The debut and popularization of BPM

[hoopthinker]

DSMok1 can you explain why DRB% has a negative coeficient?
That seems counterintuitive since DRB traditionally were regarded as something positive in bball and necessary for championchips ''No rebounds,no rings""

[Mike G]

Again quoting the 'about BPM' article:

The beauty of VORP is that ... it should track linearly with salary. A player with a VORP of 4.0 is worth, on the market, about twice what a player of VORP 2.0 is worth. ...

Since not quite 60% of NBA players even have positive VORP, only about 1/3 of all NBA player pairs can even have a relative value in such an exercise: Joakim Noah (vorp = 5.8) should be paid how much more than Carlos Boozer (-0.6) ?

To convert VORP to an estimate of wins over replacement, simply multiply by 2.7. This translates a player's point differential approximately into wins ...

... "above replacement", that is.
It seems the 2014 Sixers total about minus-7 WAR. The default/background conditions associated with 'replacement level play' generate another 23 wins. Is that about right?

[DSMok1]

DSMok1 can you explain why DRB% has a negative coeficient?
That seems counterintuitive since DRB traditionally were regarded as something positive in bball and necessary for championchips ''No rebounds,no rings""

TRB%, which includes defensive rebounds, has a large positive coefficient elsewhere (in its interaction with assists). Most of the value for rebounds comes from that term; the ORB and DRB terms just shift the value a bit more toward offensive rebounds.

Of course, that does require a player to have at least a few assists.

As an example: Anthony Davis's numbers so far this year: ORB%: 12.4 DRB%: 23.5 TRB%: 17.6 AST%:9.0

The coefficients:
ORB% 0.137600 100.0
DRB% -0.151938 100.0
sqrt(AST%*TRB%) 0.691501 100.0*100.0

The total value from these terms would be:
ORB%: .137*12.4 = +1.7
DRB%: -.152*23.5 = -3.6
sqrt(AST%*TRB%): 0.691*sqrt(9.0*17.6) = +8.7

So the total of these rebounding terms for Anthony Davis, despite his mediocre assist percentage, is +6.8.

Elite players usually have both high rebound percentages and high assist percentages. Tim Duncan, for instance, is always high on both.

[DSMok1]

Again quoting the 'about BPM' article:

The beauty of VORP is that ... it should track linearly with salary. A player with a VORP of 4.0 is worth, on the market, about twice what a player of VORP 2.0 is worth. ...

Since not quite 60% of NBA players even have positive VORP, only about 1/3 of all NBA player pairs can even have a relative value in such an exercise: Joakim Noah (vorp = 5.8) should be paid how much more than Carlos Boozer (-0.6) ?

To convert VORP to an estimate of wins over replacement, simply multiply by 2.7. This translates a player's point differential approximately into wins ...

... "above replacement", that is.
It seems the 2014 Sixers total about minus-7 WAR. The default/background conditions associated with 'replacement level play' generate another 23 wins. Is that about right?

You mention the 60% figure--most players in the NBA are below average. The median player is well below the minutes-weighted average performance. There were 434 players who played 100 minutes last season. Only 150 were at or above 0. (Yet the minute-weighted average is 0). The population is strongly skewed, since this is the right side of the total population's bell curve.

As for VORP: A 0 VORP player is a minimum salary player, so about $1,000,000 in salary. 1 point of VORP is worth about $5 million on the free agent market, though that is a moving target right now. Last season: LeBron had 7.6 VORP, so an estimated value of 5*7.6+1=$39 million.

If a player is below 0 VORP they shouldn't be playing or being paid--unless they are some sort of developmental prospect and need the playing time to develop.

Remember, though: there is a margin of error around each player's BPM. It's just an estimate.

[Mike G]

You mention the 60% figure--most players in the NBA are below average..

That's not the 60% I was referring to -- it's the <60% of players who are even above -2 BPM. You say the other 43% are development players who don't deserve any salary, and I'm saying this is far fetched.

