All-Time List based on Statistical Plus/Minus (SPM)
Recently, I released an all-time list based on Box Plus/Minus (BPM). I went and looked at another very good statistic for player evaluation known as Statistical Plus/Minus (SPM). SPM, whose formula can be found here, belongs to the same class of stats as BPM - those that combine box score stats with plus-minus. SPM empirically performs very well and achieves similar levels of accuracy as BPM. While BPM performs slightly better, SPM can give us a new look at certain players; therefore in the context of an all-time list, it's best to look at the results of both.
SPM is a very interesting statistic in that it looks at box score statistics adjusted for pace and minutes played allowing for player comparisons across eras to be possible. It even has non-linear terms such as versatility (cube root of product of minute and pace adjusted points, rebounds, and assists), while also including a usage term which is key. In order to convert SPMs to production, you can calculate a player's VORP (Value over Replacement Player) by using the formula [SPM - (-2.0)] * (minutes/total team minutes) * (games played/total games).
To obtain an all time score for each player, I first calculated their regular season VORP. Since I had to manually code SPM (it's not available on basketball-reference), it was very difficult to compute series-specific SPMs. Therefore, to properly attempt to factor in the playoffs, I instead gave higher weight to deeper playoff runs. This is indirectly rewarding good performance in the conference finals, finals, etc. Next, I calculated the weighted sum of each player's playoff VORPs. Finally, I added the player's regular season VORP and total playoff VORP.
Here are the Top 10 players in NBA history:
According to SPM, Jordan, Kareem, Lebron, and Kobe are the clear Top 4 players in NBA history. It's interesting that SPM captured the exact same Top 10 as BPM did as well, which is strong evidence in support of these players (BPM and SPM are probably the 2 best advanced stats we have right now). Lebron will pass Kareem very quickly and has a good shot at supplanting Jordan in the top spot. Furthermore, if Kobe can be productive next year, he may have a shot at passing Kareem as well (although it will require near elite level production). Feel free to leave your thoughts and feedback bellow in the comments.
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