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All Time List based on Box Plus/Minus (BPM)

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All-time lists are intended to measure a player's greatness and happen to be one of the most debated topics among NBA fans. These lists are of course a very subjective matter and an easy way to make someone angry at you.  My goal was to create an all-time list solely based on what players did on the basketball court, or in other words their production throughout their career.  The statistic I chose to use in order to do this is known as "Box Plus/Minus" (BPM). Per Basketball-Reference, "Box Plus/Minus (BPM) is a box score-based metric for evaluating basketball players' quality and contribution to the team. It is the latest version of a stat previously called Advanced Statistical Plus/Minus. BPM relies on a player's box score information and the team's overall performance to estimate a player's performance relative to league average. BPM is a per-100-possession stat, the same scale as Adjusted Plus/Minus: 0.0 is league average, +5 means the player is 5 points better than an average player over 100 possessions (which is about All-NBA level), -2 is replacement level, and -5 is really bad." BPM is of a class of statistics which look to combine box-score stats with plus minus (a "best of both worlds" stat). The weights for several box-score based stats in BPM's formulation have been empirically determined by regressing them over Regularized-Adjusted Plus Minus (RAPM). RAPM is a fairly accurate estimate of a player's actual plus/minus impact using play-by-play data and accounting for player's teammates (thereby eliminating the problems and noise with normal plus/minus). BPM is the best box-score metric available today and is more stable than RAPM itself. It is therefore the ideal stat to be used in the creation of an all-time list. BPM is purely a rate-stat and in order to convert it to actual production we must consider the amount of minutes played. This is handled by Value Over Replacement Player (VORP) which converts BPM into what a player's overall contribution to his team is measured against a theoretical "replacement" level player. The formula for VORP is [BPM – (-2.0)] * (% of minutes played)*(team games/82).

 I looked at several factors in order to determine a player's "all time score" so a list could be created. First, I calculated at a player's career total VORP in the regular season. Next, what a player is truly made of is defined in the playoffs where the best-of-the-best have shined the brightest. Just like Neil Paine, for each player I made adjustments for the level of competition faced, home-court advantage, and the leverage of each game, and recalculated their VORP for each round of the playoffs. I weight production in each successive round of the playoffs higher (e.g. conference finals matter more than the 1st round) and finally compute the weighted sum to determine a player's career playoff production. Playoff production will obviously be quite a bit lower than regular season production due to the fewer minutes and games; this undervalues some of the greatest players who have had several championship runs, for example. Therefore, I multiplied each player's playoff production by 6. After this adjustment, playoff production is in general slightly more valuable than regular season production. I personally find this to be fair since the playoffs are where teams' offensive and defensive effort are at their highest. Furthermore, the sample size of games played in the playoffs is usually pretty large for most of the greatest players in NBA history, so this is generally not a concern. Finally, I summed a player's regular season production and playoff production and put it on a scale of 1000 which results in their all time score. A score of 1000 can be thought of as the best possible career. Since BPM is not available for players before the 1973-1974 season due to certain box score stats not being recorded, it was calculated using estimates of these stats (this is for players such as Wilt, Jerry West, Oscar Robertson, etc.).
Here are the Top 20 players in NBA history:


Michael Jordan is by far the best player of all time -- who knew!?  This list will remain constant in the near future with the one exception of Lebron James. Lebron is currently 3rd all time and will likely end up as the 2nd best player ever at his current pace, passing Kareem in the next few years. It's safe to say that Jordan is untouchable. Other active players that rank highly all time include Jason Kidd (26th), Chris Paul (28th), Paul Pierce (31st), Pau Gasol (41st), and Kevin Durant (47th).

Overall, in my opinion, this all time list is as close to the "truth" as you can get since it ranks players solely based on what they have done on the basketball court, using the best metric we have to measure player performance today. Feel free to leave your thoughts and feedback you may have on improving the methodology used in the comments below. 

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1 comments:

  1. ryth16September 29, 2016 at 6:02 PM

    Considering these appear to be cumulative stats not rate stats Saying Jordan is untouchable makes no sense at all. In fact, it appears safe to say that barring injuries LeBron should pass Jordan on this list. All it would take is three more good years out of LeBron to comfortably pass Jordan. Since this seems dated 2015 it actually should be only two years now.

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