Abstract
The goal of this analysis is to better understand the similarities and differences between four NBA player metrics: Win Score, Wins Produced, Win Share, and RPM Wins in the context of calculating player output or player value using the economic concept of Marginal Revenue Product. To compare these four metrics I will focus on the Utah Jazz and their trade decisions these last few weeks. My hypothesis is that this method will be able to explain some decision making recently by the Utah Jazz. I want to find which metric, if any, gives a reasonable quanitification of player value. Once a reasonable metric is determined, it can be tested further by evaluating which players in the league are the most over/under paid by comparing the value of their output to their salary.
The quantity ‘Marginal Revenue Product’ (MRP) is defined as the market value generated by an additional unit of output. A simple example of this is outlined on Investopedia’s web page for the definition of MRP.
“For example, a farmer wants to know whether to purchase another specialized tractor to seed and harvest wheat. If the extra tractor can eventually produce 3,000 additional bushels of wheat (the MPP), and each additional bushel sells at the market for $5 (price of the product or marginal revenue), the MRP of the tractor is $15,000.”
In sports economics, one additional unit of output is one additional win. You can measure or estimate what this value would be for a given team by multiplying the value of one additional win by the number of wins a player generates. More technically MRP can be written as
\[ MRP_{ij} = MR_{win_j} \times \Delta wins_{ij} \]
where \(MRP_{ij}\) is the marginal revenue product of player \(i\) when he plays for team \(j\), \(MR_{win_j}\) is the value of an additional win to team \(j\), and \(\Delta wins_{ij}\) is the change added wins for player \(i\) on team \(j\). The hardest quantity to measure here is the change in wins for a given player. There are several widely used metrics for wins that I explored to find the most reasonable output for evaluating players and their value relative to their cost based on this idea.
| Player | Win Value |
|---|---|
| Los Angeles Clippers | $283,112,348 |
| Memphis Grizzlies | $5,012,423 |
| Phoenix Suns | $4,515,159 |
| Atlanta Hawks | $4,183,917 |
| Orlando Magic | $3,878,881 |
| New York Knicks | $3,719,152 |
| Dallas Mavericks | $3,579,354 |
| Sacramento Kings | $3,541,760 |
| Brooklyn Nets | $3,429,992 |
| Chicago Bulls | $3,312,039 |
| Charlotte Hornets | $3,256,338 |
| Detroit Pistons | $3,079,131 |
| Miami Heat | $3,051,689 |
| Los Angeles Lakers | $3,010,156 |
| Washington Wizards | $2,822,269 |
| Oklahoma City Thunder | $2,740,695 |
| Milwaukee Bucks | $2,626,203 |
| Minnesota Timberwolves | $2,553,664 |
| Portland Trail Blazers | $2,534,232 |
| San Antonio Spurs | $2,525,077 |
| Denver Nuggets | $2,345,415 |
| New Orleans Pelicans | $2,260,372 |
| Cleveland Cavaliers | $2,215,528 |
| Utah Jazz | $2,069,487 |
| Golden State Warriors | $1,992,679 |
| Toronto Raptors | $1,942,915 |
| Indiana Pacers | $1,888,596 |
| Philadelphia 76ers | $1,799,898 |
| Boston Celtics | $1,743,699 |
| Houston Rockets | $1,587,602 |
For the purposes of this analysis I am going to assume that each team values a win equally to give an adequate opportunity to compare win contribution metrics. An article from FiveThirtyEight estimating the surplus value of players claimed this number was $2,949,908.82 per team. The table above shows that this number would likely fall close to the average value of a win.
