APBRmetrics

[Dan Rosenbaum]

Indivdual Possession Usage

When we calculate individual possession usage (and offensive ratings), we count field goal attempts, free throw attempts, assists, turnovers and (sometimes) offensive rebounds.

So when the PG comes down the floor and passes to the SG cutting to the basket who then shoots the ball, that pass increases possession usage if (a) the shot goes in, but not if (b) the shot is missed (even if there is a foul that leads to free throws).

In both cases (a) and (b), the PG generated a shot attempt of exactly the same quality. But it only counts as using a possession if the shot happens to go in the basket. Had the PG shot the ball himself, it would count towards possession usage, regardless of whether the shot went in. But when he passes it off to a teammate, we only count it if the shot goes in.

That seems fundamentally inconsistent, but I doubt that I am the first to realize that. I think the reason we generally only count assists and not all potential assists is that we don't know the number of potential assists. But I think we can estimate the number of potential assists.

potential assists = assists * (0.5 * points / field goals made) / teammates' true shooting percentage

The second term (0.5 * points / field goals made) scales up the assists to include free throws and three pointers. Since it takes more passes to generate an assist on a three pointer, it is only fair to allow the assist to count more. It would be better with this formula to take out the free throw points due to non-shooting fouls. (Perhaps this could be done in some sort of average sense using the data that Ed provided for us.)

The third term in essence counts the potential assists where the shot was missed. A true shooting percentage of 50 percent would imply that it takes two potential assists to generate an assist. Ideally this term would use the teammates' true shooting percentage on attempts after potential assists, although presently we do not have the data to calculate that.

This next paragraph has been edited to fix mistakes and add clarity.

DeanO uses a one half multiplier, but only counts assists, not potential assists. This formulation uses a smaller multiplier of one third, but counts all potential assists. This formulation likely will result in assists counting a little higher in my formulation than in DeanO's. Compared to DeanO's one half multiplier, this formulation probably ends up with something between 0.53 and 0.61 with the higher multiplier for players on poor shooting teams. (Those players will have higher possession usage, but lower offensive ratings - kind of like what happens with them with shooting.)

Individual Offensive Rating

When computing offensive ratings, we are typically measuring the points created per possession. The assist possessions go into the denominator and (if I remember correctly) the assist possessions multiplied by two (or something a little greater than two) go into the numerator. Thus, getting assists will invariably push a player towards an offensive rating of 200 (or higher) with higher turnovers due to errant assist attempts being the only the only thing holding back high assisters from having really high offensive ratings.

My formulation suggests another way for assists to enter offensive ratings. In the denominator they would enter in the same way as they enter possession usage. In the numerator the number of possessions would be multiplied by 2*true shooting percentage (for potential assists). Thus, potential assists would come into the formula at the rate of points per true shot attempt (for potential assists) for the rest of the team.

Thus, a high percentage shooting PG would decrease his offensive rating by giving lots of assists to his low percentage shooting teammates. His possession usage would go up, but his offensive rating would go down.

This is why I have been probing folks about the true shooting percentage on potential assists vs. non-potential assists. If, like Ed calculated in a short study last season, the true shooting percentage for potential assists is about 10 percentage points higher than that for non-potential assists, then assists will tend to raise offensive ratings quite a bit. If not, they would not.

This is a pretty long post, so I will stop know. This post is challenging my ability to organize thoughts, so I hope it makes some sense. I may edit this original post if subsequent posts point out where I need to be clearer.

[bchaikin]

concerning "Individual Possession Usage", this is what i call Possession Factor, or touches per minute, and its calculated from the raw numbers...

you can find these touches/min numbers listed for all players over the past 27 years in the NBA stats database (or the superDB) at www.bballsports.com, and the instructions file to the application has a statistics definition file talking about it...

it is this number the simulation uses to determine how often each player should handle the ball...

[Dan Rosenbaum]

[bchaikin]

here are some APBR_analysis postings (numbers 883-886) from 4/2002, these should shed some light on your questions...

In APBR_analysis@y..., bchaikin@a... wrote:

i calculate possession factor (touches per min) by:

poss fact =
shots + passes + turnovers + times fouled = FGA + AST/X + TO +FTA/Y

where X and Y are calculated yearly and by team...

Are X and Y secret?

