Tuesday, November 04, 2008

New Offensive Numbers

As I mentioned before, there are some new offensive stats in the HD Box Score – Individual Offensive Rating, Floor Percentage, and Usage. These three stats come from three additional statistical measures – Total Individual Possessions, Individual Scoring Possessions, and Individual Points Produced. The focus of these is to try to figure out just how to break down individual value in what is truly a team game. Take the following common scenarios – a player gets a layup off of an assist; a player gets an offensive rebound, and later in the possession the team scores. In the traditional box score, the points go exclusively to the player who ultimately scores the basket. But he wouldn’t have had the opportunity to score without the assist or the offensive rebound. Those plays are, in a very real way, responsible for the points scored; that is, they help produce the points. The question is how much weight to give the assist, offensive rebound, etc., and how much to penalize the missed shot, turnover, etc. Thankfully, Dean Oliver is a statistical genius, and has come up with a series of equations that factor all aspects of offensive performance (at least those that can be recorded in a box score – so the non-assist, non-turnover pre-shot ball movement is, for lack of a better term, ignored) to produce the 6 stats mentioned above. I won’t reprint the formulas here, but if you’re interested, I will again plug Basketball on Paper – it’s really a remarkable book.

I will, however, discuss the formulas broadly. The starting point is individual possessions, which is a measure of how many possessions and individual is responsible for using over the course of a game. Scoring a basket alone, or missing a shot, does not make an individual wholly responsible for that possession – the made hoop may come off of an assist or offensive rebound, and the missed shot may be the second shot in a possession or may result in an offensive rebound. Only turnovers are fully weighted against a player (on the theory that nothing in a box score can cause a turnover except one player turning the ball over – obviously in practice, two players can contribute to a turnover, but the scorekeeper only records it against one person, so there’s no way to capture the contribution of the unrecorded action. This is one of those things that almost certainly evens itself out over the course of a season, and even if it doesn’t, there’s not a whole lot that can be done about it). As for all other outcomes, there are “parts” – on the good side of the ledger, there is a made field goal part, an assist part, a made free throw part, and an offensive rebound part; on the bad side, a missed field goal part, a missed free throw part, and a turnover part (which, as noted above, is simply the number of turnovers committed by the player). The sum total of these parts is the number of possessions an individual uses. The sum total of the parts on the good side of the ledger represents the Scoring Possessions – the number of possessions used by the individual that resulted in points for the team. Floor Percentage is based squarely on these two numbers, and measures how frequently an individual’s possessions used result in points (so scoring possessions divided by possessions used).

Offensive rating uses Points Produced, rather than Scoring Possessions, to determine a player’s offensive contribution to the team (the number for Offensive Rating is derived by dividing Points Produced by Possessions, and multiplying by 100). Points Produced is computed similarly to Scoring Possessions, in that it’s made up of four “parts” – the made field goal part, assist part, made free throw part, and offensive rebound part. The parts are computed slightly differently for Points Produced to try to capture the point value, rather than just the number of scores, regardless of the points. As a very simple example, if Scheyer and Thomas are both 1-1 from the field (with equal playing time and no other appearance in the box score) but Scheyer’s make was a 3 and Thomas’ a 2, their scoring possessions and floor percentage will be identical, but Scheyer’s points produced and offensive rating will be higher.

The floor percentage and offensive rating numbers tell us a lot about a player’s contribution to the offense, but are still incomplete. That’s because they don’t tell us how much or how little the player was involved in the game. For example, the player with the best Offensive Rating and Floor Percentage from the VUU exhibition was Steve Johnson. He got those numbers by hitting his only 2 shots, getting an offensive rebound, and not committing a turnover. But relying solely on those numbers to tell us his value to the game overstates his contribution. That’s because he not only played limited minutes, but was lightly used during those minutes. This is where Usage rate figures in. It’s derived by dividing individual possessions used by the total team possessions while that player was on the floor. In Johnson’s case, he used only about 1.4 possessions (I realize he made 2 shots, but again, because of assists, offensive rebounds, etc., a made shot is not worth a full possession) of the 11 offensive possessions he played, for a usage rate of 12.74 percent. Even distribution of possessions would put every player at 20% (100% - the team total – divided by 5 – the number of players on the court at all times). The general band is between about 18.5 and 21.5. Anything lower is a more lightly used player, with anything under 15 being very lightly used (think David McClure). Anything higher is a heavily relied upon player, with anything over 25 being the centerpiece of a team’s offense (think Redick).

These numbers will appear in the HD box this year (which will now be embedded via excel), and I’ll track them over the course of the season as well.

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