PA 100

Points Added 100" is a metric I have been working on the past couple weeks. PA 100 is an offense only metric that measures how many points a player adds (or subtracts) from a team's production across 100 offensive possessions. I will be outsourcing many of my opinions to this model in the future, so I figure I should present it on Canis Hoopus.

PA 100 uses a priori assumptions about how different statistics translate into points to parcel value among players. All of the statistics used in its construction can be found on HoopData. I had a lot of fun designing the model, and am pretty happy with the product. As you will see, probably the most interesting part of the results are how uninteresting they are. There are not many surprise players poking their head into the top 20. Players rise and fall relative to "general consensus," but more often than not the metric makes NBA decision-makers look much more competent than one like Wins Produced does.

I'm not going to get into the nitty-gritty of the model, but I outline the basic logic and explain the component parts. The key to the model is how it parcels each offensive possession into three stages. 1). Shot creation, 2). shot execution, and 3). possession continuation. I'll discuss each of these stages separately and then argue why the metric's results are worth paying attention to.

Shot creation:

Shots from certain locations and situations are more efficient than others. On average, shots at the rim and from three earn more points than mid-range jumpers, and assisted shots are more effective than unassisted shots. Ideally, teams would only take the highest efficiency shots; however, gaining access to those shots can be very difficult. Shot creation represents the fact that opposing defenses aren't going to sit around at let you take layups all game. There is a reason most teams take 50% of their shots from mid-range. Often that is the only shot you can get. I include shot creation in the model to credit players who help their team get better shots and punish players who do not.

Valuing shot creation, and in particular devaluing its absence, is where this metric most distinguishes itself from popular evaluation metrics. Wins Produced and the related Wins Score metrics give all the benefits of creating a better look to the player who drops in the uncontested layup or open three, while placing the entire cost of failed shot creation on the player who ultimately takes the contested mid-ranger. PER simply gives players credit for any shot with a FG% over 30.4. That certainly gives points to creators, but fails to discriminate between "creators" and "chuckers." Both of these metrics give credit for assists, but neither appreciates the range in assist value, and more importantly, neither controls for the value that an assist passes along to its recipient. Appreciating shot creation (and the lack thereof) improves our understanding of which players make the offense work and improves our ability to parcel team performance among the individual players.

To calculate shot creation, I start with the basic assumption that a team can take an unassisted jumper any time it wants. I call this the "settle." Taking a "settle" shot does not confer any value because it is, on average, the lowest quality shot a player can take. Player's generate increasing value for assisted jumpers, unassisted threes, assisted threes, unassisted shots at the rim, and assisted shots at the rim in that order (note 1: I factor situational expected foul rates into these values; note 2: I also estimate the number of missed assisted shots, or "potential assists," and give players credit for those.) This value is equivalent to the league mean of those shot types minus the league mean value of "settling" (an unassisted jumper). Player values aren't set by actual points scored, but instead are based on how they change the situation and thus improve on "expected points scored." I give all of this value to the player who either gets the look on his own, or makes the pass into the situation. I do not credit pass recipients for shot creation. This is a false simplification, but I think an acceptable one.

Here is a list of the top Shots Created scores at each position in 2011:

Not surprisingly, point guards dominate this rating. Offensive creation is the explicit role of point guards, so it would be a concern if they didn't shine here. The first two values show how many expected points each player creates by taking unassisted threes and getting to the rim. The third value "solo.cre" is just a combination of the two ways players can create shots for themselves. The next four lines capture how a player can create expected value by setting up teammates with better looks. Shots at the rim are both higher value and more common than three-point shots, so that is where the most expected value is earned. The "Shots Created" (SC 100) score is the sum of all of the different ways a player can add expected value to an offensive possession minus turn-overs above/below the NBA mean (turnovers are valued as an average possession.) The value indicates the expected points added by that player over 100 possessions. Players like Nash and LeBron who are good at creating opportunities at the rim consistently dominate this score.

Shot execution:

While there is a league average value of shots at the rim, shots from range, and assisted jumpers, the player taking the shot also makes a huge difference. What I am looking for in "shot execution," is a player's ability to transcend the expected value of different types of shots. An unassisted mid-range shot is much more valuable when it comes from Dirk Nowitzki than when it comes from Darko Milicic. This is true for every type of shot. Players who shoot above the expected value on different looks improve their teams point production by either enhancing the value of good shot creation or by dampening the sting of possessions that fail to produce quality shots.

Calculating shot execution is easy. Players have an expected value at each location on the floor based on the percentage or their shots that were assisted and the league-wide expected value of assisted and unassisted shots at that location. For example, a player who takes four shots at the rim every 100 possessions is expected to add about 5 points above the baseline expectation of "settling." I subtract this expected value from the player's actual contribution to find how much value his execution adds at the rim. I do this for each player in each situation and then sum across them to find their "Shot Execution" (SE 100) scores.