| Player | Win Score |
|---|---|
| Rudy Gobert | 1441.5 |
| Andre Drummond | 1378.5 |
| Giannis Antetokounmpo | 1370.0 |
| Nikola Vucevic | 1223.0 |
| Karl-Anthony Towns | 1205.0 |
| Nikola Jokic | 1182.0 |
| Clint Capela | 1112.0 |
| Joel Embiid | 1064.5 |
| James Harden | 1021.0 |
| Ben Simmons | 1014.5 |
| Anthony Davis | 1012.5 |
| Paul George | 980.5 |
| Steven Adams | 966.0 |
| Russell Westbrook | 964.0 |
| Kevin Durant | 943.0 |
| LaMarcus Aldridge | 937.5 |
| Hassan Whiteside | 918.5 |
| Deandre Ayton | 874.0 |
| Willie Cauley-Stein | 853.0 |
| Jusuf Nurkic | 852.0 |
Win Score produces an interesting ranking compared to the other metrics outlined in the next sections. Rudy Gobert makes the No. 1 spot and James Harden is in 9th. This could yield an objective way to compare players based on season stats but it doesn’t have the correct units to evaluate MRP.
For Wins Produced I am following the formula outlined in The Wages of Wins Journal article titled ‘How to calculate Wins Produced’. This article outlines a complicated formula that involves using regression coefficients with variables that are similar to Win Score but then makes adjustments for defensive rebounds, assists, position, and league averages. The article also mentions that some of these adjustments don’t end up making a large difference because of the robustness of the coefficients and league averages given the amount of data available. For simplicity I am excluding the adjustment due to position because I don’t have data on the changing positions of each player.
| Player | WP |
|---|---|
| Rudy Gobert | 31.9329 |
| Andre Drummond | 29.1275 |
| Giannis Antetokounmpo | 26.8373 |
| Clint Capela | 24.3827 |
| Karl-Anthony Towns | 24.3795 |
| Nikola Vucevic | 23.3072 |
| Anthony Davis | 23.0022 |
| Joel Embiid | 21.3959 |
| Hassan Whiteside | 21.3415 |
| Jarrett Allen | 18.4117 |
| Deandre Ayton | 18.2807 |
| Nikola Jokic | 17.9704 |
| Ed Davis | 17.7688 |
| JaVale McGee | 17.1122 |
| LaMarcus Aldridge | 16.9245 |
| Steven Adams | 16.7231 |
| Jusuf Nurkic | 16.3004 |
| Derrick Favors | 16.2188 |
| John Collins | 15.7903 |
| Montrezl Harrell | 15.4370 |
The rankings show that these numbers are more interpretable than Win Score and even have a similar ranking and mix of players in the top spots. However, to say that a player like Rudy Gobert accounts for more than half of the total wins of the Jazz in 2018-19 seems like a long shot. This led me to look into Real Plus-Minus wins to see if I could get a more conservative number than the metrics so far.
Originally developed by ESPN, RPM Wins or Real Plus-Minus Wins provides an estimate of the number of wins each player has contributed to his team’s win total on the season. This metric takes into account the players Real Plus-Minus which is the point differential when the player is on/off the court and the number of possessions played.
| Player | RPM Wins |
|---|---|
| Paul George | 19.86 |
| James Harden | 18.54 |
| Stephen Curry | 15.24 |
| Giannis Antetokounmpo | 15.22 |
| Nikola Jokic | 14.91 |
| Damian Lillard | 14.52 |
| Kevin Durant | 14.10 |
| Nikola Vucevic | 13.67 |
| Rudy Gobert | 13.10 |
| Joel Embiid | 12.90 |
| Jrue Holiday | 12.28 |
| Karl-Anthony Towns | 11.37 |
| Pascal Siakam | 11.30 |
| Danny Green | 11.23 |
| Brook Lopez | 11.07 |
| LeBron James | 11.04 |
| Jimmy Butler | 10.97 |
| Kyle Lowry | 10.97 |
| Anthony Davis | 10.81 |
| Kemba Walker | 10.69 |
The ranking shows a mix of different players compared to Win Share. For example Lebron James doesn’t even make the top 20 for Win Share but has a reasonable number for RPM Wins. This ranking seems more realistic to me and the consensus across analysts seems to indicate a bias more towards RPM Wins than Win Share. Of course the argument has been made in many articles that these advanced stats are somewhat meaningless given the fact that each is crediting wins to an individual rather than to the entire team. I am aware of these criticisms but would like to ignore those at this point.
