I’ve always wondered what it would look like if one were to calculate the money a professional athlete deserves based on their production. The other day, Reddit user /u/aeisenst posted a rant that mentioned how a player’s productivity can be viewed as the number of wins they generate for their team. This got me thinking about what would happen if each player’s salary was calculated based on their statistical productivity – specifically, I wondered how this number would differ from their current salary.

In this post, I will explore this question. First, we need to choose a way to measure a player’s total production over a season. For now, let’s equate production with players’ total Win Shares (as opposed to, for example, the Wins Above Replacement stat chosen by /u/aisenst).

Now, we need data. I wrote a script that gathered player data from basketball-reference.com. It scraped the salary and total WS for each NBA player for the 2015-2016 season.

For each team, we need to calculate total win shares (roughly equal to the team’s wins over the season) and total salary paid for each team. Then, for each player, we need to calculate their percentage of the total team win shares. To calculate their Deserved Salary, multiply their percentage of team win shares by the total salary given out by the team.

After calculating Expected Salary, we need to also note the difference between this number and each player’s actual salary. From now on, we’ll just refer to this as the Difference.

At this point we should note that we’ve chosen statistics that measured total productivity instead of average productivity. As such, players that missed games across the season will have lower total WS - and thus a lower total expected salary.

This puts players like Kyrie Irving and Blake Griffin, regardless of productivity, near the bottom - low total win shares numbers reflect poorly on a high salary. To try and eliminate these inconsistencies, we should filter our data to only include players who played 58 games or more during the regular season. (This is also the threshold the NBA uses to decide which players are eligible for the scoring title.)

The first results are straightforward. The players with the highest Expected Salary are, by and large, the players that produced the most over this past season.

Top 10: Players With The Ten Highest Expected Salaries

Player Tm G GS WS salary WS% Expected Salary Difference
James Harden HOU 82 82 13.3 \$15,756,438.00 0.3166666667 \$28,559,663.80 \$12,803,225.80
LeBron James CLE 76 76 13.6 \$22,971,000.00 0.2365217391 \$25,055,133.83 \$2,084,133.83
Stephen Curry GSW 79 79 17.9 \$11,370,786.00 0.2640117994 \$24,739,805.70 \$13,369,019.70
Chris Paul LAC 74 74 12.7 \$21,468,696.00 0.2470817121 \$23,350,761.60 \$1,882,065.60
Kevin Durant OKC 72 72 14.5 \$20,158,622.00 0.242881072 \$22,982,053.10 \$2,823,431.10
Russell Westbrook OKC 80 80 14 \$16,744,218.00 0.2345058626 \$22,189,568.51 \$5,445,350.51
Brook Lopez BRK 73 73 6.2 \$20,000,000.00 0.2731277533 \$21,391,156.70 \$1,391,156.70
DeAndre Jordan LAC 77 77 11.5 \$19,500,000.00 0.2237354086 \$21,144,390.43 \$1,644,390.43
Jimmy Butler CHI 67 67 9.1 \$15,260,000.00 0.2439678284 \$20,831,412.11 \$5,571,412.11
Lou Williams LAL 67 35 4.7 \$7,000,000.00 0.2701149425 \$19,510,436.06 \$12,510,436.06

Okay, fine, Brook Lopez and Lou Williams aren’t top ten players in the NBA. One interesting consequence of our system is the fact that decent players on bad teams have a high percentage of their team’s win shares, even if they weren’t specially productive. Combine this with a couple of big-spending teams (the Lakers and the Nets, for example) and players that would be lucky to crack an NBA top 50 list pop up in our top 10.

Now let’s look at the players with the lowest Expected Salaries. One weird consequence of the complicated formula used to calculate win shares is that players with bad shooting percentages and high turnover rates can occasionally end up with negative win shares for a game – or, in rare cases, an entire season.