I mentioned 31 players with >1000 minutes who are <0 VORP. The uncertainty spread may have inadvertently caught them in the 'negative value' zone, but then others who just escaped might as easily fall into it. Here they are, along with some other 'candidates' near the sub-R zone, ranked by salary (millions) :

Code: Select all

replaceables       $al    Tm   Min    BPM    PER    WS   WS/48   e484   eW
Amar'e Stoudemire 23.4   NYK   1466   -3.1   18.8   3.8   .124   1.25   3.8
Carlos Boozer     16.8   CHI   2141   -3.2   14.4   3.4   .076   1.52   6.7
Kevin Garnett     12.4   BRK   1109   -1.9   13.3   1.2   .054   1.13   2.6
Andrea Bargnani   11.9   NYK   1257   -2.3   14.5   1.5   .058    .94   2.4
Luis Scola        11.3   IND   1399   -3.4   13.4   2.4   .084   1.11   3.2

Kendrick Perkins   9.7   OKC   1207   -2.1    6.3    .8   .031    .28    .7
Jeff Green         9.4   BOS   2805   -2.0   13.1   3.3   .057    .88   5.1
Marcus Thornton    8.6   SAC   1121   -1.9    9.7    .9   .038    .33    .8
Rodney Stuckey     8.5   DET   1950   -4.0   14.0   2.2   .053    .72   2.9
O.J. Mayo          8.0   MIL   1346   -3.9   11.2    .1   .002    .59   1.6

replaceables       $al    Tm   Min    BPM    PER    WS   WS/48   e484   eW
Ersan Ilyasova     7.9   MIL   1478   -3.1   13.8   1.6   .053    .91   2.8
Glen Davis         7.8   ORL   1354   -2.3   13.7   1.5   .053    .86   2.4
Tayshaun Prince    7.7   MEM   1948   -2.4    8.2   1.5   .038    .27   1.1
Avery Bradley      7.2   BOS   1855   -2.5   12.7   1.8   .046    .81   3.1
Travis Outlaw      7.0   SAC   1065   -2.4   10.4   1.4   .062    .40    .9

Evan Turner        6.7   PHI   1886   -3.8   13.2    .7   .017    .88   3.4
Derrick Williams   6.3   SAC   1658   -2.1   11.9   2.5   .073    .51   1.7
Jarrett Jack       6.3   CLE   2252   -2.2   11.5   2.3   .049    .57   2.7
Jason Thompson     6.0   SAC   2007   -2.5   11.1   2.7   .064    .63   2.6
Enes Kanter        5.7   UTA   2138   -3.7   15.6   2.2   .050   1.07   4.7

replaceables       $al    Tm   Min    BPM    PER    WS   WS/48   e484   eW
Tristan Thompson   5.1   CLE   2594   -1.9   14.9   5.7   .106    .98   5.2
Nick Young         5.0   LAL   1810   -1.9   16.0   2.5   .067    .95   3.6
Ramon Sessions     5.0   CHA   1305   -2.3   14.6   2.0   .075    .92   2.5
Jose Barea         4.7   MIN   1471   -3.1   11.6    .7   .024    .93   2.8
Dion Waiters       4.1   CLE   2072   -1.9   14.0   1.6   .037    .95   4.1

Bismack Biyombo    3.9   CHA   1072   -2.5   13.3   3.2   .144    .64   1.4
Alonzo Gee         3.3   CLE   1020   -2.5    8.6    .9   .041    .19    .4
Mike Scott         3.3   ATL   1482   -2.9   15.3   2.6   .084   1.04   3.2
Anthony Morrow     3.2   NOP   1426   -2.3   13.9   2.4   .081    .63   1.9
Darrell Arthur     3.2   DEN   1161   -2.7    9.4    .7   .029    .41   1.0

replaceables       $al    Tm   Min    BPM    PER    WS   WS/48   e484   eW
Ben McLemore       3.0   SAC   2187   -2.8    7.7    .7   .016    .21   1.0
Will Bynum         2.9   DET   1054   -3.3   14.4   1.0   .047    .87   1.9
Ke Caldwell-Pope   2.8   DET   1583   -2.1    9.4   1.8   .055    .22    .7
Brian Roberts      2.7   NOP   1667   -2.7   13.4   2.2   .063    .77   2.7
Trey Burke         2.5   UTA   2262   -2.3   12.6    .9   .020    .81   3.8

Austin Rivers      2.4   NOP   1339   -3.6   11.6    .6   .023    .56   1.5
Shelvin Mack       2.4   ATL   1490   -2.2   13.2   2.3   .074    .82   2.5
Tobias Harris      2.4   ORL   1850   -1.9   16.5   4.1   .107   1.16   4.4
Norris Cole        2.0   MIA   2014   -2.5    8.8   1.2   .029    .29   1.2
Gian Antetokounmpo 1.9   MIL   1897   -1.8   10.8   1.2   .031    .42   1.6

replaceables       $al    Tm   Min    BPM    PER    WS   WS/48   e484   eW
Andrew Nicholson   1.5   ORL   1174   -6.4    9.9    .6   .025    .49   1.2
Evan Fournier      1.5   DEN   1503   -2.2   10.3   1.3   .043    .53   1.7
Tony Snell         1.5   CHI   1231   -2.8    8.0   1.6   .063    .25    .6
Alan Anderson      1.3   BRK   1773   -1.9    9.5   1.7   .047    .28   1.0
Tim Hardaway       1.3   NYK   1875   -2.1   12.7   3.1   .080    .52   2.0

