# Searching for Value in NBA Contracts

US Presswire

Introduction

A few weeks ago, Kevin Pelton of ESPN looked at the best contracts in the NBA by multiplying a player’s WARP (wins above replacement level) by the average amount that teams pay for each WARP. I’d like to approach this same problem from a different angle: namely, how much value are teams getting out of the salaries they pay their players? Instead of looking at WARP, I’ll focus on win shares, another metric of player value. While Pelton’s methodology assumes that the overall NBA salary market is priced correctly (therefore attaching a value to each WARP a team pays for), my method makes no assumptions about overall pricing accuracy and instead seeks to evaluate relative player salary and performance.

At a basic level, my goal is to quantitatively evaluate the best and worst contracts in the NBA. To do so, I construct a simple metric that I call the “value ratio.” This is defined as: (Player Salary/Median Salary)/(Player Win Share/Median Win Share). In effect, I am comparing the amount over (or under) which a player is being paid vs. the median NBA player with that player’s production over (or under) that of a median player. Comparing salaries and win shares with median values serves as a way of normalizing these metrics and making them more readily comparable to each other. A simple way to think about this metric is the following: if the ratio is less than 1, the player is undervalued; if the ratio is greater than one, the player is overvalued; if the ratio equals one, the player is properly valued. In short, the most valuable players will be those with the smallest value ratios.

Data and Methodology

Win shares is a measure of player value that represents the number of wins that a player contributes to his team. For any given season, the sum of the win shares of all the players on a team should be close to the actual total wins of that team (more on how win shares are calculated can be found here). Instead of looking at win shares from this season alone, I used a three-year average of win-share data, where available (rookies for example, would have only one year of data). This serves to avoid penalizing players having an off-year compared with their historical production—for example, looking at one year’s win shares data might show that someone like Pau Gasol is severely overvalued. In reality, however, a 7-foot big man posting all-star levels of production throughout his career is probably worth \$19mm per season. Using an average of win shares data over a three-year time frame provides a more reliable measure of player productivity. In this post, I use win share data from Basketball Reference.

Instead of only looking at current year salary, I took an annual average of a team’s current and future salary commitments to each player. This is again a smoothing technique that accounts for the fact that a player’s current salary is not necessarily a good reflection of his future salary. James Harden, for example, is being paid only \$6mm this season but is due nearly \$80mm over the next five seasons. Taking an average of a team’s future salary commitments gives a better picture of how teams value players in the long-run. For the purposes of this exercise, I assume that all team and player options are picked up, all unguaranteed years will be fulfilled, all qualifying offers are extended, and no early termination options are exercised. All salary data is courtesy of ShamSports.

I also set a minutes-threshold to define a smaller subset of NBA players. This helps to exclude players like Derrick Rose who have been devastated by injury this season as well as those who haven’t played enough for their statistics to have meaning. On average, NBA teams have played roughly 50 games so far: at 48 minutes per game, that’s 2,400 available minutes per player. I set the minutes-threshold at 500, which incorporates most rotation players in the league and gives us a sample of 285 players to work with.

Results and Analysis

This first table encompasses all the players our dataset. It’s interesting to note that the players with the lowest value ratios (i.e. the most undervalued players) tend to be rotation (non-star) players on cheap/rookie contracts. Matt Barnes, for example, earns \$850k this year (his is an expiring contract) but produces a three-year win share average of 3.8. The list of most overvalued players includes a number of rookies as well as traditionally inefficient players such as Ben Gordon and Michael Beasley. The four players with negative value ratios all had negative win shares over the past three years; as such, they are the least valuable players in the league.

In this next table, I limited the sample to players who have played more than 1,150 minutes this season. This produces a sample size of 148 players (compared with 150 starters across the league), most of whom are starters or sixth-men getting heavy minutes. The players at the top of the undervalued list remain the same, although it’s interesting to see both rookies (Kyle Singler) and grizzled veterans (Jason Kidd) represented. The overvalued list has two names of note: Joe Johnson and Brook Lopez. The former has a gargantuan contract that pays him as if he’s a franchise player (which he’s not). The latter is being paid at an all-star level and has produced accordingly this season; his three-year win share average, however, is marred by last year’s injury-riddled season.

This table includes only those players being paid more than \$12mm per year over the life of their contracts. In other words, these men are being paid like all-stars. It’s somewhat comforting to see the three players generally viewed as the league’s best at the top of the undervalued all-star contract list (and in their typical order, to boot). The rest of the top 10 is also composed of productive star players on fair (or as this suggests, cheap) contracts. The two Brooklyn Nets players pop up again on the overvalued players list, as does Kobe, who will be hard-pressed to produce at a level commensurate with his near-\$30mm salary this season and next.

This next table is restricted to players on rookie-scale contracts. Once again, productive players with cheap contracts produce the lowest value ratios. Chandler Parsons and Isaiah Thomas rate as the best rookie contracts, a fact that may surprise many who may expect to find greater value in players on rookie contracts who produce at an all-star level (Kyrie Irving, DeMarcus Cousins).

