## Friday, February 07, 2003

##### What is the value of an assist? Part I

The first big issue I’d like to tackle is to consider what the actual value of an assist is. In a lot of player rankings, they give an assist the value of 2 points, since it’s a pass that leads to a bucket for your team. But this is obviously wrong, since even if you didn’t make the pass that led to the assist, your team would still have a good chance to score. So it didn’t add a value of two points to your team. This gives us a first cut at determining the value of an assist. Since the average points scored per possession is 0.876, then an assist adds a value of 1.124 points to your team (2 points for the basket off the assist minus the average points the team would otherwise have scored, 0.876.)

But it’s actually worth more than this, since that 0.876 number includes all the baskets with assists. If you assume that all baskets with assists are sure scores (FG% of 100), then you have to subtract those off to determine the average number of points scored without an assist. The average NBA team shoots 80.6 times per game, making 35.68 shots, with 21.08 assists. Pulling out the assists leaves the team making only 14.6 shots out of 59.52 attempts, for a paltry shooting percentage of 24.5%. The impact of 3-pointers is small, leaving the value added by the assist of 1.47 points. Note that this is the absolute upper bound on this value, assuming that every assist is a great pass that leads to an easy basket.

But this isn’t true, of course. Many assists come off of routine plays. If I’m at the top of the key and swing the ball to the wing, who then hits a jumper, chances are I’ll be awarded an assist. But I really didn’t do anything. I was just lucky enough to pass the ball to a guy who then made a shot. So a lot of assists don’t really provide much value at all.

So let’s take a step back here and think about what a good pass, the sort that might lead to an assist, actually does. A good pass finds an open player and gives him the ball in a position to score. To put it another way, a good pass creates a shot opportunity for a player, with a higher percentage than they could have gotten on their own. A good pass increases the FG% of the recipient. At an extreme case, it finds a player under the rim for a lay-up, resulting in an essentially 100% score, as in the analysis above. At the low end, it doesn’t do anything, and you just happen to get lucky and pick up an assist off of another player good play.

But basically, what you’d expect to see is some sort of correlation between assists and shooting percentage. More assists means more good passes for easier, higher percentage shots, and a concomitant increase in the FG%. If you can look at the numbers to find out what that relationship is—how much the FG% increases with increasing assists, you can then quantify exactly how much value the average assist provides to the team. And that’s what I’m going to try and do in part II of this piece, coming soon.
##### Possessions, the fundamental stat

Probably the most important statistic, or at least a necessary one for any additional analysis, is the number of possessions a team gets in a game. Simply looking at points scored doesn’t tell the whole story, because different styles of play will lead to different numbers of possessions. If a team play slow-down ball, almost running the shot clock to zero each possession, then there will be fewer total possessions in the game. Essentially, this shortens the game, since the real length of the game in practical terms is how many possessions each team gets.

This is another basic misconception in broadcasting—equating points scored and points given up with offensive and defensive quality, without properly normalizing for possessions. If a team shoots really quickly every time down the floor, they could score 95 points per game, but still not be a good offensive team, because they might only be scoring 0.75 points per possession. (The league average in 2001-2002 was 0.876 points per possession, a number I’ll be coming back to.) Similarly, that same team will give up a lot of points, too, simply by virtue of the sheer number of possessions (and corresponding large number of shots.) But they might still be a good defensive team, if they hold opponents to a low number of points per possession.

And the effect can be significant. In the 2001-2002 season, the number of possessions per game ranged from a high of 101.9 for Sacramento, down to a low of 89.3 for Miami. If you just look at points scored, the Knicks look like one of the worst teams in the league, averaging a lowly 88.7 points per game. But their .989 points per possession was right at the league average and was actually slightly superior to the numbers posted by Toronto and Orlando, the 5th and 6th highest scoring teams in the league at 97.6 and 97.5 point per game, respectively.
##### Evaluating players

The holy grail of basketball analysis is to try to find a way to measure the value of individual players. Is Kobe better than Tracy McGrady? How does Jason Kidd compare to the best point guards of previous eras? Was Houston right to draft Hakeem instead of Michael Jordan? Those are the really fun sorts of questions, and what I’d like to get to, eventually.