Top 10: Players With The Ten Lowest Expected Salaries

Player Tm G GS WS salary WS% Expected Salary Difference
Emmanuel Mudiay DEN 68 66 -2.1 \$3,102,240.00 -0.0625 -\$3,527,131.13 -\$6,629,371.13
Rashad Vaughn MIL 70 6 -0.8 \$1,733,040.00 -0.0251572327 -\$1,739,069.84 -\$3,472,109.84
Kobe Bryant LAL 66 66 -0.4 \$25,000,000.00 -0.02298850575 -\$1,660,462.64 -\$26,660,462.64
D’Angelo Russell LAL 80 48 0 \$5,103,120.00 0 \$0.00 -\$5,103,120.00
Charlie Villanueva DAL 62 4 0.2 \$1,499,187.00 0.004761904762 \$340,906.08 -\$1,158,280.92
Ben McLemore SAC 68 53 0.3 \$3,156,600.00 0.008595988539 \$609,000.87 -\$2,547,599.13
Johnny O’Bryant MIL 66 4 0.3 \$845,059.00 0.009433962264 \$652,151.19 -\$192,907.81
Kelly Oubre WAS 63 9 0.4 \$1,920,240.00 0.01023017903 \$804,335.72 -\$1,115,904.28
Tayshaun Prince MIN 77 44 0.4 \$1,499,187.00 0.01173020528 \$805,735.54 -\$693,451.46
Tony Snell CHI 64 33 0.4 \$1,535,880.00 0.01072386059 \$915,666.47 -\$620,213.53

Looks like these are mostly rookies/sophomores that haven’t learned to hold onto the ball and take high percentage shots… and Kobe.

(One statistical anomaly worth mentioning: after posting 0.7 offensive and -0.7 defensive win shares, D’Angelo Russell ended his rookie season with a whopping 0.0 WS. Those are rounded figures, but still… Cheers.)

Now let’s get to the good stuff. By finding the difference between our Expected Salaries and the actual salaries doled out by franchises, we have created an empirical way to calculate which players are overpaid and which deserve more money.

Top 10: Most Underpaid Players By Expected Salary

Player Tm G GS WS salary WS% Expected Salary Difference
Hassan Whiteside MIA 73 43 10.3 \$981,348.00 0.2172995781 \$18,646,197.56 \$17,664,849.56
Brandon Bass LAL 66 0 4.1 \$3,000,000.00 0.2356321839 \$17,019,742.10 \$14,019,742.10
Giannis Antetokounmpo MIL 80 79 7.1 \$1,953,960.00 0.2232704403 \$15,434,244.80 \$13,480,284.80
Stephen Curry GSW 79 79 17.9 \$11,370,786.00 0.2640117994 \$24,739,805.70 \$13,369,019.70
James Harden HOU 82 82 13.3 \$15,756,438.00 0.3166666667 \$28,559,663.80 \$12,803,225.80
Lou Williams LAL 67 35 4.7 \$7,000,000.00 0.2701149425 \$19,510,436.06 \$12,510,436.06
Anthony Davis NOP 61 61 7.2 \$7,070,730.00 0.238410596 \$19,045,836.72 \$11,975,106.72
Karl-Anthony Towns MIN 82 82 8.3 \$5,703,600.00 0.2434017595 \$16,719,012.51 \$11,015,412.51
Gorgui Dieng MIN 82 39 5.9 \$1,474,440.00 0.1730205279 \$11,884,599.25 \$10,410,159.25
Nikola Jokic DEN 80 55 6.7 \$1,300,000.00 0.1994047619 \$11,253,227.88 \$9,953,227.88

Now we’re talking. Whiteside makes sense in our top spot – a near-all star making less money than almost everyone he shares the court with. (As we speak, he’s upgraded from a \$980k contract to a \$98m one. Good for that guy.)

Curry and Harden seem right, too - as two of the most productive players in the NBA, they were bound to deserve more than the salary their team gives them. Curry, astoundingly, is credited with over a quarter of the Warriors’ 73 wins this season. Harden isn’t far behind.

Some of the other guys are surprising. As previously addressed, Lou Williams is a bit of an outlier. Bass, too. But the other guys - Giannis, Towns, Dieng, Jokic - they have bright futures.

Finally, the other end of the spectrum. The players that make more money than they’ve earned are, by our classifications, overpaid. Let’s examine.

