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June 2015
Updated BPM All Time - 2015
Daniel Myers, the creator of Box Plus/Minus (BPM), has recently released a new and updated version of BPM. This, along with the completion of the 2015 playoffs, led me to updating the BPM All Time list. The new version included big improvements to defense and underrates perimeter defenders far less. For the methodology, I kept it far simpler, and used hall rating, which is derived from baseball. Basically, it takes into account longevity (wins over replacement) and peak (wins over average). I computed this for the regular season and playoffs for each player and added them to get a player's total hall rating. Although I suppose one could give playoff hall rating higher weight, it is unclear what the weight should exactly be -- so I didn't bother trying to do that for now.
For players for whom BPM was not available (seasons before 1978), I used an approximation of BPM based on a formula provided by Neil Paine of Fivethirtyeight.com -- 0.15*(PER - 15) + 30.5 *(WS/48 - 0.1). Also, Lebron has made the jump to 2nd all time and is now the greatest playoff performer ever. It will be interesting if he can catch Jordan and will largely depend on how much longer he plays along with how many elite years he has left.
Here are the Top 10 players in NBA history according to BPM:
For players for whom BPM was not available (seasons before 1978), I used an approximation of BPM based on a formula provided by Neil Paine of Fivethirtyeight.com -- 0.15*(PER - 15) + 30.5 *(WS/48 - 0.1). Also, Lebron has made the jump to 2nd all time and is now the greatest playoff performer ever. It will be interesting if he can catch Jordan and will largely depend on how much longer he plays along with how many elite years he has left.
All-Time List based on PER (Player Efficiency Rating)
As part of my on-going series on the construction of all-time lists based on various advanced metrics, I bring to you the all-time list for the highly popular statistic, PER. PER, which was created by John Hollinger, is perhaps the most well known advanced statistic today. In order to convert PER (a rate stat) to actual production, we can rely on Hollinger's estimated wins added (EWA), which computes the number of wins a player added to a team based on their PER, position, and minutes played.
The methodology for computing a player's all time score from their EWA was simple. First I computed their regular season EWA. Next, I computed their EWA in each round of the playoffs and gave higher weight to successive rounds (e.g. conference finals matter more than the opening round). Finally, I simply summed the player's regular season EWA and weighted playoff EWA.
The methodology for computing a player's all time score from their EWA was simple. First I computed their regular season EWA. Next, I computed their EWA in each round of the playoffs and gave higher weight to successive rounds (e.g. conference finals matter more than the opening round). Finally, I simply summed the player's regular season EWA and weighted playoff EWA.
Here are the Top 10 players in NBA history according to PER:
The Top 2 players of all time (MJ, Kareem) are consistent so far across all of the metrics that have been looked at (BPM, SPM, PER). Lebron just passed Wilt for 4th all time on this list during this current playoff run. He has a very good shot at passing Shaq and moving to 3rd by the time his career is over. Kobe and Duncan are not surprisingly very close to each other and are ranked 6th and 7th; both have a shot of passing Wilt in the next season or two (although it's not very likely). Please share your thoughts and feedback in the comments below.
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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