# Explaining the NBA Cap and the Value of a win

*I think it’s much more interesting to live not knowing than to have answers which might be wrong. I have approximate answers, and possible beliefs, and different degrees of certainty about different things, but I’m not absolutely sure of anything, and in many things I don’t know anything about, such as whether it means anything to ask why we’re here, and what the question might mean. – Richard Feynman, The Pleasure of Finding Things Out*

I have been working thru the numbers this offseason.

52 Wins, 50% of the Basketball related income (BRI), 30 Teams. These are the numbers to keep in mind when working out the value of a win in the NBA.

Sounds simple right? Surprisingly (or perhaps unsurprisingly), a lot of what I read shows that people have a hard time understanding the process and the variables that affect the actual value of a player to an NBA team. On Friday, I took on the Free Agent value question straight on and I promised followups on how I arrived at my conclusions.

Today we start with the seemingly simple issue of value.

Somewhat unsurprisingly for a blog called the wages of wins, we talk extensively about the value of a win and the value of players to a team. The Overpaid/Underpaid discussion is a even a regular feature at this site. We do however tend to oversimplify this somewhat. Let me illustrate.

For the last overpaid piece we used the following numbers:

- 1.92 Billion in Salary paid to player in 2012
- 30 times 66 games dived by 2 for 990 wins to be had in the season
- 1920/990 = $ 1.94 million dollars per win.

Nice, simple and clean and correct in purely economic terms. The problem is that it assumes that the end goal for a GM is to win 50% of his games and that the salary level is fixed at the same level for every team. It’s a little more complicated than that.

Teams want to build rosters that can win championships (and 52 wins is the magic number there) . The Salary level for each team is also a flexible and continually changing beast. If you’re a GM attempting to evaluate the value of the players on your roster and that of Free Agents that are available you need to consider all these factors in setting your price per win.

Arturo the GM is coming out after the jump.

The first thing to start with is what the teams actually have to pay the players. This is the first that everyone gets wrong ( all the info here is coming from Larry Coon’s Fantastic Salary Cap FAQ ).

- The NBA agreed to pay players 50% of total Basketball Related Income (BRI) starting next year. It can go up or down slightly to 51% or 49% (based on 60.5% of the difference in the BRI estimate to reality) but 50% is the number. This number does not change. If the owners underpay the players (say 48% of BRI), the players get that 2% back at the end of the year, no exception.
- The Salary Cap is set at 44.74% of BRI divided by 30 teams. Yes, you are not misreading that, it is less than what is owed the players (about 12% less). For all intents and purposes that means that on average teams have to go over the cap by 12%.
- Teams have to pay out a minimum of 80% of the cap number this year, 85% of the cap number next year and 90% every year afterward. This means that the minimum wage is going up for teams by 13% over the course of the next two years. Remember that player salaries are fixed at that 50% number, what is actually happening is that the minimum allowed share of the salary load for teams is increasing.
- The luxury tax is set at 53.51% of BRI divided by 30 teams. Consider this the salary share ceiling for teams. The interesting bit here is that it’s a soft celing. What that means is that in theory a team can increase this as much as they want, they just have to pay increasing penalties. Functionally, this kind of increase would serve to depress every other teams’ payroll. So the big market teams paying the tax actually serves to subsidize other teams and help the league (who has full discretion in how it spends the tax penalties).

In essence we have a system with a hard minimum, a fixed target and soft celing. It looks something like this:

So now that we have our salary levels, the next part is to pick a win target. As I said, If I’m a GM I’m going for 52 wins and a chance at the title.How does that look like at 2012-13 levels?

Around $1.38 million is my target for success. Now if I draft well (like say San Antonio) I can afford to have that number go higher because I will be getting cheap wins thru the draft. But again, that’s just the one year, If i want to truly do this properly I need to at least look at the future as well.

That’s how it projects out thru the rest of the CBA based on league projections. Note that revenues are growing at about a 4 to 4.5% clip yearly. Still 2021 is a bit far out in terms of planning . Four seasons is a more reasonable projection.

So the magic number I would (and did use on friday) is $1.47 million per win for the next four years. I would be willing to go as high as $1.86 for Free Agents under the assumption that I’m using my rookie model for the draft.

Next up is the Age Model but you’re going to have to wait till my next post for that one.

-Arturo