One simple test to evaluate if this method works and which quantity of wins is more accurate/reasonable is to check if a player-for-player trade produces a near break-even value. The Utah Jazz recently traded Jae Crowder, Kyle Korver, and Grayson Allen to the Memphis Grizzlies for Mike Conley. This trade only makes sense for the Jazz if they expect Conley to replace the output of the other three based on his past performance and hopefully exceed that in the near future. One can simply compare the total MRP before and after the trade to not only compare which measure of wins gives an equal trade value but also show if the Jazz are getting a good deal.
In each section below the MRP is calculated for each player using the chosen metric for wins and compare that to the player salary. To calculate the value a player is producing we can simply take the difference between MRP and player salary to show if the player is worth what they are being paid. We will simply call this number ‘Net Output Value’ or ‘NOV’ for short. More formally the \(NOV\) for player \(i\) on team \(j\) is
\[NOV_{ij} = MRP_{ij} - \text{Salary}_{ij}.\]
If a player is producing more value than they are being paid \(NOV\) is positive otherwise the team is losing money on the player and \(NOV\) will come up negative. First we show what these values are before the trade for each player, then evaluate what the total value of the team is before and after the Conley trade.
| Player | MRP | Salary | NOV |
|---|---|---|---|
| Rudy Gobert | $94,199,143 | $23,241,573 | $70,957,570 |
| Derrick Favors | $47,843,981 | $16,900,000 | $30,943,981 |
| Royce O’Neale | $9,873,935 | $1,378,242 | $8,495,693 |
| Ekpe Udoh | $9,232,625 | $3,360,000 | $5,872,625 |
| Jae Crowder | $11,921,467 | $7,305,825 | $4,615,642 |
| Thabo Sefolosha | $9,612,868 | $5,250,000 | $4,362,868 |
| Georges Niang | $4,382,385 | $1,512,601 | $2,869,784 |
| Tony Bradley | $930,106 | $1,679,520 | $-749,414 |
| Raul Neto | $-453,106 | $2,150,000 | $-2,603,106 |
| Kyle Korver | $2,757,280 | $7,560,000 | $-4,802,720 |
| Grayson Allen | $-5,683,884 | $2,074,320 | $-7,758,204 |
| Donovan Mitchell | $-6,669,154 | $3,111,480 | $-9,780,634 |
| Joe Ingles | $1,544,867 | $13,045,455 | $-11,500,588 |
| Dante Exum | $-5,497,745 | $9,600,000 | $-15,097,745 |
| Ricky Rubio | $-9,682,781 | $14,975,000 | $-24,657,781 |
Before the trade the total \(NOV\) of the Jazz is $51,167,971. If Crowder, Korver, and Allen are removed the Jazz total \(NOV\) becomes $52,828,129.
| Player | MRP | Salary | NOV |
|---|---|---|---|
| Mike Conley | $2,745,480 | $30,521,116 | $-27,775,636 |
When Conley’s production is added to the Jazz the total \(NOV\) becomes $25,052,493. Wins Produced is showing that the Jazz are lost almost 28 million on this trade. I’m skeptical of this number because this is drastically underestimating Conley’s output relative to his salary. It seems unreasonable that the Jazz would lose 28 million from a trade.
| Player | MRP | Salary | NOV |
|---|---|---|---|
| Donovan Mitchell | $25,664,207 | $3,111,480 | $22,552,727 |
| Joe Ingles | $29,617,085 | $13,045,455 | $16,571,630 |
| Rudy Gobert | $38,643,806 | $23,241,573 | $15,402,233 |
| Royce O’Neale | $12,655,109 | $1,378,242 | $11,276,867 |
| Jae Crowder | $11,652,140 | $7,305,825 | $4,346,315 |
| Derrick Favors | $19,203,906 | $16,900,000 | $2,303,906 |
| Ricky Rubio | $16,430,992 | $14,975,000 | $1,455,992 |
| Raul Neto | $3,008,907 | $2,150,000 | $858,907 |
| Thabo Sefolosha | $5,545,829 | $5,250,000 | $295,829 |
| Georges Niang | $943,971 | $1,512,601 | $-568,630 |
| Ekpe Udoh | $2,123,934 | $3,360,000 | $-1,236,066 |
| Tony Bradley | $117,996 | $1,679,520 | $-1,561,524 |
| Kyle Korver | $5,457,331 | $7,560,000 | $-2,102,669 |
| Grayson Allen | $-1,887,942 | $2,074,320 | $-3,962,262 |
| Dante Exum | $1,268,461 | $9,600,000 | $-8,331,539 |
Before the Trade the \(NOV\) of all the players is $57,301,716. If Crowder, Korver, and Allen are removed the Jazz total \(NOV\) becomes $59,788,438.
