Of Grant Hill and Basketball Relationships

Dateline: 02/19/98

THE SAN FRANCISCO ZOO CELEBRATED Valentine's Day by promoting their "Animal Sex Tour" along with champagne and truffles. Being the romantic guy that I am, I was immediately struck by the unique link the zoo was making between romance and science. Given the scientific bent I bring to basketball, I decided to ask my girlfriend how to make the link between romance and scientific basketball research.

"Impossible," she said, not even looking at me.

"What? You hear all the time that Americans have a love affair with professional athletes, that there is a natural romance to sports!"

"But not to science. Throw science into anything and there goes the romance. Never ever give me scientifically grown roses, for instance," -- something I logged into my girlfriend database. "I read romantic fiction about strong women and strong men who have a special physical and emotional tension." I quickly considered that and instinctively flexed a bicep just to check. She continued, "You read science fiction where the women have metallic bras, the men solve problems with technogadgets, and what is called romance is when the man needs to borrow a component from the woman's bra in order to build a technogadget."

I could have fought her on that point for hours, naming numerous counter-examples, claiming that I have never read such a shallow sci-fi story, but I have found that logic gets me nowhere with her. So I just tried to shift the conversation to the zoo. "You know, the zoo is celebrating Valentine's Day with an Animal Sex Tour. They've got champagne and truffles. I know a few people bringing dates to that today."

"That's not romance! That is PBS!" At least she was looking at me after that comment. "There was a recent study showing that the more people watch PBS and nature specials, the more sex they have."

"Someone funded a study like that?" I answered, marvelling at the money people throw at subjects that can only serve to uncover the tricks men use to get women into bed.

"And it was about sex, not romance. Scientific studies are about sex, not romance. Science has absolutely no relationship to romance."

Sensing I was losing even worse than before, I decided to get personal, "What if Grant Hill were to take up science?"

"Ooooh." She closed her eyes, apparently imagining the possibility.

"So was that a carnal 'oooh' or a romantic 'oooh'?" I asked, knowing her inability to admit to base carnal urges.

The dirty look I got after that comment was one to last.

So we went to the zoo.

Somewhere around the giraffe exhibit, I began to sense that I was in trouble. Back at the shrew exhibit, I had mentioned that I was thinking about a "Kiss-and-Tell" study in the spirit of Valentine's Day, where I'd look at whether good players that get traded help their new teams beat their former teams more than the rest of the league. Her response at that point was sarcastic, "Ahh, that's romantic."

By the giraffe exhibit, I had already realized that the study was boring. The answer was obvious: there are two sides to a trade and there would likely be no "Kiss-and-Tell" effect, something I checked anyway (later) and found to be true.

So at the giraffe exhibit, I tried to get sincere, "If you help me find a link between my work and romance, we'll have fondue and go dancing tonight," both activities scoring major points with her.

A big smile and, "Grant Hill."

"What about Grant Hill? How is Grant Hill romantic?"

"He just is."

"You're losing your fondue."

"Grant Hill has a mystery about him, an untouchability. Grant Hill can take charge, but still look humble if he gives you a rose -- a non-scientifically grown one, I'm sure. Grant Hill can make anything romantic because women love him and guys love women who have sports heroes."

She was saying "Grant Hill" so much that it was beginning to replace in my head the phrase that had infected it the past two weeks: "We'll return to Nagano after these messages."

So I'll talk about Grant Hill. In particular, I am interested in how his performance is related to the players surrounding him.

What makes Grant Hill interesting - besides his ability to get my girlfriend into a good mood - is that he plays on a team that made a huge trade this year. That trade very dramatically altered the kinds of players around him and changed his own effectiveness. Grant Hill, if you will, changed his relationship with his teammates as much as he's changing my relationship with my girlfriend.

Hill was scoring a lot before the trade, but that scoring average dipped with the acquisition of Jerry Stackhouse. Most people would say that's a bad thing for Hill, but it isn't necessarily. Stackhouse came in to relieve a very large load that Hill had taken on. The Detroit Pistons' brass decided that Hill would be more efficient if he didn't have to take on as large a scoring load. Stackhouse can take on that scoring load. But what the Pistons gave up was an ability to handle other loads. Maybe they thought they had the players to handle the rebounding and the individual defense. Maybe they thought that Hill would be more efficient redistributing his energy to these other loads.

But they were inherently managing chemistry. They were trying to get Grant Hill to work together with his teammates as well as my girlfriend and I work together to come up with this story idea.

I have traditionally evaluated players using offensive ratings and floor percentages, two measurements of a player's efficiency. But both of these measures are reflections of more than the player's efficiency at scoring. They also reflect the impact of teammates who can take pressure off or put pressure on a player like Hill by their own performances.

In general (though it's not always true), a player who can score efficiently and frequently will make his teammates better. If Michael Jordan, John Stockton, Karl Malone, and Shaquille O'Neal were Hill's teammates, his offensive numbers would be better. There can be little doubt of that. That is one reason why the All-Star Game typically features good offense -- lack of defensive intensity being another.

