Box Plus/Minus

Box Plus/Minus is the successor stat to Advanced Statistical Plus/Minus (ASPM), which used to be hosted on this site.  Since Basketball Reference now produces Box Plus/Minus (BPM) for the NBA (and does it for the D-League and NCAA Men’s Basketball also), neither of these stats are now produced on this site.

However, the old pages for ASPM are still located on this site and will remain as is.

The full documentation for Box Plus/Minus is located at About Box Plus/Minus on Basketball Reference.

 

If there are any questions about Box Plus/Minus calculations, please feel free to ask them in the comments section below.  I will be migrating questions about Box Plus/Minus from my comments page and other locations to this page to keep them all together.

 

21 Comments

  1. Eric

    Mr. Myers, I have read your BPM article on basketball-reference with great interest. I am in the midst of a project comparing four methods (yours, WS, WP, and EWA), and I can’t figure out one part of your methodology: replacement level is -2.0 BPM, but what is the win total for a team of replacement level players? If I sum up all the VORP for 2014, I get 810.2 wins above replacement level, which leaves 420.2 for the replacement level, which divides rather neatly to 14 wins. Is that a coincidence, or is 14 wins the number? I get 810.8 wins for 2013 too but I thought asking directly was most prudent.

    • Daniel M

      Since a team of -2.0 players will produce about 14 wins (depending on how you do the team points to wins conversion–pythagorean method, linear, etc.), that is the number of wins a replacement level team will produce according to VORP.

      The number that was derived directly was the -2.0 value, per the extremely long thread on Tom Tango’s blog (linked to in the BPM writeup). A team of replacement players will produce some wins; the difficulty lies in establishing that number. Several methods were used in the later portions of the Tom Tango comment thread, and all basically came up with the -2.0 value.

  2. Kevin Martell

    Dan,

    I’m loving your Box Plus/Minus stat. One thing I noticed is that guards seem to have better BPM and VORP than bigs. Is this an accurate observation? Is there anything in BPM that favors perimeter players over bigs? Thanks!

    • Daniel M

      Over the entire time period that BPM covers (since the mid 1970s), there is no significant positional bias; all positions average near 0.

      I just checked a bunch of time intervals, and there is no strong bias anywhere. Maybe a slight tilt toward small forwards, (averaging about +0.25), but there are a number of possible reasons for that.

  3. Jaewoo

    Dan,

    I’m loving your BPM stats, so I’d like to calculate BPM/VORP of Korean Basketball League.

    But Korean League is 40 minute games and 54 game season. Would I need to alter the coefficient? Thanks!

    • Daniel M

      Let’s talk via email about that. It’s a good question.

      EDIT: we got Box Plus/Minus up and running for the Korean Basketball league, back into the 1990s. If anyone is interested in that data, contact me and I’ll put you in touch with Jaewoo.

  4. pete palmer

    I’m looking at Basketball-reference BPM calc. I assume TO% is what they call TOV%, don’t know what reMPG is, something to do with MPG?, also 3PAr some kind of relative 3PA?

  5. It looks like 3PAr is 3PA/FGA. It is not in the bkref glossary, but is in the advanced stats. TO% looks like a number between 0 and 1, not TOV% which is 0-100.
    I tried TOV%/100 but that didn’t work. So what is TO%?

    • Daniel M

      TO% is the turnover percentage that Basketball Reference uses, defined as turnovers per player possession. I simply divided TOV% by 100, as you stated.

  6. Steve Vickers

    Daniel-

    Love your work. I’ve been playing around with creating BPM numbers for the last 20 years of ACC basketball (spoiler: Duncan was amazing). Question: On the spreadsheet I downloaded from B-R.com, the “Raw SPM” column (column AS) adds up four of the five to its left, but not “Val/Shot.” When calculating “Raw OBPM” (column BG), it adds up all five columns to the left, including “Val/Shot.” Is this right?

  7. Hi Daniel.

    I’m trying to get a hold of Box Plus Minus and I have found that the best way to do that, is to try to calculate it myself.

    So I downloaded the big excel-file on basketball-reference to look into the machinery.

    First of all. Nice job.

    I have a question: How do you calculate the replacement-level? You have values that you subtract from each of the component of BPM (“Reb/Vers”, “Defense”, “Offense” and “MPG + Int”). But I cannot see where you get those values from?

    • Nevermind. I figured it out 🙂

      I think it has something to do with me running an old version of Excel that doesn’t support everything you’ve done in the spreadsheet. So not everything is there.

      • Daniel M

        There’s quite a bit of VBA in this spreadsheet that has to be activated to get everything to run. I wasn’t using a new version of Exel when I wrote the sheet, so that shouldn’t be an issue. I think I was using 2007?

    • Daniel M

      For everyone else’s reference, the Excel spreadsheet has some “average values” subtracted out of each component of the BPM, simply for presentation within the Excel file (so everyone is centered on 0). Since this is before the team adjustment, those values have no bearing on the final result.

  8. Y2J

    Hello, I have some questions about BPM.

    1. In Bkref’s Sheet, BPM is in Reb/Vers, Offense, Defense, MPG. But OBPM it includes Val/Shot, And You said it may be a bug. But the OBPM Numbers in Basketball Reference Page provides the result which is closer to data including Val/Shot, so it means the site itself has the bug??

    2. In Playoff BPM, How should I Credit Net, Offensive Rating of a Team? Should I Use Net Rating as Team’s PO ORtg-Team’s PO Drtg, and Offensive Rating as Team’s PO ORtg – Lg’s PO Avg ORtg?

    3. In Calculating Team Rating in PO, Just Multiply The Player’s PO Time * Regular Season BPM and sum it, and devide by Sum of PO Time and Multiply 5?

    These are my Questions. Thanks.

    • Y2J

      And I have one more question, that when I calculate Playoff BPM, Should I calculate All player’s BPM and make it average to Zero?

    • Daniel M

      Hello, Y2J, thanks for your question!
      1. Has that not been fixed yet? I’ll check into it. Val/Shot was just an intermediate term in the offensive calculation. Basketball Reference could certainly have the same bug, since they simply copied my (perhaps buggy!) Excel file to create BPM for their site.
      2. The Team Ratings to use in the playoffs are a bit different than the regular season. I take the actual efficiencies and adjust by the strength of their opponents. So if an offensive rating is, say, 113 vs. a playoff average of 107, that would be a +6. Then the strength of schedule adjustment would be applied to that +6 number. I calculate strength of schedule based on the actual playoff lineups, using the players’ regular season BPMs.
      So, suppose the Spurs used Duncan and Manu 35 MPG in the playoffs, then their “expected strength” would be based on Duncan and Manu’s regular season BPM, but using the playoff distribution of minutes. Most teams will be better in the playoffs due to their tightened rotation of players.
      So back to the original team. It was +6 in the playoffs. It played, say, the Mavs 4 times and the Spurs 7 times. The Mavs had an “expected defensive strength” of +1, and the Spurs an “expected defensive strength” of +6. So the team’s strength of schedule would be (4*1+7*6)/(4+7) = +4.2. Therefore the “Adjusted Offensive Rating” for that team in the playoffs would be +6 + 4.2 = +10.2.
      Does that make sense?
      3. That’s the calculation for “expected strength” of a team in the playoffs, which I just referred to in the paragraph above. That is used, as discussed, in determining a team’s strength of schedule in the playoffs.

      And for the last question:
      Playoff BPM will not sum to 0, because it’s on the same scale as the regular season. All the players on one team will be adjusted to sum to their team’s playoff adjusted ratings, but that’s the only adjustment of the numbers.

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