Let me also ask whether the factor matches what you would see in a
game. For instance, if we calculate a player's touches per minute to
be 2 per minute, would that mean that, if he played 35 minutes, he
would touch the ball, on average, 70 distinct times in those 35
minutes?

yes - but my original research/analysis took place over the span of 3 seasons in the late 80s / early 90s, watching just under 1000 NBA games on tape, charting team and individual player ball possessions. the formulas are extrapolated from this data and streamlined for each season and each team (based on avg team yearly possessions and then each team's calculated possessions)...

I ask because the formula seems to not include rebounds. Obviously,
guys touch the ball when they get rebounds. If X and Y are team and
year specific, then it is possible to have a couple guys with very
different rebounding totals with similar possession factors. For
instance, Jon Barry and Ben Wallace aren't terribly different in the
main factors you list. Wallace has lower totals in all but FTA. But
he had 800 more rebounds than Barry. How do these guys stack up?

think about it...to calculate how often a player handled the ball on offense you either have to count all the times he first gained possession of the ball while on offense, or what he did with the ball (how he got rid of it) each time he had the ball...again, what can a player do with the ball once he has it in his hands? he can either shoot it, pass it, get fouled, or turn it over (FGA + AST/X + FTA/Y + TO). other things can occur (off foul, double fouls, jump ball, techs, etc) but these occur only occassionally such that they can be ignored - if they were all measured they could be included...

or how can a player gain possession of the ball while on offense? he can either start the team possession (get a pass from a player from out of bounds after the opposition has scored), start the team possession by catching an inbounds pass on an out-of-bounds play, simply receive a pass from another player on the court, or get an offensive rebound. i do not use def rebs because rarely does a player score immediately after getting a def reb (players do occassionally get rebounds, dribble the length of the court, and score, but the total # of times is insignificant compared to the total possessions and this parameter is tough to measure. if we had these numbers they could be added)..

as for barry and wallace, i just uploaded the 01-02 reg seas stats to the online database so you can compare them there. just limit the database to the 01-02 season, and sort by possession factor, and you'll see how two players can have the same possession factor but different stats that when added up and divided by minutes played equal similar touches-per-minute ratings (poss fact)...

also you can have two players with absolutely identical stats from two different seasons and they could easily have two different possession factors - because part of the rating is based on league averages. a simple example is shot blocking - two players can have the same # of blocks and minutes played in two different seasons but have their shot block rating vary by as much as half a percent or more based on what the rest of the league did that specific season. example - this past season jermaine o'neal blocked 166 shots in 2707 minutes and had a shot blocking rating of 3.6% (he blocked 3.6 of every 100 shots taken by the pacers opposition). in 1978-79 rich kelley of the jazz blocked 166 shots in 2705 minutes but had a shot blocking rating of only 3.2%....

What was the original goal of the stat? Is it better to say that it
is an estimate of touches on the offensive end?

the goal was to determine exactly how often each player handled the ball on offense so the computer could model the game, i.e. knowing how often each player handled the ball on offense and what he did with it (how often he would shoot, pass, get fouled, TO) once he did get the ball makes for an easy model for the computer to simply play a game...

are the formulas "secret"? not really. complicated? not at all - four parameters (statistical categories - FGA, TO, passes, times fouled) and two variables. but there are upwards of 30+ formulas per season (one for each team), every season, although each is quite similar, and some modifictions for players traded between teams of widely varying game pace...

the best way to explain this would be to download a copy of the simulation software i developed (www.bballsports.com) - again its free - and when you run a full season for any team it charts ALL ball possessions such that they can be added up easily. this is the best way to see "possession factors" or "touches per minute ratings" in action. plus the online stats databases lists possession factors for every player since 1977-78 for the NBA and even earlier for players in the ABA...

[Dan Rosenbaum]

Bob, thank you very much for finding these old posts. I am not sure that I had read these posts, but they were almost exactly what I suspected that you were doing. You are estimating touches based upon current traditional statistics based upon patterns derived from past charting. I think this is a great way to combine charting and traditional statistics.

I hate to hijack this thread away from my original topic, but do you worry that with the new defensive rules and dramatic increase in three pointers that patterns for touches that you developed more than a decade ago may not apply so well today?