Here I list all thirteen players who had a value ratio between 0.95 and 1.05, meaning that their contracts were properly valued. A few surprising names jump out—conventional wisdom holds that Jeff Green, Carlos Boozer, and Kris Humphries are overpaid to varying degrees but this table suggests that their contracts are very fair indeed.

When looking at value ratios by position I expected to find that big men are overpaid relative to their productivity because of the relative scarcity of productive big men in the league (a simple case of supply and demand dynamics). Instead, no position appears to be consistently overvalued while power forwards seem to be the most consistently undervalued players in the league.

Conclusion

While conventional wisdom holds that the most valuable (and undervalued) NBA contracts are those of superstars (think Lebron, Durant, Chris Paul) and of all-star caliber players on rookie contracts (Kyrie Irving, for example), my methodology pinpoints productive rotation-level players on cheap contracts as the best value in the league. While many superstar-level players qualify as undervalued (with a value ratio below one), they do not rank amongst the most undervalued players in the league. The upshot is that the list of players I define as the best values in the NBA is vastly different from those in Pelton’s article, which largely reaffirms the conventional wisdom.

Caveats

As with any such study, there are a number of methodological caveats to consider:

• If I’m using Win Shares data over the past three seasons, it may make sense to incorporate salary over past three seasons as well. A player’s current team, however, may not have paid for that production; the point is to evaluate how good the contracts are at present and in the future, not in the past.
• Ideally, I should project this season’s Win Shares to date over an entire year; the three-year average helps mitigate this to an extent.
• Incorporating three year’s worth of Win Share data penalizes players who are having breakout years (most likely young, improving players) and is more lenient towards older players in decline.
• By using annualized future salary commitments, I’m making the assumption that player productivity will stay the same. But that’s essentially what the team is paying for and expecting, so it seems fair to evaluate these contracts in this manner.
• The biggest flaw of this methodology is that it assumes that all win shares are created equal and that they are not increasingly difficult to produce on the margin. For example, going from 1 to 2 win shares is probably not that difficult; but going from say 8 to 9 and then 9 to 10 is probably significantly harder. In other words, the marginal value of each additional win share may not be equivalent and probably increases in a non-linear fashion. As such, a comparison of player win shares with league median win share may be too simplistic. A method that properly accounts this factor will probably place a higher value on star players that produce more win shares and will probably produce results that adhere more closely to the conventional wisdom.

*Editor’s Note: If you’re digging these numbers, I created a Tableau Visualization so you can play with the whole data set and filter it anyway you want.

This is incredible

• Pistons All The Way

Ming Wang, aren’t you that guy that’s running a half-marathon week, bro?

• JonCBK

Rough to include Brook Lopez’s five game season last year as part of his three year sample size. Drop that season (where he was just getting the rust off) and pick up one of his earlier years and he at least claws himself out of the bottom ten. Joe Johnson may have a terrible contract, but he is at least a good shooting guard. Assuming to me as a fan that I don’t care if my team pays the luxury tax (and since Brooklyn is a big market team they don’t care either), I just want starters who are at least average and hopefully good. Joe seems good to me. Yes, Win Share has him as average. But two months of having Avery Johnson just run ISOs for his aging SG has to have reduced those numbers. The team leaned on him a lot. He came through more, I think, than most would have.

Nice work though.

And wow, i had heard T Robinson was having a bad season. But I don’t really watch Sac much. And he doesn’t play much, so I hadn’t focused in him. Yikes. I guess he won’t be telling Davis to check the numbers anytime soon.

• Butthurt

Haha nets are overpaid and overhyped. “TAKIN’ OVA”

• http://hickory-high.com/ Ian Levy

You’re right Jon, there’s some work that probably needs to be done to smooth out spots where players have missed games due to injury. However, health is a significant factor that effects value and the Nets were paying him all season last year, even though he wasn’t playing.

I’m building a Tableau Visualization with Ming’s numbers that should go up tomorrow that will help illustrate how all these numbers relate to each other. You might feel differently about Johnson after looking at that.

The biggest issue about the Nets in these numbers to me, was Deron Williams as one of the worst values for players making over \$12million. It’s incredible how much his level of production has dropped since coming to the Nets, and I think this really underscores that.

And yes, Thomas Robinson has been a disaster.

• Bob Koca

It is strange how a lower value ratio is good but then a negative one is suddenly terrible. Also you have Robinson with win share of -.1 rated the lowest instead of Austin Rivers with Win share of -1.3. If you turned the ratio upside down so that it is larger numbers that are better those problems would disappear.

Bob Koca

• http://hickory-high.com/ Ian Levy

Good suggestions Bob. I’ll pass those along to Ming and see if we can look at a better solution for that problem than what we have now. Thanks for reading and commenting!