Tony Wroten        1.2   PHI   1765   -4.2   12.9   -.9  -.025    .74   2.7
Ish Smith          1.0   PHO   1006   -2.1   11.7   1.0   .048    .54   1.1
John Salmons       1.0   TOR   1281   -1.9    7.6   1.4   .052    .13    .4
Diante Garrett      .9   UTA   1048   -4.8    7.1   -.8  -.036    .02    .0
E'Twaun Moore       .9   ORL   1506   -2.2   11.1   1.7   .055    .34   1.1

replaceables       $al    Tm   Min    BPM    PER    WS   WS/48   e484   eW
James Anderson      .9   PHI   2309   -2.5   10.9   1.9   .039    .43   2.0
Kendall Marshall    .9   LAL   1564   -4.2   12.6    .9   .029    .77   2.5
Nate Wolters        .9   MIL   1309   -3.5   12.7   1.2   .043    .61   1.6
Robert Sacre        .9   LAL   1089   -2.3   12.1   1.4   .061    .49   1.1
Hollis Thompson     .8   PHI   1742   -3.0    9.5   2.0   .055    .17    .6

Matthew Dellavedova .8   CLE   1271   -2.1   10.7   2.1   .078    .37   1.0
Phil Pressey        .8   BOS   1132   -4.1    8.8    .1   .005    .24    .6

Some players were with more than one team, perhaps with better numbers.
A lot of these players rate above NBA avg in PER, ws/48 and/or eW/484.
A number of them got a substantial raise this year, after putting up these numbers last year.

[DSMok1]

You mention the 60% figure--most players in the NBA are below average..

That's not the 60% I was referring to -- it's the <60% of players who are even above -2 BPM. You say the other 43% are development players who don't deserve any salary, and I'm saying this is far fetched.

I mentioned 31 players with >1000 minutes who are <0 VORP. The uncertainty spread may have inadvertently caught them in the 'negative value' zone, but then others who just escaped might as easily fall into it. Here they are, along with some other 'candidates' near the sub-R zone, ranked by salary (millions) :

Some players were with more than one team, perhaps with better numbers.
A lot of these players rate above NBA avg in PER, ws/48 and/or eW/484.
A number of them got a substantial raise this year, after putting up these numbers last year.

Replacement level was set based on what the average "10th player on the team" did, and also on what the average "minimum salary vet." did. Both of those groups of players averaged -2.0.

BPM is imperfect, particularly in quantifying defense. However, I am confident that the replacement level itself is set very near correctly. The full thread (I recommend reading it) is at http://tangotiger.com/index.php/site/co ... nba-player and http://www.apbr.org/metrics/viewtopic.php?f=2&t=8635 . Please read it through.

I agree that the 2.0 feels a bit high, but it's been corroborated through several methods.

[Mike G]

I did try to read that thread, but it goes on and on.
And in any case, it shouldn't be very hard to explain how 40% of NBA rosters -- players 10 thru 15 -- are considered to be replaceable. Obviously, there aren't 180 players available that are the caliber of Jeff Green or most of these others. Maybe one team could fire a handful of players and find equivalent replacements, but I doubt it.

I may look up salaries and plug them in. What I have now (incomplete) is that players who made 1.1 mill or less had avg BPM of -3.8 last year, and that's not weighted for minutes.
Wouldn't an available replacement player not even have a contract at the start of the season?

[DSMok1]

I did try to read that thread, but it goes on and on.
And in any case, it shouldn't be very hard to explain how 40% of NBA rosters -- players 10 thru 15 -- are considered to be replaceable. Obviously, there aren't 180 players available that are the caliber of Jeff Green or most of these others. Maybe one team could fire a handful of players and find equivalent replacements, but I doubt it.

I may look up salaries and plug them in. What I have now (incomplete) is that players who made 1.1 mill or less had avg BPM of -3.8 last year, and that's not weighted for minutes.
Wouldn't an available replacement player not even have a contract at the start of the season?

No. Replacement player is a player who wouldn't play minutes, in general, to start the season. Wouldn't get minutes in a game that mattered if the team was healthy.

Also, when looking at salaries, make sure to exclude rookie contracts.

By the way--RPM agrees that Jeff Green is at or below replacement level: http://espn.go.com/nba/statistics/rpm/_ ... position/5

[Mike G]

Including rookie contracts, the avg 10th-best pay on a team this year is $1.95 million.

