度受到跟你一起上場球員的影響。
For example, in the basic +/- numbers, Thunder backup point guard
Reggie Jackson is ranked 27th in the league. But he's also spent
the majority of his minutes playing alongside Kevin Durant, the
league's likely MVP. What we really want to know is how much of
Jackson's elite rating is attributable to his own play, and basic
+/- simply can't tell us.
舉例來說，如果只看一般的+/-值，你會發現雷霆的替補控衛
Reggie Jackson在聯盟能排到第27位！但是他大部份上場的時間都是
和今年最有可能的MVP-Kevin Durant一起。我們真正想要知道的是，
這個+/-有多少能看成是Jackson自己的功勞，而不是靠KD，而一般的
+/-值並不能告訴我們這一點。
But real plus-minus can.
但是真實正負值可以。
Where does real plus-minus come from?
RPM是從哪來的咧？
Drawing on advanced statistical modeling techniques (and the
analytical wizardry of RPM developer Jeremias Engelmann, formerly
of the Phoenix Suns), the metric isolates the unique plus-minus
impact of each NBA player by adjusting for the effects of each
teammate, opposing player and coach.
從進階的數據分析技術而來（分析師Jeremias Engelmann），
這個分析把隊友，對手和教練的影響考量進去，
把個別NBA球員的正負影響分離出來。
The RPM model sifts through more than 230,000 possessions each NBA
season to tease apart the "real" plus-minus effects attributable
to each player, employing techniques similar to those used by
scientific researchers when they need to model the effects of
numerous variables at the same time.
RPM模型是利用NBA每一季超過23萬次球權來分析有多少+/-屬於
個別球員的貢獻。這裡運用的運算技術和科學研究上常常要用來
分析多種變異值是類似的。
RPM estimates how many points each player adds or subtracts, on
average, to his team's net scoring margin for each 100 possessions
played. The RPM model also yields separate ratings for the
player's impact on both ends of the court: offensive RPM (ORPM)
and defensive RPM (DRPM).
簡單來說，RPM預計該球員上場時，平均能為球隊在100次球權
中帶來多少的正負變化。因此，RPM可以更細分為防守RPM(DRPM)和進攻RPM
(ORPM）。
So, Gibson or Crawford?
所以，是Gibson還是Crawford強？
Let's return to the previous comparison of Taj Gibson and Jamal
Crawford. The chart shows their respective RPM ratings.
讓我們回到Gibson vs Crawford的問題上。看看下表。
REAL PLUS-MINUS (2013-14)
PLAYER ORPM DRPM RPM
T. Gibson 0.70 3.42 4.12
J. Crawford 1.53 -1.96 -0.43
Crawford has the higher
offensive RPM (+1.53 versus +0.70), but the advantage turns out to
be surprisingly small, given Crawford's scoring talents. It's
worth only about one additional point per game.
Crawford有著更高的ORPM，但是差別比想像中小，尤其如果
考量Crawford是個搶分高手。但是Crawford只勉強比Gibson多一分。
And on the other end, the players are miles apart. In fact,
Gibson's defensive impact (+3.42 DRPM) is large enough to give him
a truly elite overall RPM rating (+4.12), placing him in the
company of All-Stars like James Harden (+3.44 RPM), Chris Bosh
(+3.75), Joakim Noah (+3.89), Russell Westbrook (+4.09) and Dwight
Howard (+3.99).
另一方面，兩個球員相差就不可以道里計了。
事實上，Gibson的防守影響讓他的整體RPM(+4.12)甚至可以和全明星
James Harden(+3,44), Bosh (+3.75), Noah (+3.89), 西河(+4.09)
DH12 (+3.99)相提並論。
In contrast, Crawford appears to give away a bit more on defense
(-1.96 DRPM) than he contributes on offense, with an overall RPM
impact (-0.43) that's slightly below the league average.
相反的，Crawford在防守端成為球隊的負擔（-1.96)，
這甚至讓他的整體RPM(-0.43)略低於聯盟平均(0)。
The Durant factor
Durant效應
RPM can also shed light on our question about the true impact of
third-year guard Reggie Jackson, as the table shows.