Here is a list of the top Shot Execution scores at each position in 2011:

SE 100 is the sum of all of the preceding columns. The first three columns represent how many points these players add by executing from the field at different locations. Note, Dirk's efficiency from mid-range earned the Mavericks 3.4 extra points per 100 possessions last season. This is not something that other metrics are going to capture. The fourth column, ft.exe represents how much value players added by getting to the line and knocking down free throws above expectation. You can see from these numbers that being better at drawing fouls is probably the single best way to generate SE 100 value. I think it is a sad commentary on the state of the NBA, but not a surprising find.

Possession continuation:

Offensive rebounds keep possessions alive and thus allow new opportunities to create and execute shots. Nothing is more disheartening to a defense than forcing a team to take an ugly shot only to have a player reclaim the possession and start the shot creation process over again. Possession continuation (Poss+) value comes solely from offensive rebounds. This is the simplest calculation of the three. For every offensive rebound above or below the league mean, players gain or lose point-value equal to an average possession. I won't bother posting examples of these guys, just go to HoopData and sort by ORR.

Putting it all together.

PA 100 is the summed value of these three sub-metrics.

PA 100 = SC 100 + SE 100 + Poss+ 100

Here is a list of the best and worst offensive players over the last 5 seasons based on PA 100

We get to see a few Wolves players here... unfortunately they are all on the wrong side of the ledger. As I said earlier, the results are extremely boring. The best offensive players are pretty much exactly who everyone thinks they are. LeBron and Howard have their positions locked down, Kobe passed the shooting guard crown to Wade in 09 and Paul and Nash traded off years as the top point guard. Similarly, the worst players are unlikely to draw much debate. They are all players generally considered to be offensively limited.

So why should you take these results seriously? What utility does this metric add?

PA 100 is descriptive:

I multiplied the mean value of a possession by 100 and then added the NBA mean "Shots Created" value five times to set the NBA mean points per 100 possessions. I then summed the value of player possessions for each NBA team and added those values to the expected NBA points per 100. The resulting values retrodict team Offensive Efficiency (pp100) over the past 5 years with an r of 0.95.

In addition to describing team performance, the component values in PA 100 make a nice roster construction tool. They make it easy to identify promising passer and finisher pairing, they make skillset dearths and redundancies apparent, and they help decide who to give the ball in different shooting situations for optimal results.

PA 100 is predictive:

PA 100 scores remain relatively stable across time. A player's performance in one season is a pretty solid predictor of his performance in the next season. I still haven't specifically looked at prediction following team changes, nor have I tried improving prediction with age curves, but the initial results are promising.

Among players with at least 2000 possession, PA 100 in one season has a 0.82 correlation with PA 100 in the next season. This isn't a perfect relationship, but I bet controlling for age curves will improve it quite a bit. Looking at the component parts, Shot Creation and Possession Continuation are much more consistent than Shot Execution. There is a .91 year to year correlation in SC 100 and a 0.95 correlation in Poss+ 100. Given that assists and rebounds are very stable across NBA careers this isn't surprising. Shot Execution in one season only has a 0.8 correlation with SE 100 in the following season. These results aren't very surprising. Accuracy is a volatile skill. All shooters are "streaky shooters" to some extent, for the same reason that batting averages in baseball are notoriously difficult to project year to year. Fine grained skills seem to bounce all over the place, but they do tend to stick around a stable central tendency if you give them enough time.

I still haven't tried using summed PA 100 values from the previous year to predict team offensive efficiency in the following year, but it shouldn't be too different from the predictive power of individual PA 100 scores.

Problems?

The biggest problem right now is that I don't have a defensive counterpart to the PA 100 metric. I have a pretty good idea for how I want to construct the defensive model, but I don't have the data. Basically what I hope to do is reconstruct the location data kept on hoopdata for players' defensive matchups. This data is theoretically recoverable from Play-by-Play and matchup data, but I don't currently have the programming chops to pull it off.

Not having a defensive metric is unfortunate, but it should be noted that defensive metrics aren't very good. There seems to be powerful coaching and team effects on defensive that aren't nearly as problematic on the offensive end. I think my planned method will help parcel out a lot of individual contribution to defense, but I don't expect it to give a perfect answer. For now, just remember that this is an offense only metric; steals, blocks, defensive rebounds, and man-defense are not reflected in any way in PA 100. I think it is a good reflection of the value individual players bring on the opponents end of the court, but says absolutely nothing about the other half of the game.

As a conclusion, here are the PA 100 scores for the current NBA season organized by team.