User:Andy yutong Zhou/Efficiency (basketball)

Efficiency (Basketball)
Player efficiency rating (PER) is an integrated basketball scoring invented by John Hollinger, trying to reduce the player's contribution to a single number. Hollinger used detailed formulas to develop a system to evaluate the performance of each player.

PER
PER evaluates the player's contribution per minute and adjusts it according to the rhythm of the game. At each minute, we can compare two players with different playing time; after adjusting the tempo, we can compare the efficiency of two players on different teams. For each season, the league has a fixed league average PER of 15.00, which also allows players from different seasons to be compared.

PER takes into account many positive effects on the team, such as shooting, free throws, three-pointers, assists, rebounds, blocks, and steals, as well as negative effects on the team, such as missing shooting, turnovers and personal fouls. This formula adds different weights according to different technical statistics, adds up the positive data, and subtracts the negative data. Then adjust the score of each player to a minute-based basis to compare players with different playing times, for example, main players and substitutes. Also adjusted according to the team's game rhythm. Finally, a number is used to summarize the players' performance in that season.

Hollinger's work has benefited greatly from the observations of baseball analysts such as Bill James. One of the main observations is that traditional counting statistics in baseball, such as hits and wins, are not reliable indicators of player value. For example, base runners are highly dependent on the opportunities created by their teammates. PER extends this thinking on statistics to basketball, pointing out that the player’s chance of accumulating statistics depends on the player’s playing time and the pace of the game.

Formula to calculate the PER
uPER = (1 / MP) *

[ 3P

+ (2/3) * AST

+ (2 - factor * (team_AST / team_FG)) * FG

+ (FT *0.5 * (1 + (1 - (team_AST / team_FG)) + (2/3) * (team_AST / team_FG)))

- VOP * TOV

- VOP * DRB% * (FGA - FG)

- VOP * 0.44 * (0.44 + (0.56 * DRB%)) * (FTA - FT)

+ VOP * (1 - DRB%) * (TRB - ORB)

+ VOP * DRB% * ORB

+ VOP * STL

+ VOP * DRB% * BLK

- PF * ((lg_FT / lg_PF) - 0.44 * (lg_FTA / lg_PF) * VOP) ]

Top 10 players with highest PER (NBA)
Here is list for the top 10 players with highest PER among history

Problems of PER
PER mainly measures the offensive performance of players. Hollinger admitted frankly that the two defensive statistics it contains-blocks and steals (not considered official statistics until 1973)-can create misunderstandings about the value of players, and that PER is not a measure of a player's defensive ability. Reliable indicators. For example, Bruce Bowen, who is widely regarded as one of the best defenders in the NBA (at least in the 2006-07 season), often hits single-digit PER. Some people believe that PER overestimates players who play very little time and players who play against the opposing second team.

PER is considered to encourage inefficient shooting. To quote Dave Berri, the author of "The Wages of Wins": "Hollinger believes that a two-pointer is worth 1.65 points and a three-pointer is worth 2.65 points. However, once the iron is hit, the team will lose 0.72 points. Simple mathematics We can know that if a player’s two-point shooting percentage reaches 30.4% and three-point shooting percentage reaches 21.4%, the points will be balanced. If a player exceeds these two thresholds, in fact almost every NBA player can If he does, the more shots he takes, the higher his PER will be. So a player may be an inefficient scorer, but he can exaggerate his value with a lot of shots."