Did you estimate X and Y separately by position in case the touch patterns differ by position?

I still am a little confused what a touch is conceptually? It surely is not how many times you touch the ball in a possession. Otherwise, I think you would have multipliers on FGAs and TOs as well. What in your mind are touches measuring? Should we think of it as some weighted average of FGA, TO, FTA, and AS?

[HoopStudies]

[HoopStudies]

[bchaikin]

sorry, my above equation wasn't quite accurate, let me try again. to calculate a player's possessions (touches) i use this:

player possessions =

shots + turnovers + passes thrown + # times fouled =

FGA + TO + AST/X + FTA/Y

and to calculate his possession factor (touches/min) i use:

poss fact = (FGA + TO + AST/X + FTA/Y)/MIN

I still am a little confused what a touch is conceptually?

any time a player has the ball on offense and subsequently shoots, passes (my definition of a pass, see below), gets fouled, or turns the ball over...

It surely is not how many times you touch the ball in a possession. Otherwise, I think you would have multipliers on FGAs and TOs as well. What in your mind are touches measuring? Should we think of it as some weighted average of FGA, TO, FTA, and AS?

to calculate passes way back when i first did this, the only passes i counted as "passes" were those that in my opinion had to have had an opportunity to be an assist, since assists were the only statistical parameter i had access to that correlated in some way with passes (i.e. assists are a subset of passes). thus if in my opinion while watching games if after receiving a pass a player had immediately shot and scored, i would count that as a "pass" for the player who threw it. passes thrown by players that in my opinion did not have any chance of being an assist i did not count as a "pass"....

so if on a particular possession a team had a half dozen passes in the backcourt without any defensive pressure whatsoever as they brought the ball up the floor to midcourt, since those passes in reality did not have any real opportunity to be an assist, i did not count those as "passes", i.e. they were superfluous. yet if for example a player was right underneath the basket with the ball, but passed it out away from the basket to a teammate at the top of the key who immediately shot the ball, that was counted as a "pass" because had the shot gone in the player throwing the pass would assuredly have been credited with an assist....

I know this is a critical part of Bob's simulator.

absolutely - if the computer doesn't how how often each player should handle the ball on offense, the stats won't come out right in re-creating what happened in real life. and the simulation does indeed re-create what happens in real life...

To me, it is just interesting. Very interesting. Bob's simulator and my individual win-loss records often end up similar through apparently very different methods.

The other thing I never sat down to think about is how his simulator partitions touches when players get blended together.

what's really neat about possession factor is just this - seeing how players change with new teammates. if you use the stats database look up for example adrian dantley. when dantley was traded from UTA to DET (8586/8687) his scoring dropped from 30 pts/g to less than 22 pts/g, playing about the same amount of minutes. but does anyone know why? it turns out that his touches/min simply decreased by about 25% (a large drop) as he went from a team with low touches/min players in two key positions (mark eaton and bob hansen) to a team with average touches/min at those two key positions (bill laimbeer and joe dumars). but - and this is key - what he did per touch, i.e. how often he shot, passed, got fouled, and turned the ball over - did not change (significantly) in going from one team to the other. now this in and of itself is not really a revelation, but at least it can be quantified with numbers. yes his stats per minute like FGA and FTA went down, but in reality he still did what he had always done - per touch - he simply had his touches reduced...

[Dan Rosenbaum]

[Dan Rosenbaum]

And Bob, now I see what touches are. They are the sum of field goal attempts, turnovers, free throws (multiplied by something like 0.44), and what I am calling potential assists. They are not really the same thing as DeanO's individual possessions, since you are potentially counting multiple touches in a single possession. You also are assuming that a turnover touch, a shooting touch, and a potential assist touch are equivalent, whereas that is not done in individual possession calculations.

One difficulty you must always face in your simulations is figuring out the relationship between touches per minute (or possession usage) and offensive efficiency. If a player like Adrian Dantley moves to a team where he touches the ball less, does his efficiency improve or does it stay about the same. DeanO in BoP suggest that most of the time there is an inverse relationship between touches (usage) and efficiency. But I would bet that relationship varies a lot from player to player and is very difficult to estimate from existing data.

[Kevin Pelton]

[HoopStudies]

[Dan Rosenbaum]

[Dan Rosenbaum]

[HoopStudies]