5

Personally, I am interested in a player's personal contribution to the game. Therefore, I want to compare the team's performance when he is on the field versus when he is not on the field. I believe that it originates from basketball, but it can obviously be extended to other sports.

Example

Suppose a player plays 12 minutes out of a 48 minutes NBA match. In the time he is on the field, the score is 25-20 for his team. In the other 36 minutes, the score is 70-70. So, his team is performing '5 points better per 12 minutes' when he is on the field. After rescaling to full match time, the statistic would be +20 for this player in this hypothetical match.

Question

Is there a statistic that describes this effect or any one closely related? If not, could you explain why this statistic is not of interest? Personally, I think it says a lot about a player that cannot be counted explicitly, for example defensive positioning.

  • So +/- per minute? I don't know if anyone keeps that stat, since a) +/- is already flawed (I play if and only if my teammate LeBron is on the floor, so I have a great +/-) and b) it would likely be dominated by garbage time players with tiny sample sizes. – Michael Myers May 15 '15 at 17:08
  • @MichaelMyers (b) is easily fixed by looking only at players with more than (mumble) average minutes per game. – Philip Kendall May 15 '15 at 17:53
  • @PhilipKendall: Still, being +10 in 40 minutes seems better than +5 in 12 minutes. But it depends also on the replacement player. This is why there are tons of advanced/adjusted/real/whatever plus/minus systems around. – Michael Myers May 15 '15 at 17:57
  • @MichaelMyers, if I were a coach, I would give someone, who gets +5 in 12 minutes time and time again, more playing time to use his skill in a longer period of the game. Probably, his +/- per minute will drop. However, a statistician coach would find an optimum amount of playing time per player. I think that (a) is rarely the case in the long run (although I'm not familiar with basketball so much). – Braamstruik May 18 '15 at 14:54
  • If it happens consistently, then the sample size is no longer a problem. – Michael Myers May 18 '15 at 23:23
8

The statistic you are discussing is Plus/Minus per minute, or per 48 minutes, as @MichaelMyers stated in the comments. It is also called Net Rating.

This forms one component of one of the earliest advanced stats for the NBA, the Simple Rating (or Roland Rating, after Roland Beech, who developed it and has since worked for a number of NBA teams.) See the column "On Court/Off Court - Net" at the 82games.com Simple Rating Page for the results of the 2014/15 NBA season.

Now, as mentioned in the comments above, this stat is highly dependent on who else is on the floor, and if there is a lot of collinearity ("I always play with LeBron", like @MichaelMyers says) then the stat is not very useful. Most teams structure their lineups with large amounts of collinearity, with certain players usually playing together (like the starters), so this is a huge issue.

The natural progression of this stat was to adjust for who else was on the floor, and to try to split the credit up. This is the genesis of pure Adjusted Plus/Minus, which was originally developed by Wayne Winston and Jeff Sagarin (The Numbers Game) and then refined by Dan Rosenbaum (Measuring how NBA Players Help Their Teams Win)

Further progression to again try to deal with the statistics issues (collinearity in particular) led to Regularized Adjusted Plus/Minus (RAPM) and then to Real Plus/Minus (RPM), and the research in that area continues to move forward--but that is outside the scope of this discussion.

-1

It is called "Plus/minus". According to this piece, the NBA itself has officially tracked it since the 2007-08 season.

There is the obvious problem raised in the comments above. To mitigate this problem, people have come up with their own adjusted versions of plus/minus: e.g. ESPN's 'real plus/minus', basketball-reference.com's 'box plus/minus'.

  • No, because plus/minus isn't normalised for amount of time spent on court. – Philip Kendall May 24 '15 at 6:35
  • 1
    @PhilipKendall: If that is what you absolutely insist on, then you can simply multiply each player's plus/minus for each game by (48 minutes ÷ Player's playing time for that game). Alternatively, look at either of the two adjusted versions given by ESPN and basketball-reference.com. Both of them are adjusted to a per 100 possession basis. – Kenny LJ May 24 '15 at 14:21

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