Player Efficiency Rating (PER) is the closest statistic that sports analysts have to measure a player’s per-minute overall value. John Hollinger, the creator of Player Efficiency Rating, defined his statistic as this: “The PER sums up all a player’s positive accomplishments, subtracts the negative accomplishments, and returns a per-minute rating of a player’s performance.”
Before we get into calculating Player Efficiency Rating for each player on Plymouth State University’s men’s basketball team this past season, we need to know a few things. First, Player Efficiency Rating is not a flawless statistic. Although it is meant to add up all positive accomplishments and subtract the negatives, PER only accounts for steals and blocks on the defensive end of the floor. This means that players that play great defense but don’t fill up the steal and block categories in the box score will have a smaller PER than they probably should. Another flaw of Player Efficiency Rating is that it can give too much credit to players who play limited minutes and/or minutes against second units, and not enough credit to players who have the versatility and skill to play starter’s minutes.
Along with individual player statistics, Player Efficiency Rating requires statistics for the team, in this case Plymouth State, and for the league, in this case the Little East Conference. After copying and pasting the statistics on the Little East website into an Excel spreadsheet, we can divide fields goals made and attempted, 3-point field goals made and attempted, and free throws made and attempted by the number of games played to find averages for each team. Once we have the averages for every statistic used in the Player Efficiency Rating formula, we can add up all of the team averages and divide the sum of those averages by the number of teams in the league, which for the Little East is 9 teams. Now that we have averages for each statistic for each team and for the league, we can almost plug them into our Player Efficiency Rating formula.
Looking at the formula, we see that we need to calculate values for factor, VOP (value of possession), and DRB% (Defensive Rebounding Percentage). For the factor variable, we plug in 14 for league assists, 27.2 for league field goals, and 13.3 for league free throws per game. After plugging in the values and doing some calculating, we come up with a factor value of 0.6. For the VOP variable, we plug in 75.3 for league points, 63.2 for league field goals attempted, 11.5 for league offensive rebounds, 15.7 for league turnovers, and 19.3 for league free throw attempts. After plugging in the values and calculating, we come up with a VOP value of 0.99. Finally, for the DRB% variable, we plug in league total rebounds and league offensive rebounds and calculate to give us a value of 0.697.
After plugging factor, VOP, and DRB% into the PER formula, we look to see what other team and league statistics that are needed. Team assists should be 15.3 and team field goals should be 27.73. League free throws is 13.3, league free throw attempts is 19.3, and league personal fouls is 17.9. Now we can plug in our values for each individual player to find unadjusted PER, which I will explain later.
I went about doing this calculation the same way it is shown in the image above: by splitting it up into sections. Then I went through and found any sections that would be the same for each individual player and calculated those. These are the four big examples of this:
(2 – factor * (team_AST / team_FG)) * FG
Team assists divided by team field goals, or 15.3/27.73, will always be 0.55. We then multiply 0.55 by our factor, 0.6, to get 0.33. We can then subtract 0.33 from 2 to get 1.67. Now this section looks a lot more manageable, as we only have to find the player’s total field goals made and multiply it by 1.67.
(FT *0.5 * (1 + (1 – (team_AST / team_FG)) + (2/3) * (team_AST / team_FG)))
We already know that team assists divided by team field goals is 0.55. We then subtract 0.55 from 1 to get 0.45, and then add 1 to that difference to get 1.45. At the end of the equation, we multiply 2/3, or 0.66, by 0.55 to get 0.363. Now we add 1.45 and 0.363 together to get 1.813. Our equation is now (FT*0.5*(1.813)).
VOP * 0.44 * (0.44 + (0.56 * DRB%)) * (FTA – FT)
Here we are just looking to find (0.44 + (0.56*DRB%)). We know DRB% is 0.697, which we multiply by 0.56 to get 0.39. Then we just add 0.39 to 0.44 to get 0.83.
PF * ((lg_FT / lg_PF) – 0.44 * (lg_FTA / lg_PF) * VOP)
Here we divide league free throws made by league personal fouls, or 13.3/17.9, to get 0.74. We do the same for league free throws attempted, which is 19.3/17.9, to get 1.08. Remembering our Order of Operations, we can multiply 1.08 by 0.99 (VOP) to get 1.07, and multiply that product again by 0.44 to get 0.47. Now inside the parenthesis is (0.74 – 0.47), which we can subtract to get 0.27. Instead of calculating the equation above for every player, we only need to find PF*(0.27).
Now that the Player Efficiency Rating formula has been simplified, we can plug in the rest of the variables with each players’ individual statistics. I have decided to find the Player Efficiency Rating for each player using player totals, as that made for the cleanest calculations. However, I was not sure whether to use total minutes or average minutes per game for each player, so I have calculated a PER for both. Before sharing the results, I should mention that I am calculating uPER, or unadjusted Player Efficiency Rating, for each player. To find an accurate PER that could be compared throughout the league, you would have to adjust uPER for the pace of play, which is adjusted PER, or aPER. Even after that, to find just PER, you need to plug in aPER into this formula:
PER = aPER * (15 / lg_aPER)
Here 15 is considered to be the average PER in the NBA. Luckily for us, we are only comparing the Player Efficiency Ratings for the players on Plymouth State for the 2018-19 season, so uPER will work fine.