| Player | MRP | Salary | NOV |
|---|---|---|---|
| Mike Conley | $27,729,143 | $30,521,116 | $-2,791,973 |
When Conley’s production is added to the Jazz the total \(NOV\) becomes $56,996,465. Using RPM Wins in place of the other metrics produces the closest value to break even for this trade of the three other methods. This is a good indication that RPM Wins might be the best of the others to incorporate into the calculation of MRP.
To further evaluate this what the results of using MRP together with RPM Wins to get player value I can also look at the recent acquisitions and trades the Jazz have made. The Jazz added Bojan Bogdanovic, Ed Davis, Jeff Green, and Emmanuel Mudiay. The Jazz also traded Derrick Favors for some draft picks. I am ignoring the new acquisitions during the draft because I don’t have the necessary data. The table below shows the new roster ordered by \(NOV\).
| Player | MRP | Salary | NOV |
|---|---|---|---|
| Donovan Mitchell | $25,664,207 | $3,111,480 | $22,552,727 |
| Joe Ingles | $29,617,085 | $13,045,455 | $16,571,630 |
| Rudy Gobert | $38,643,806 | $23,241,573 | $15,402,233 |
| Ed Davis | $15,752,513 | $4,449,000 | $11,303,513 |
| Royce O’Neale | $12,655,109 | $1,378,242 | $11,276,867 |
| Jeff Green | $8,761,229 | $2,393,887 | $6,367,342 |
| Bojan Bogdanovic | $15,988,506 | $10,500,000 | $5,488,506 |
| Raul Neto | $3,008,907 | $2,150,000 | $858,907 |
| Thabo Sefolosha | $5,545,829 | $5,250,000 | $295,829 |
| Georges Niang | $943,971 | $1,512,601 | $-568,630 |
| Ekpe Udoh | $2,123,934 | $3,360,000 | $-1,236,066 |
| Tony Bradley | $117,996 | $1,679,520 | $-1,561,524 |
| Mike Conley | $27,729,143 | $30,521,116 | $-2,791,973 |
| Emmanuel Mudiay | $1,238,962 | $4,294,480 | $-3,055,518 |
| Dante Exum | $1,268,461 | $9,600,000 | $-8,331,539 |
When Conley, Davis, Bogdanovic, Green, and Mudiay are added to the roster the total \(NOV\) of $72,572,304. This would indicate that the Jazz would be much more productive next season with these new players supposedly producing almost 20 million more value compared to the end of regular season. You can also see in the ranking of \(NOV\) that the top five almost line up with the starting five for next season with the exception of Mike Conley who I believe is under valued and will rise in the rankings throughout his first season with the Jazz as he gets more opportunity to play and as the Jazz win games.
Given that there is now a realistic way to compare player values using RPM Wins, it can be applied it to the rest of the NBA. Below I show the players with the highest value of output (MRP) as well as the highest and lowest \(NOV\) which correspond to being the most over/under valued players.
