Friday, May 05, 2006

The Contract Year in the NBA


I want to see how much of an affect statistics have on the size of the contract an NBA player receives. If the team personnel were intelligent, rational beings, I would assume that they would use statistics as their only predictor. However, the contracts in the NBA are guaranteed for their duration, meaning players have an incentive to slack off until the year before they are released into free agency. This means that these rational team peronnel SHOULD look at more than just a player's most recent season in order to determine their value. In practice, teams usually do not perform this rationally and are tricked into picking a player who only considers money an incentive to perform and therefore only performs in contract years. I will be testing 2 things

1) I expect that players will perform better in their contract year due to this strong incentive, so I will test whether this year differs from their mean output over time.
2) I expect that teams will not take into account past performance and will be swayed by contract year performance, so I will test which is a better predictor of contract amount: cumulative output or contract year output.

Empirical Strategy

For my first hypothesis, I need to first create a model of performance over time. A player typically will perform better with time as he learns about the league and improves his skill, but will begin to slide once he reaches a certain age and can no longer perform physically as well. This model will be an aggregate of all players, however I am not exactly sure how this will be implemented. I can use this model to help determine what kind of mean output a player should have during his contract year according to his age, which will be compared to his actual statistics.

For my second hypothesis, I need to first aggregate statistics in some way (this may be necessary for the first hypothesis too). I intent to use a fantasy scoring system to come up with a universal statistic for all players. Additionally, I may use the Hollinger index from, which uses a more complex equation to homogenize statistics between players and teams, as variability such as the pace a team plays, its overall point totals, etc., affect how one players statistics are compared to another's. The regression of contract amount on statistics will be conducted, controlling for coaching change, team change, and playoff appearance during contract year (dummy). I will check the regression on career statistics (possibly excluding 1st and 2nd year stats if these are shown to be much different) and on contract year statistics. I believe the latter will be the better predictor and will therefore have a higher R^2 value.


One concern I have is with the statistics. There are many intangibles involved with players, especially on the defensive side of the ball. If a player is an extremely great shut-down defender but does not get many blocks or steals, this is not taken into account. Also, outliers may bias the results. Superstars are affected by large amounts of hype and speculation which coaches and personnel eat up. This may be controllable by a variable for media appearances but the affects of positive or negative hype are not exogenous, as different coaches perceive these things with varying interest. The easiest way to remove this bias would be to remove some superstars and my initial plan is to take out the 20 highest paid players from each year. This will give an affect that more closely approximates how the average NBA player reacts to the contract year as anecdotal evidence from the media focuses almost solely on superstars.


The two issues here are pretty clear. You seem to have a reasonably good grasp of this.

Empirically, you seem to be struggling a bit.

For the first hypothesis, you want to estimate equations using individual fixed effects. That is, you want to run:

output of player i in year t = a + b*last year of contract(i,t) + [other things which might change player's performance in year]'*d + player fixed effect + e

to do this you type:

areg output contractyear [other controls], absorb(player)

The trick is to appropriate control for other shocks to player producitivity.

For the second hypothesis, I think a basic OLS will be ok. The goal here is to compare the contracts of players who are basically similar but differ in how much "better" they play in their contract year. So you want to estimate something like:

contract = a + b*(contract year output) + c*(avg output in non-contract year) + [other player controls like position, height, age, ...]'*d + e

These may not be precisely correct, but they are on the right track. Just keep thinking about what you want to argue and what someone might argue who doesn't believe your estimates.
I think another approach, and please correct me if I am wrong Bryce, is to use a differences in differences approach. The reason for this is that one reason players might do better the year before their contract is because they had an extra year to get better. While this may not apply to players like Kobe, it certainly applies to playes in the league under five years. First, I think you should eliminate rookies with one year contracts from the sample because you have no standard to compare their improvement against. Then, I think you should calculate the average difference in performance during non-contract years and subtract it away from the difference in performance in a contract year. This should also eliminate any player fixed effects and isolate the effects of the contract.
I think the most effective way to deal with Varun's concern is to (as I mentioned at our original meeting) include a trend variable. That is, you should have a control for the number of years the player has been in the NBA in your regression.
You may want to check out chapter 5-3 of Baseball Between the Numbers, which takes on the contract year phenomenon in baseball. (Admittedly, I haven't read it through. Still on chapter 3.)
This is a really cool topic, one that I've definitely seen in effect--just look at Jerome James or Bonzi Wells this year. Correct me if you are already looking at this, but I think it would be interesting to do some kind of matched pairs statistical test to compare the contract year with the year after signing the contract.

In this sense, it might be cool to look at whether players who get big contract deals because of good contract years perform better than those who receive smaller deals (maybe they feel more pressure to perform with the big salary). Just some thoughts, it might be tought to incorporate all of it.
Instead of trying to aggregate the statistics into one index, you may want to keep the varous stats separate. I think that you might find that players amp up their scoring (but decrease their assists) in contract years. If you find this true, I think it could further the economic motives behind your argument. Although assists might actually help the team win games, scoring might have a bigger impact on the individual's contract. This might overcomplicate your paper, but it could give you more to work with in your analysis. Good luck.
While this model seems to incorporate most of the aspects involved for this type of situation, i think that it would still be difficult to conclude that a player was not trying as hard because he just got a big deal a lot of times the reason for the decline in player output have much more to do with externalities. One example is that the player is signed by a different team than they played on the year before and the team simply doesn't play as well, or perhaps the the coach is not putting him in situations that he is comfortable with which will lead to a less productive player.
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