Replacement player is a player who wouldn't play minutes, in general, to start the season. Wouldn't get minutes in a game that mattered if the team was healthy.

And yet some <0 VORP players are starting and/or leading their teams in minutes. How is this so?

Strangely, b-r.com says the Celtics are the best team in the East, at 1-3 with 5.73 SRS
Jeff Green leads this team in minutes.

[DSMok1]

Including rookie contracts, the avg 10th-best pay on a team this year is $1.95 million.

Replacement player is a player who wouldn't play minutes, in general, to start the season. Wouldn't get minutes in a game that mattered if the team was healthy.

And yet some <0 VORP players are starting and/or leading their teams in minutes. How is this so?

Could be many reasons. Lack of depth at that position on that team, really bad roster overall, bad minute allocation by coach, issues with BPM accurately assessing value. It isn't a surprise, though.

[schtevie]

One part mischief and one part response to the recent inquiry to make old debates familiar to newcomers...

And why, again, do we care about/choose to establish "replacement level" as the reference point, as opposed to the very-well-understood, good ol' zero?

It isn't because of the immutability of -2 (never mind the lack of common knowledge of its value) and by extension, for those who are oddly drawn to VORPy WAR, it doesn't provide any intuition as to what a team of such players should be expected to yield in terms of wins. (WAR, what is it good for? .... )

Can we not just say one big "sorry" for all the hurt feelings of the majority of NBA players (their wives, mothers, agents, etc.) whose "value" is necessarily going to be "negative", then ever thereafter enjoy the myriad benefits that attend the clear intuition and presentational clarity of 0?

A boy can dream.

[DSMok1]

I agree to a large extent, schtevie. BPM itself is very useful, and easy to translate to wins. VORP is a little more fuzzy.

VORP, and replacement level in general, is only useful when trying to estimate overall contribution to a team, which is primarily useful for evaluating salaries/contracts. Usually I sort my list, if looking for best players, by BPM with a minutes threshold (100 minutes usually does the trick--BPM stabilizes pretty fast).

[permaximum]

I have 2 simple questions... Not just for me but everyone else.

1. Where should we use the metric?
2. Why should we use it instead of RAPM or something else?

[DSMok1]

I have 2 simple questions... Not just for me but everyone else.

1. Where should we use the metric?
2. Why should we use it instead of RAPM or something else?

1. Best box score metric, has the advantages and disadvantages of box score metrics.
2. When a good quality RAPM is not available or doesn't measure what you want. RAPM is good for a specific situation: estimating true talent level over a period of months and years. If you want a stat that will stabilize quickly over smaller periods of time, BPM is far, far better than RAPM. For instance--who has been playing best this year? 5 games in, BPM can give you a good idea, RAPM cannot. Also, if you don't have access to lineup data (history or other leagues), then BPM is the best option. Even with multi-year samples for estimating true talent level, RAPM can still struggle with multicollinearity issues, hence the need for RPM/xRAPM. Even at the end of this season--if you asked me who played better this year, I think BPM is more accurate than RAPM, and perhaps even xRAPM/RPM (since prior years are included). (Remember, though, BPM doesn't capture defense extremely well.)

[permaximum]

I have 2 simple questions... Not just for me but everyone else.

1. Where should we use the metric?
2. Why should we use it instead of RAPM or something else?

1. Best box score metric, has the advantages and disadvantages of box score metrics.
2. When a good quality RAPM is not available or doesn't measure what you want. RAPM is good for a specific situation: estimating true talent level over a period of months and years. If you want a stat that will stabilize quickly over smaller periods of time, BPM is far, far better than RAPM. For instance--who has been playing best this year? 5 games in, BPM can give you a good idea, RAPM cannot. Also, if you don't have access to lineup data (history or other leagues), then BPM is the best option. Even with multi-year samples for estimating true talent level, RAPM can still struggle with multicollinearity issues, hence the need for RPM/xRAPM. Even at the end of this season--if you asked me who played better this year, I think BPM is more accurate than RAPM, and perhaps even xRAPM/RPM (since prior years are included).

Thanks for the answers and explanation. I knew most of the things you mention but I guessed it's good to have them here for visitors.

Since we're talking about the mainstream, what do you think about the use of BPM for the league awards? Will BPM give us more accurate ratings for MVP, MIP, ROK, ALL-NBA Team etc. than EFFICIENCY, PER, WS, WP, WAR, RPM, RAPM? Today, is it the best statistical argument for the MVP race, at the end of the season?