A Tidy Model of Team Salaries

I attempted to illustrate the problem of salary inequality in my September 26th post, but my explanation was a bit clumsy; let me try again in clearer language this time. The percentage of Basketball-Related Income that players in aggregate receive (currently pegged at 50% in the latest negotiations, and formerly 57% in the 2005 labor agreement) determines total salaries, but does not determine the inter-player distribution of salaries. Let us take a simple example. Say total BRI is projected at $100. Say there are only two teams in the league, each with six players-- five starters and a sixth man. Let us use the 57% number from the '05 deal. Under such terms, all players combined will receive $57. The top two stars (LeBron James and Kobe Bryant, say) might receive $16 each. (Assume player salaries are capped at $16.) If the "mid-level exception" is capped at $5.33 per year, then some team will likely sign a secondary free-agent player (Jamal Crawford, David West) at $5.33. [Why wouldn't a team sign free agents for less? Is Jamal Crawford really 1/3 as good as James or Bryant? In a competitive bidding scenario, with limited quality free agents, teams are forced to overbid up to the individual cap, lest they wind up with nothing, which would guarantee that their roster will remain stagnant.] Each team then pays a total of ~$7.2 (averaging $1.79 per player) to its remaining four players, so each team's payroll is $28.5 and aggregate league spending is $57. So to recap, here are the salaries:

Team King
LeBron James - $16
Jamal Crawford - $5.33
King Scrub 1 - $1.79
King Scrub 2 - $1.79
King Scrub 3 - $1.79
King Scrub 4 - $1.79

Team Mamba
Kobe Bryant - $16
David West - $5.33
Mamba Scrub A - $1.79
Mamba Scrub B - $1.79
Mamba Scrub C - $1.79
Mamba Scrub D - $1.79

Now imagine the season's Basketball-Related Income is tallied up and it is not actually $100, but really $90, which is 10% under $100. Every salary thus will be rolled back by 10% to maintain the 57% of BRI ratio. The new salaries will be:

Team King
LeBron James - $14.4
Jamal Crawford - $4.8
King Scrub 1 - $1.61
King Scrub 2 - $1.61
King Scrub 3 - $1.61
King Scrub 4 - $1.61

Team Mamba
Kobe Bryant - $14.4
David West - $4.8
Mamba Scrub A - $1.61
Mamba Scrub B - $1.61
Mamba Scrub C - $1.61
Mamba Scrub D - $1.61

Now total salaries are $51.3 (57% of $90). However, notice that regardless of how the total dollar amount of BRI comes out, if we fix aggregate salaries at 57% of BRI and assume certain other individual salary caps, then the best player on the team will always earn three times what the second-best player makes, and about 9x the salary of each role player.

Now, let us assume again that total BRI is $100, but, after some bitter labor negotiations, let us tweak two features of the system: first, player share of BRI falls to 50% (so each team has a payroll of $25), and the mid-level exception salary for free agents falls to $3. Assume the maximum salary remains at $16. What now?

Team King
LeBron James - $16
Jamal Crawford - $3
King Scrub 1 - $1.5
King Scrub 2 - $1.5
King Scrub 3 - $1.5
King Scrub 4 - $1.5

Team Mamba
Kobe Bryant - $16
David West - $3
Mamba Scrub A - $1.5
Mamba Scrub B - $1.5
Mamba Scrub C - $1.5
Mamba Scrub D - $1.5

Notice, now, that James and Bryant make more than five times the salary of their respective running mates, and nearly 11x the salary of their scrubs. [Now imagine again that BRI falls to $90 instead of $100. The numbers immediately above will all be reduced by 10%, but the ratios of salaries between different players will remain the same. I will omit that presentation so as not to bore you too much.]

Who suffers here? Obviously, mid-level-exception-caliber players suffer a lot, seeing their salary reduced by 44%, from $5.33 to $3. Scrub players also see their salary reduced by 16%, which is more than the percentage reduction, 12%, in the players' aggregate BRI share. Mid-level players are asked to bear much of the player suffering, and scrubs get hurt as well, disproportionately to the union's overall hit. Superstars like James and Bryant don't suffer one bit, at least in my example (and, I believe, in the owners' actual proposal).

Of course, if I scaled up the dollar value of BRI sufficiently (more and more eyeballs are watching the Association in China), I could construct a set of numbers where Crawford, West, and the scrubs are making an equal or better salary in dollars under the new regime, compared to the old regime. Say BRI blows up to $180 (so the players' share is $90 and each team has a payroll of $45), and the individual max salary, and the mid-level exception salary, are both increased by 80%.

Team King
LeBron James - $28.8
Jamal Crawford - $5.4
King Scrub 1 - $2.7
King Scrub 2 - $2.7
King Scrub 3 - $2.7
King Scrub 4 - $2.7

Team Mamba
Kobe Bryant - $28.8
David West - $5.4
Mamba Scrub A - $2.7
Mamba Scrub B - $2.7
Mamba Scrub C - $2.7
Mamba Scrub D - $2.7

This scenario is entirely possible with the projected growth in league revenues during the coming decade. The scrub salary (which is also the median player salary) is higher under such assumptions. And perhaps the inability of teams with one superstar to sign another very good player (due to the paltry mid-level-exception salary for tax-paying teams) will encourage parity among teams, thus juicing fan interest. Posit for a moment that the new system could actually contribute, by itself, to BRI growth, and my imagined 80% growth of revenues would not happen with the 2005-2011 rules. So why wouldn't players be happy with this deal? Well, note that now, as I mentioned above, the superstar makes over 5 times the salary of his best teammate, and over 10 times the salary of his worst teammates. Under the 2005-2011 regime, those values were 3 and 9.

So inter-player inequality is worse under the new system, even if the average player is earning more money. Is that enough to make the deal objectionable? Note that most of the NBPA could be charitably called "scrubs": only about 3 players on each real team are vital for amassing wins, and the rest are interchangeable. The composition of the NBPA's executive committee suggests this: 8 of the 9 guys are far from All-Stars. It is the scrubs whom union President Fisher and Executive Director Hunter toil for. How much do players mind inequality of income between them and their best teammate? Perhaps the knowledge of 11-fold inequality could lead to locker-room resentment, even if James, Bryant, Wade, Howard, Durant, and the like really do drive ticket and jersey sales to that degree. Looking beyond pro hoops at the broader political-economic system in our society, a majority of Americans don't seem to like the extent of income and wealth inequality that has developed during the past 30 years.

I am not sure whether the players are really resentful over the prospect of intra-union salary inequality, or whether they are just mad at losing their 57% and not inclined to give the owners a "win" just yet. However, judging from the rhetoric of some player representatives, there is a good argument that the players might rather be poorer and more equal, rather than richer and further apart.