RPM也可以讓我們知道前面所說的Jackson對球隊的真實影響力。
REAL PLUS-MINUS (2013-14)
PLAYER ORPM DRPM RPM
K. Durant 6.10 0.67 6.77
R. Westbrook 4.08 0.01 4.09
S. Ibaka 0.47 2.63 3.10
R. Jackson 0.67 0.82 1.49
RPM accounts for the contributions of OKC stars Durant, Russell
Westbrook and Serge Ibaka (as well as Jackson's other teammates).
RPM會考量OKC其他隊友的貢獻來作修整。
After doing so, RPM indicates Jackson has had a moderately
positive impact this season on both sides of the ball. His total
RPM rating (+1.49), while far below that of his more heralded
teammates, is consistent with the play of a quality NBA starter,
and it's higher than that of more established guards such as Lance
Stephenson, Kevin Martin and Wesley Matthews.
在修整後，我們看出Jackson的確也還維持著正面的影響(+1.49)，
但是跟他的明星隊友比就還是差了一個檔次，基本上這說明他足以擔當
合格的先發，他的RPM比Lance Stephenson, Kevin Martin和Wesley Mattews
都還高。
The King of RPM?
RPM的王？
Let's close with a quick look at the game's greatest all-around
player, LeBron James.
讓我們回頭來看看NBA裡最全能的球員Lebron James。
LeBron has been accused of coasting at times this season, and RPM
reveals where the charge may have merit.
Lebron本季被外界說常常養身，讓我們用RPM來看看
這個指控是否成立。
REAL PLUS-MINUS (2013-14)
PLAYER ORPM DRPM RPM
L. James 8.32 -0.21 8.11
While LeBron was aptly named to the NBA All-Defensive Team last
season, his defensive impact this season has been surprisingly
mediocre, at least as measured by RPM (-0.21 DRPM). His rating is
consistent with the claim that James has not consistently given
his best effort this season on the defensive end.
去年Lebron毫無疑問的入選ＮＢＡ防守第一隊，
今年他在防守端的表現卻非常一般，甚至對球隊帶來些微負面的影響(-0.21)。
這讓那些指控他在防守端上未盡全力的看法不謀而合。
Does the same hold true on offense? No. Offensively LeBron has
been as dominant as ever, and his +8.32 ORPM leads the league by a
comfortable margin. This means that despite his less-than-stellar
defensive contribution, LeBron's total RPM (+8.11) still rates as
the NBA's highest this season.
不過在進攻端上是否也是如此呢？不。
進攻端上Lebron還是很有統治力。他的ORPM(+8.32)領先聯盟其他人
不止一個檔次。事實上，這樣的領先讓他即使扣掉他不及格的DRPM後，
整體RPM(+8.11)依然是聯盟最高。
Of course, that doesn't necessarily mean he should be regarded as
the league's MVP. There's a certain prolific scorer in OKC who has
also put up a stellar RPM number this season, and he's done so
while playing more possessions than LeBron.
當然，這不代表他就應該奪得聯盟的MVP了。因為在雷霆的那位
也不是吃素的，同樣有著相當高的RPM，並且他進攻和防守的球權次數
也比Lebron更高。
Later this week we'll look at how RPM can be used to estimate the
number of wins each player adds to his team. In other words, we'll
introduce a new lens through which to view this season's MVP
race. (Spoiler alert: It's close. Very close.)
接下來我們將會用這項新的數據來幫我們預測哪個球員
對他的球隊提供了最多勝利。也就是說，我們用一種新的方向
和思維去看本季MVP應該獎落誰家。（爆雷：比數很接近，非常接近。）
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說實話這篇敘述文沒有提到任何公式，還滿難看懂是怎麼算的。
不過提到這個改良版的+/-有考量一起上場的隊友因素和球隊勝敗因素等等
不管怎樣應該是比傳統+/-值有參考價值?