If you don't care about sports or statistical process analysis, this isn't the post for you… but it was interesting for me to try to wrap my head around the data behind a headline that I'll write about here.
Previous Discussion About This
Back in 2011, right after the end of the NFL regular season, I wrote a blog post about how contractual individual player incentives, paying them bonuses for individual statistics, could distort the game:
This Week's Headline
Now that the NBA regular season has just ended (Go Spurs, Go!), I heard about this story featuring Maurice Harkless of the Portland Trail Blazers, as they move into the first round of the playoffs:
How did he get a bonus for NOT shooting the ball? Many basketball players LOVE to shoot and score. A player's individual “points per game” average has traditionally been one measure of how great a player is, which affects their ability to negotiate future contracts and pay. Of course, some of that is changing in the NBA thanks to the “analytics” movement that spread from baseball (see my posts on “Moneyball“) and has been led by a fellow MIT alum, Daryl Morey in Houston.
There's a natural intrinsic motivation for a player to shoot the ball, especially so to make the shot… scoring points, of course, means a better chance to win the game.
Let's look at some data (yes, we can do that in the Lean methodology)…
In this past season, Harkless took an average of 2.5 three-point shots per game. For his five-year career as a whole, he's averaged 1.9 of those per game.
Why did he only take ONE shot in his last four games of the season, as shown in the game log?
See how his end-of-season three point percentage (3P% in the first table) was .351?
That meant he made 35.1% of his three-point shots for the season.
As reported, he had an INCENTIVE CLAUSE.
“As pointed out by The Vertical's Bobby Marks, Harkless could earn a $500,000 bonus by shooting 35% or above from three-point range for the season.”
Half a million dollars! His annual salary for the season was just under $9 million, so $500,000 is meaningful.
At the end of game number 77, when he made 3 of 5 of those shots in the game, his percentage sat at .3523 for the season (68 out of 193).
His next game, where he went 0 for 1 from behind the arc, brought the percentage down to .3505 for the season, just above the threshold for the bonus.
SCARY! If he knew about the stats and how close he was.
The allegation is that Harkless avoided three-point shots in the last few games:
“So, rather than risk that bonus, Harkless did the smart thing — avoid taking a three-pointer.”
We don't know that for a fact, but Harkless tweeted about it after the end of the season, indicating that he at least knew about the incentive after the fact:
I'm not blaming Harkless for being selfish or doing the wrong thing. You get what you incentivize, right? It's not a huge scandal or anything, just an interesting scenario.
Possible shooting performances in those past four games that would have affected his bonus:
|Shots Made||Shots Attempted||Final %||Bonus / No Bonus|
So if he had gone “0 for anything,” he'd lose the bonus for being below .350.
A funny scenario would have been going 2 for 6, which would have left the numbers at exactly 70 shots made out of 200 on the season, or exactly .350.
Would .350 on the nose have gotten the bonus? Wow, that would really depend on the contract language. It supposedly said “35% or above” in the contract, so I guess so.
Portland had already clinched a playoff spot, so the last few games were pretty meaningless.
There might have been a situation where he or another player would be pressured into trying to score a lot of points to hit an incentive threshold.
Or, had he taken one and missed, he would have had a great incentive to put up another shot… since making it would get him back above the threshold. That could have become a situation where, as in blackjack, you might be “throwing good money after bad.” Had he missed four, he'd have to make two in a row to get back about .350.
We could have seen a situation where Harkless would have been launching tons of threes in the last game to try to earn a bonus.
Or, the team could have sat him to avoid getting (or avoid losing) the bonus.
Why Do You Need Incentives?
It's interesting to think about WHY an incentive like this would be needed to extrinsically motivate a player. I'm not a salary cap expert, but maybe incentives count differently against the cap?
From this page:
74. Can incentives be built into a contract? How do they apply to team salary?
“Performance incentives are classified as either “likely to be achieved” or “not likely to be achieved,” with only the likely incentives included in the player's salary and team salary amounts.”
“Incentives must be structured so that they provide an incentive for positive achievement by the player or team, and are based upon numerical benchmarks (such as points per game or team wins) or generally recognized league honors1. The numerical benchmarks must be specific — for example, a bonus may be based on the player's free throw percentage exceeding 80%, but may not be based on a relative measure such as the player's free throw percentage improving over his previous season's percentage. Certain kinds of incentives are not allowed, such as those based on the player being on the team's roster on a specific date or for a specific number of games.”
Man, this gets complicated. Harkless, before this season, was a career .300 shooter.
Was hitting .350 “not likely to be achieved?” I bet the team categorized it as such, to not hit their salary cap?
Here's a run chart of his three-point percentages for his five seasons, including this year:
In his second season, he shot almost 40%… so I guess he showed it was possible?
Is Harkless improving or is he part of a “stable system” with stable performance? Will his shooting percentage regress to the mean next year? Stay the same? Get better? We don't know from the data. Your hypothesis is as good as mine, especially if you're watched him play.
As Business Insider said
“[likely] had a bonus attached to his three-point percentage, as incentive to improve.“
Incentive to improve??? He already had a lot of incentive to improve, including:
- Helping his team win
- Keeping his job
- Increasing his future salary
- Being a good teammate
- Not wanting to embarrassed by missing shots
Do the Data Suggest Harkless Was Intentionally Altering the Way He Played?
To answer the question of “was his performance unusual in the last games?” or “was that special cause?”, I did a run chart of his three-point shots per game this season — it's great that you can download this data into a spreadsheet. Games where he didn't play are not included.
The most shots Harkless took in a game was 7. Until it got late in the season, he never played a game without taking a least one three. It looks like there was a bit of a downward trend over the season, but I warn against using linear trend lines for workplace data.
Minutes per game was pretty stable throughout the season, an average of 28.9 per game. Here's a run chart visualization of that:
If I draw a control chart (or “process behavior chart” using the first 20 games as the baseline numbers, we get this chart for three points attempted per game (3PA):
The original lower and upper “natural process limits” (as Don Wheeler calls them) are 0.63 and 6.95, so the games where he took 7 shots are perhaps “special cause,” mean it's unlikely to just be chance or noise in the data. I don't know what was different about those games when he took 7 shots. That was unusually high.
Any game with zero attempts would have indicated a special cause, such as playing less than normal in the game.
As the season went on, we see many stretches of eight consecutive points below the old average, which indicates the system had changed… that run of 8 points below the average is also a “special cause” indicator (see the “Western Electric Rules“) because it's unlikely to be due to chance. Something changed.
With shifted limits, indicating the new system, the lower and upper limits become -0.28 (or zero, in effect) and 4.48, with an average of 2.1 shots per game.
Toward the end of the season, the one game where he took 5 three-points was above the natural process limit.
There's a stretch of what looks like 12 games below the new mean, which indicates another process shift.
So it looks like the Harkless season was three different systems, as shown below:
Toward the end of the season, there's the one positive outlier game. But, we can't conclude that his last four games of 1 shot, then zero, zero, zero is anything more than “noise in the system.”
What Do I Conclude?
It's possible that Harkless was intentionally not taking threes because of the bonus… but the data doesn't indicate that it's necessarily true. You'd have to ask him.
It could be just randomness or how the games went.
He might have been gunning for .350 (by not firing way) or he didn't notice until after the season.
In the workplace, process behavior charts can help us test a hypothesis about things being stable or something changing.
I did similar analysis in 2012 after American Airlines pilots were accused of staging a “sickout.” The data showed that the number of illnesses was likely chance or randomness (or “common cause” variation).
Have you used charts like this to prove or disprove a workplace performance hypothesis?
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