This document is an explanation of the playerstats spreadsheet as well as discussion about evaluating players in general. Please read my other document, nbastats first, if you haven’t already. Here are a list of the abbreviations used and a quick explanation: MPG, minutes per game, FGA field goal attempts, FTA free throw attempts, OR offensive rebounds, AST assists, TO turnovers, PPG points per game, OE offensive efficiency, OP offensive possessions, Exp PPG expected points per game, EPPG – APPG expected points per game minus average points per game, WAA wins above average. The stats with a star will be discussed later.
Note: Only players with at least 20 games played and 15mpg were included in the spreadsheet, and in determining average statistics at a given position.
The purpose of this spreadsheet was to create a wins above replacement stat, similar to baseball. The method that I use to calculate the WAA is as follows: first the expected change in points the player would create on an “average” team is calculated. The “average” team is modeled using statistics from league wide averages (derived via the nbastats spreadsheet). Then, the player’s OP are subtracted from the team’s OP and the PPG the team would score are calculated over the new OP number. The player’s PPG average is then added to the newly calculated PPG average. The possessions created or lost is then calculated by taking the average turnovers, subtracting the average offensive rebounds, and then prorating the possessions created or lost in the same amount of minutes played as the player. The result is then compared to the player’s offensive rebounds and turnovers, and the league OE is then multiplied by the difference between the average possessions created or lost and the player’s possessions created or lost. This is then added to the PPG total previously calculated, and the new total is then the amount that an average team with the player would score per game. This average is then compared to the average of players at the same position as the player. The resultant PPG change the player creates over the average player at his position is then used to calculate the number of wins the PPG change creates over a season.
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Formulas
The expected PPG formula is as follows:
(((89.5-OPP)*1.041)+PPGP)+((TOA-ORA)*(MPGP/MPGA)+ORP-TOP)*1.041
where the subscript P and A denote the player and the average of players at that position respectively. The numbers 89.5 and 1.041 are the league wide team OP and OE averages respectively.
The WAA formula is as follows:
((Exp PPG P -Exp PPG A)*2.706)
where the subscript P and A denote the player and the average of players at that position respectively, and Exp PPG is derived using the expected PPG formula. The number 2.706 is 3.3% of 82, where as explained in the nbastats document that 1ppg is worth 3.3% in winning percentage, and 82 is the number of games played per season.
Interpreting Results
WAA is not a perfect stat and does have flaws. First and foremost, it does not in any way shape or form consider defense, as the stats needed to evaluate defense do not currently exist.
Second, several subjective decisions were made that alter the values shown. In particular, two trends are not represented in the WAA stat. First, assists are not included. I have done some research into assists and their effects on OE, and I can say that I have noticed a correlation, but that correlation is not represented in the WAA stat (yet). Second, OP/MPG is also not included. I have done even less research in this area, but I do believe it will be found that as OP/MPG increases, OE decreases. This is rather easily demonstrated: Jeff Foster actually has a higher OE than does Shaq. However, nobody in their right mind would consider Foster to be either a better offensive player or a more valuable offensive player than Shaq, and I certainly don’t. The reason for this is that if one were to hypothetically “build” a team of all Jeff Fosters and one of Shaqs, the team of Fosters would average about 52.2 OP per game, while the team of Shaqs average 118.7. Now, the average team in the NBA averages 89.5, so even if you were to compare the production of the Shaqs over 89.5 OP, it would beat the team of Fosters because they can only average 52.2. What this is driving at then is that production at a high OP/MPG is much more valuable than production at a low OP/MPG, because the average team uses 89.5 OP per game. If one were to replace Shaq with Jeff Foster, while you would get more points per each individual possession used, you would be forced to spread out the extra 13 OP to the rest of the team, likely lowering their OE. The unfortunate part is that I have not done enough research to be able to quantify the effects or place a value on OP/MPG, and it is therefore not included in the WAR stat (yet).
In addition, what position a player is considered to play can change their WAA value greatly. An example of this is Derek Fisher, who this year by any measurement was absolutely terrible. However, Fisher is considered against other point guards rather unfairly. Fisher did very little ball handling and therefore his TO/MPG ratio is extremely low for most players at the PG position. Because TO and OR are fairly important in determining WAA value, Fisher’s value is artificially boosted. Fisher likely should be considered a SG or at least a guard, but I made the decision when inputting the stats myself to use the position that Yahoo had assigned them.
Also, in creating the formula I decided to prorate offensive rebounds and turnovers but not shots. I decided that TO and OR are simply functions of time, whereas a shot attempt is an independent action and decision by the player. Shot attempts may also be limited by OP or any other number of factors (like the coach running plays for the player), and without trying to get too complex I simply decided not to prorate FGA.
Lastly, in some situations players such as Vlade, Shaq, and Ray Allen who do much more ball handling and/or passing than the average at their position have higher turnover rates per MPG. For non-guards, I probably should have considered TO/OP as opposed to TO/MPG as the amount of actual ball handling for non-guards is usually non-existent (This situation is similar to the Fisher situation described above). However, it is difficult to quantify exactly how much ball handling a player does, and while an increase in OP generally means an increase in ball handling, an increase in ball handling is not necessarily tied to an increase in OP. The ideal of course is to examine the number of TO per unit of time ball handling, but unfortunately, that isn’t really possible with the stats we have available right now.
With all that said, I do believe WAA gives very valuable insight into player values. It is up to the person passing judgment however to determine how effectively a player’s value is represented. In some situations it may not be, and considering the factors that are weighed in the formulas is key to understanding why a player may or may not be accurately portrayed. I do not believe that WAA should be an end all be all stat in determining player value but should be one of many things in considering a player’s worth.
The Star
As I mentioned earlier, I said I would discuss the stats with the star on them. For reasons mentioned in the previous passage, there are some situations where the WAA stat artificially boosts or decreases some players’ values. The stats with a star then are simply the same as the stats they share names with, except that the stats with a star consider shooting only. That is to say, OR and TO are not considered, and the Exp PPG* value is simply ((89.5-OPP)*1.041)+PPGP, and the WAA* value is simply the number of wins expected based off the change in PPG that the player’s shooting would cause.
Written by Will Carr
June 17, 2004