The results for each players’ uPER, using both total minutes and minutes per game, as well as the calculated team and league averages in the Little East Conference, can be found in the Excel spreadsheet linked below. In the first sheet titled LEC, we can see averages for each necessary statistic for every team, with Plymouth State being highlighted in green. The bottom row shows league averages in bold. The second sheet, titled uPER, shows each players’ minutes and uPER, as well as where each of the players’ rank in each statistic listed on the team. Each player with surprising and/or significant results are highlighted in green.
Now that we have found our results, we can start to interpret what they mean. We can see one of the biggest flaws of Player Efficiency Rating standing out in our results, which is that players with a small amount of minutes may have an inflated score. This is true for both total minute uPER and minutes per game uPER, although total minute uPER does seem to be more inflated than minutes per game uPER. Dante Rivera, who ranks first on the team in total minutes, minutes per game, and minutes per game uPER, ranks third on the team in total minutes uPER behind Janvier Johnson and Junior Boley. However, seeing that Janvier Johnson and Junior Boley have less combined total minutes than Dante Rivera averages, we can see how a small sample size can skew the total minute uPER statistics. For this reason, we will be looking mostly at minutes per game uPER when evaluating Plymouth State’s players.
Let’s start with the players who deserve more minutes based on their uPER. Junior Boley ranks last on the team in total minutes and minutes per game, but ranks second in total minute uPER and 12th in minutes per game uPER. Junior has a large difference in team ranks for his uPER statistics, which we can chalk up to his inflated total minute uPER from his small sample size of minutes, as well as his statistics when he was in the game. It’s unreasonable to say that since Junior ranks second on the team in total minute uPER that he deserves to play the second most minutes on the team. It’s even unreasonable to think that he should be playing starters minutes based on his statistics during his seven minutes of court time. However, when looking at his minutes per game uPER rank of 12, we can make an argument that he deserves more minutes based on his play.
Another player who may deserve more playing time based on their uPER statistics and ranks would be Janvier Johnson. Again, Janvier’s uPER statistics are inflated from his small amount of playing time, but his team ranks are still impressive. Javier Johnson ranks first on the team in total minute uPER and fourth in minutes per game uPER. We will mostly disregard his total minute uPER, as we did with Junior Boley, due to his lack of playing time. But ranking fourth on the team in minutes per game uPER is significant. Does this mean he should be playing starter’s minutes? Probably not. But a rise from his 2.1 minutes per game seems warranted. Based on his play in limited minutes, Janvier Johnson at least deserves a longer look, maybe in the Sopie Pek-Ryan Roggenbuck range of 8 to 9 minutes a game.
Moving into the players who have underwhelmed based on their uPER statistics, the team may benefit from Bryton Early playing a few less minutes per game. Bryton ranks sixth on the team in total minutes and minutes per game, although he ranks 12th in total minute uPER and 10th in minutes per game uPER. There isn’t a huge gap between minutes and uPER rankings, and there are a few other players that have similar gaps in their rankings, but Bryton plays the most minutes out of that group. Again, this does not mean Bryton should be playing the 10th most minutes on the team, as that would put him in the Ryan Roggenbuck range of 9.2 minutes per game, a 12.7 minutes per game drop. But a drop from 21.9 minutes per game to 17-18 minutes per game seems reasonable based on his uPER. Those extra 4-5 minutes per game could be given to overachieving players based on their uPER’s, such as Chris McCarthy, Ryan Roggenbuck, and Janvier Johnson.
Another player who has struggled in uPER related to the amount of minutes he plays would be Dimmone Marshall. Dimmone ranks 12th on the team in total minutes and 14th in minutes per game, although he ranks last in both total minute uPER and minutes per game uPER. Dimmone Marshall is also the only player on the team who had a negative uPER, which shows that he hasn’t been effective during his time on the court. We can’t reasonably say, however, that Dimmone doesn’t deserve to play. There’s usually reasons why some players play more than others. Dimmone Marshall ranks below Chris Canlan in uPER, but he also plays three times as many minutes than Chris does. We can’t assume Chris Canlan would play better than Dimmone if he was given Dimmone’s minutes. Players such as Liam Densmore, who ranks lower than Dimmone Marshall in total minutes and minutes per game, is a better comparison due to Liam’s larger sample size (playing time) than Chris Canlan. Based only on our uPER statistics, we can infer that players like Liam Densmore and Sopie Pek should be playing more minutes than Dimmone Marshall, as they have been much more effective in their time played.