Top 10: Most Overpaid Players By Expected Salary

Player Tm G GS WS salary WS% Expected Salary Difference
Kobe Bryant LAL 66 66 -0.4 \$25,000,000.00 -0.02298850575 -\$1,660,462.64 -\$26,660,462.64
Derrick Rose CHI 66 66 0.4 \$20,093,063.00 0.01072386059 \$915,666.47 -\$19,177,396.53
Dwyane Wade MIA 74 73 4.9 \$20,000,000.00 0.1033755274 \$8,870,521.17 -\$11,129,478.83
Wesley Matthews DAL 78 78 3.7 \$16,400,000.00 0.0880952381 \$6,306,762.41 -\$10,093,237.59
Carmelo Anthony NYK 72 72 6.4 \$22,875,000.00 0.1833810888 \$13,737,606.79 -\$9,137,393.21
Dwight Howard HOU 71 71 6.6 \$22,359,364.00 0.1571428571 \$14,172,464.74 -\$8,186,899.26
Chandler Parsons DAL 61 51 4.3 \$15,361,500.00 0.1023809524 \$7,329,480.64 -\$8,032,019.36
LaMarcus Aldridge SAS 74 74 10.1 \$19,500,000.00 0.1461649783 \$12,695,508.23 -\$6,804,491.77
Emmanuel Mudiay DEN 68 66 -2.1 \$3,102,240.00 -0.0625 -\$3,527,131.13 -\$6,629,371.13
Omer Asik NOP 68 64 1.7 \$11,000,000.00 0.05629139073 \$4,496,933.67 -\$6,503,066.33

These include dark years of some of the largest contracts in the NBA. The Knicks now have #2 on our list (Rose) in addition to #5 (Melo). The Hawks just gave even more money to Dwight Howard. And in a sense, Kobe got paid 25 million dollars this year to lose 40% of one game for the Lakers. That’s tanking at its finest.

And sorry to LaMarcus Aldridge that he ended up on this list at all. This isn’t a knock on your performance. A large portion of the Spurs’ budget is dedicated to you, and your team won 67 games. There was no way around this.

As an aside, I’d like to include one final table of statistics: for the players whose salaries match up most closely with their Expected Salaries.

Middle 10: Most Correctly Paid Players By Expected Salary

Or: Top 10 of players by minimum absolute value of difference between expected salary and their actual salary

Player Tm G GS WS salary WS% Expected Salary Abs(Difference)
Trey Burke UTA 64 0 2.1 \$2,658,240.00 0.04430379747 \$2,653,930.38 \$4,309.62
Aaron Brooks CHI 69 0 0.9 \$2,000,000.00 0.02412868633 \$2,060,249.55 \$60,249.55
Tyler Zeller BOS 60 3 1.7 \$2,616,975.00 0.03490759754 \$2,549,282.54 \$67,692.46
Greg Monroe MIL 79 67 7.5 \$16,400,000.00 0.2358490566 \$16,303,779.72 \$96,220.28
Kyle Korver ATL 80 80 4.1 \$5,746,479.00 0.082 \$5,853,006.33 \$106,527.33
Jerian Grant NYK 76 6 0.8 \$1,572,360.00 0.0229226361 \$1,717,200.85 \$144,840.85
Rajon Rondo SAC 72 72 4.6 \$9,500,000.00 0.1318051576 \$9,338,013.31 \$161,986.69
Nemanja Bjelica MIN 60 0 1.9 \$4,000,000.00 0.05571847507 \$3,827,243.83 \$172,756.17
Johnny O’Bryant MIL 66 4 0.3 \$845,059.00 0.009433962264 \$652,151.19 \$192,907.81
Devin Harris DAL 64 0 2.5 \$4,053,000.00 0.05952380952 \$4,261,325.95 \$208,325.95

In conclusion, I’d like to add the disclaimer that I don’t think that Win Shares - or any advanced statistic, for that matter - are the be-all and end-all of measuring a player’s performance. In fact, I don’t think that any statistic will ever measure a player’s overall productivity with complete accuracy. Each advanced statistic has drawbacks. I chose Win Shares as a simple measure of a player’s total productivity over a season. I don’t mean to imply that the figure is fully accurate. Rather I find it to be a nice (and reasonably correct) avenue for making generalizations about players’ overall performance.

This was originally taken from a post I made on reddit. If you’d like to view my code or raw data, check them out on Github.