The form that this usually takes is to look at each statistic, and assign them particular values. If a player scores 20 points, that’s worth so much. Each assist is worth so much, etc. And at the end, you add up all the numbers to get a value. I’ll probably end up with something like that eventually, since I don’t see any real way around it (although my valuations might be somewhat more complicated that simply adding a bunch of weighted stats together.)

In the meantime, however, I’m going to be looking at team values, for a few reasons. First, because the game is played at a team level. It doesn’t really matter how any individual player does—results are determined by how the team does. Second, it allows you to get around some of the synergistic effects mentioned before. It’s hard to tell how important someone’s assists were, without looking at how the rest of the team performed. By looking at the team level first, those effects are automatically factored in. And lastly, they’re easily available online and provide large enough samples to be statistically significant.
##### A pet peeve about turnovers

Before getting into more involved points, a brief note about what is one of my biggest pet peeves. Namely, announcers saying after a missed shot or turnover followed by a made bucket on the other end, "that was a four point swing there!" The implication here, and one that I've seen carried out in some analyses, is that a turnover costs you two possessions. After all, you lose your own possession and the opposing team gets a possession, right?

Wrong.

A turnover only costs you one possession. Consider--no matter what you do on your own possession, whether you make a basket, miss one, or turn the ball over, the opposing team gets the ball back. The turn over (or missed shot) simply ended your own possession, it did not create a bonus possession for the other team in addition. They were going to get that possession anyway. The turnover just wasted your own chance at a basket.
##### Welcome to Court Analysis!

I've long been a big fan of Bill James, and the type of statistical analysis which he brought to baseball. I found his work fascinating and enlightening, and it made me and a host of other fans see aspects of baseball in whole new light. I'm a much bigger fan of basketball than baseball, however, so I've long wanted to try and apply some of the same methodology to that game, as Bill James did to baseball.

Now, I'll admit up front there are some problems with trying to do this. Specifically, basketball is a team game in a way that baseball is not. Baseball is, more or less, an individual game--there are few, if any, synergistic effects. That is, each player simply has to do his own job. How good the shortstop is does not effect how well the right fielder plays. And how good the leadoff hitter is has only a small effect on the statistics of the clean-up man. So in baseball, you can seperate things out pretty neatly for analysis.

Basketball, on the other hand, is a game of 5 on 5. To get people open shots will almost always involve the coordinated actions of several players, sometimes all 5. Defense, even more so, is played by all 5 players as a unit. Because of these effects, there is much more potential for intangibles, things which don't show up on the stat sheet, to effect a game. A guy setting a really good pick isn't recorded, nor is the ability to rotate over on defense.

But, despite these problems, which are fundamental to the game, I think there's still a lot that can be said, and a lot of insight that can be gained from analysis. I don't have any specific plan of attack, or any preconceived notions about what I might find. But I'll enjoy looking, and hopefully some readers will enjoy it as well.

A few quick technical notes. First, the analysis I'll be doing will (until and unless I say otherwise) be based on the stats for the 2000-2001 NBA season, since that's what I found first on ESPN on its web site. My hope is that any conclusions I draw will have general relevance, but of course that is something that will need to be checked. I plan on doing so when I have time to transfer over the 2001-2002 season stats as well.

Second, a book along the same lines as I'm suggesting here recently came out--the Basketball Prospectus. As of now I have not read this book except for the player reviews of Michael Jordan and Frank Williams, so any conclusions I come to will be my own, not based on his previous work. I intend to read that book eventually, and will mention it if and when I do.

Finally, a brief word about my qualifications, beyond simply being a fan of Bill James. I received a B.S. in physics from MIT and a Ph.D. in physics from the University of Illinois. After graduating, I spent more than four years at a company which did operations research and systems analysis work, which is really what Bill James did. Operations research is applying mathemtical techniques and methodology to quantify and analyze real world processes. I would describe what I wish to do as being an operations research analysis of basketball, so I think I have exactly the sort of broad ranging technical, analytical background this sort of project needs. Plus I'm a huge hoops fan and play at the rec league level.