| Player | MRP | Salary | NOV |
|---|---|---|---|
| Paul George | $58,585,189 | $30,560,700 | $28,024,489 |
| James Harden | $54,691,310 | $30,431,854 | $24,259,456 |
| Stephen Curry | $44,956,610 | $37,457,154 | $7,499,456 |
| Giannis Antetokounmpo | $44,897,612 | $24,157,304 | $20,740,308 |
| Nikola Jokic | $43,983,141 | $24,605,181 | $19,377,960 |
| Damian Lillard | $42,832,676 | $27,977,689 | $14,854,987 |
| Kevin Durant | $41,593,714 | $30,000,000 | $11,593,714 |
| Nikola Vucevic | $40,325,254 | $12,750,000 | $27,575,254 |
| Rudy Gobert | $38,643,806 | $23,241,573 | $15,402,233 |
| Joel Embiid | $38,053,824 | $25,467,250 | $12,586,574 |
| Jrue Holiday | $36,224,880 | $25,976,111 | $10,248,769 |
| Karl-Anthony Towns | $33,540,463 | $7,839,435 | $25,701,028 |
| Pascal Siakam | $33,333,970 | $1,544,951 | $31,789,019 |
| Danny Green | $33,127,476 | $10,000,000 | $23,127,476 |
| Brook Lopez | $32,655,491 | $3,382,000 | $29,273,491 |
| LeBron James | $32,566,993 | $35,654,150 | $-3,087,157 |
| Kyle Lowry | $32,360,500 | $31,200,000 | $1,160,500 |
| Jimmy Butler | $32,360,500 | $20,445,779 | $11,914,721 |
| Anthony Davis | $31,888,514 | $25,434,263 | $6,454,251 |
| Kemba Walker | $31,534,525 | $12,000,000 | $19,534,525 |
| Player | MRP | Salary | NOV |
|---|---|---|---|
| Kevin Knox | $-17,522,458 | $3,739,920 | $-21,262,378 |
| Collin Sexton | $-10,885,164 | $4,068,600 | $-14,953,764 |
| Jamal Crawford | $-5,811,320 | $2,393,887 | $-8,205,207 |
| Wayne Selden | $-5,398,333 | $1,544,951 | $-6,943,284 |
| Antonio Blakeney | $-4,129,872 | $1,349,383 | $-5,479,255 |
| Cedi Osman | $-4,100,373 | $2,775,000 | $-6,875,373 |
| Jonathon Simmons | $-3,864,381 | $6,000,000 | $-9,864,381 |
| Will Barton | $-3,805,382 | $11,830,358 | $-15,635,740 |
| Nik Stauskas | $-3,569,390 | $1,621,415 | $-5,190,805 |
| Frank Ntilikina | $-3,510,391 | $4,155,720 | $-7,666,111 |
| Frank Jackson | $-3,126,903 | $1,378,242 | $-4,505,145 |
| Elie Okobo | $-2,920,410 | $1,238,464 | $-4,158,874 |
| Jerryd Bayless | $-2,684,417 | $8,575,916 | $-11,260,333 |
| Shelvin Mack | $-2,684,417 | $2,029,463 | $-4,713,880 |
| Timothe Luwawu-Cabarrot | $-2,654,918 | $1,544,951 | $-4,199,869 |
| Allonzo Trier | $-2,566,421 | $3,382,000 | $-5,948,421 |
| Marquese Chriss | $-2,389,426 | $3,206,160 | $-5,595,586 |
| Josh Jackson | $-2,005,938 | $6,041,520 | $-8,047,458 |
| Grayson Allen | $-1,887,942 | $2,074,320 | $-3,962,262 |
| Patrick Patterson | $-1,828,943 | $5,451,600 | $-7,280,543 |
| Player | MRP | Salary | NOV |
|---|---|---|---|
| Pascal Siakam | $33,333,970 | $1,544,951 | $31,789,019 |
| Brook Lopez | $32,655,491 | $3,382,000 | $29,273,491 |
| Paul George | $58,585,189 | $30,560,700 | $28,024,489 |
| Nikola Vucevic | $40,325,254 | $12,750,000 | $27,575,254 |
| Karl-Anthony Towns | $33,540,463 | $7,839,435 | $25,701,028 |
| James Harden | $54,691,310 | $30,431,854 | $24,259,456 |
| Danny Green | $33,127,476 | $10,000,000 | $23,127,476 |
| Donovan Mitchell | $25,664,207 | $3,111,480 | $22,552,727 |
| Giannis Antetokounmpo | $44,897,612 | $24,157,304 | $20,740,308 |
| De’Aaron Fox | $25,015,227 | $5,470,920 | $19,544,307 |
| Kemba Walker | $31,534,525 | $12,000,000 | $19,534,525 |
| Nikola Jokic | $43,983,141 | $24,605,181 | $19,377,960 |
| Ben Simmons | $25,015,227 | $6,434,520 | $18,580,707 |
| Patrick Beverley | $23,068,287 | $5,027,028 | $18,041,259 |