We have some evidence of this as a result of the trade Detroit made for Jerry Stackhouse. What Detroit gave up were Theo Ratliff and Aaron McKie, two guys who don't create a lot of offense. What they got was Stackhouse, who does create a lot of offense, albeit inefficiently. Stackhouse, however, has been slightly more efficient than the two guys who left (though Ratliff has reverted to the form of last year since going to Philadelphia) -- that combined with him scoring more often has made Grant Hill's offensive numbers improve dramatically.

Below is a figure showing the offensive efficiency of Detroit players before and after the trade.

Offensive efficiency of Piston players
before and after Stackhouse trade.

The following is a figure showing what percentage of the team's possessions each of the player's used, a representation of how much a defense has to pay attention to them.

Percentage of team possessions for Piston players
before and after Stackhouse trade.

First of all, take a look at the guys traded. The two guys who left, Ratliff and McKie, both produced less than 100 points per 100 possessions and used about 13% of the team's possessions each. (If both of them were on the floor, they'd use about 26% of the team's possessions.) Stackhouse, though putting up relatively poor efficiency numbers with the 99.9 rating, has been drawing the defense more simply by using almost 26% of the team's possessions while he is on the floor.

The influence of Stackhouse on Hill has been dramatic. Hill's offense has gotten much more efficient. (You can look at every other player on Detroit and, using a statistical significance of 95%, only Hill has significantly changed since the trade.) There are two factors here, (1) Stackhouse's offense has been more efficient than Ratliff/McKie, and (2) Stackhouse has scored more frequently than they did, effectively drawing more defense. Both factors would presumably help everyone on the team and most players have improved; Brian Williams is the only player whose decline is close to significant. Overall, the Detroit offense has improved about 4.5 points per 100 possessions since acquiring Stackhouse. (The defense has declined because Ratliff was an outstanding defender.)

This complimentarity of players is hard to analyze because every player is affected by the presence of every other player. For instance, if Hill had Tim Hardaway and Rik Smits on his team, the trade would probably not have helped Hill at all; it likely would have hurt him.

This is a little touchy-feely to this point. (But isn't that what romance is about?) I can add a little science to this by being more concrete in what is going on.

Grant Hill's offensive efficiency is determined by several things:

The offensive efficiency of Hill's teammates is determined by similar things:

Finally, the defense faced by Hill and his teammates is determined by these things:

To summarize, everyone's play -- offensively and defensively -- is dependent on everyone else's play. In science, this is called many things, from a feedback process to nonlinear optimization to one !$%^!@# hard problem. [To strictly define this for the hardcore scientists out there, you can formulate this as a nonlinear optimization problem where we can probably reasonably assume that both the defense and the offense have maximized their benefit (a minimax problem) that results in the above table of offensive ratings and percentages of possessions used. Anyone who can solve for the underlying functions is worthy of a Ph.D. -- and I have ideas for how to do it.]

The fact that basketball players and coaches get a sense for how to maximize their offensive efficiency given the complicated math underlying it is a tribute to the human brain. Obviously, the human brain ain't perfect -- witness the recent deluge of NBA trades involving former high draft picks (and the recent departure of my girlfriend). The human brain can use some help in designing teams and that is where I am going with a lot of this research. This avenue is a tough one to follow, but this discussion was a big step.

According to my girlfriend, just by talking about Grant Hill, I made this a romantic column. So you can take this to your girlfriend, read it to her, and you won't have to wash dishes for a week...


Below is a table of the data showing the performance of Detroit players before and after the trade. It also shows on the far right the percentage of the team's possessions that the player is responsible for while in the game.

Floor Percentage Offensive Rating Pct. Team Poss.
Player Before After Before After Before After
Hill 0.495 0.540 97.0 104.1 29.1% 28.8%
Williams B. 0.530 0.492 103.4 96.6 24.5% 21.1%
Hunter 0.473 0.455 100.1 97.8 20.5% 19.3%
Sealy 0.513 0.516 103.1 103.0 18.8% 17.9%
Dumars 0.421 0.452 96.5 107.4 17.3% 18.3%
Ratliff 0.510
McKie 0.436
Williams J. 0.482 0.525 91.2 100.3 19.0% 15.9%
Long G. 0.519 0.528 98.9 102.1 10.7% 9.7%
O'Bannon 0.438 0.407 85.7 83.6 14.0% 18.5%
Pollard 0.526 0.811 104.2 155.0 10.5% 16.5%
Reid 0.527 0.587 98.4 114.9 13.1% 12.8%
Mahorn 0.386 0.469 71.4 91.0 14.6% 10.7%
Pct. Team Poss. = The percentage of the team's possessions that a player ends while they are in the game. Since there are five players on the court at any time, a perfectly balanced offense would have five guys at 20%. Since substitutions occur, these percentages do not add up to 1.