| Kevon Looney | $18,495,928 | $1,567,007 | $16,928,921 |
| Joe Ingles | $29,617,085 | $13,045,455 | $16,571,630 |
| Malcolm Brogdon | $18,023,943 | $1,544,951 | $16,478,992 |
| Willie Cauley-Stein | $21,091,848 | $4,696,875 | $16,394,973 |
| Jamal Murray | $19,380,901 | $3,499,800 | $15,881,101 |
| Eric Bledsoe | $30,767,549 | $15,000,000 | $15,767,549 |
| Player | MRP | Salary | NOV |
|---|---|---|---|
| Carmelo Anthony | $471,985 | $25,534,253 | $-25,062,268 |
| Chandler Parsons | $619,481 | $24,107,258 | $-23,487,777 |
| Kevin Knox | $-17,522,458 | $3,739,920 | $-21,262,378 |
| Ryan Anderson | $442,486 | $20,421,546 | $-19,979,060 |
| Kevin Love | $5,132,841 | $24,119,025 | $-18,986,184 |
| Gordon Hayward | $12,242,122 | $31,214,295 | $-18,972,173 |
| Dwight Howard | $914,472 | $18,919,725 | $-18,005,253 |
| Allen Crabbe | $1,032,468 | $18,500,000 | $-17,467,532 |
| Andrew Wiggins | $8,525,236 | $25,467,250 | $-16,942,014 |
| Tristan Thompson | $707,978 | $17,469,565 | $-16,761,587 |
| Evan Turner | $1,297,960 | $17,868,852 | $-16,570,892 |
| Bismack Biyombo | $471,985 | $17,000,000 | $-16,528,015 |
| Tyler Johnson | $3,067,905 | $19,245,370 | $-16,177,465 |
| John Wall | $3,244,900 | $19,169,800 | $-15,924,900 |
| Enes Kanter | $2,861,412 | $18,622,514 | $-15,761,102 |
| Jabari Parker | $4,247,869 | $20,000,000 | $-15,752,131 |
| Will Barton | $-3,805,382 | $11,830,358 | $-15,635,740 |
| Brandon Knight | $-855,474 | $14,631,250 | $-15,486,724 |
| Kent Bazemore | $3,097,404 | $18,089,887 | $-14,992,483 |
| Collin Sexton | $-10,885,164 | $4,068,600 | $-14,953,764 |
Keep in mind that these MRP numbers correspond to a given player on a given team. If the team isn’t winning very much, its hard for a star player to have a high MRP because Win Share and RPM Wins will be lower for all players on that team. Thus a star player could appear over-valued, but only when playing for that team. The numbers could change drastically if they move to a more productive team.
Overall using MRP with RPM Wins to get Net Output Value is simple and it seems to work well given the examples with the Jazz and the recent trades and acquisitions. I also found that Win Share can be used in place of RPM Wins but it seems to overestimate what both of these metrics are trying to quantify. I also found that Win Score and Wins Produced aren’t realistic for calculating MRP. But it is important to remember that these quantities are heavily debated and there is no silver bullet to measuring the value of player output to a team. I look forward to evaluating this again after next season to see what has changed and if there are any insights by comparing results. I also want to explore comparing the MRP of each team, although it is hard to compare team to team by dollar amounts rather than win-loss record and regular season stats. There are a lot of ideas that came out of this analysis and I look forward to more research. Go Jazz!
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[8] McDonald, R. (2019, June 18). What would a Mike Conley trade mean for the Utah Jazz moving forward? Retrieved from https://www.deseretnews.com/article/900075833/what-would-a-mike-conley-trade-mean-for-the-utah-jazz-moving-forward.html
[9] Understanding Marginal Revenue Products (MRPs). (2011, July 18). Retrieved from https://www.investopedia.com/terms/m/marginal-revenue-product-mrp.asp