Defensive Usage

[MisterHibachi]

This is just an idea I've been thinking about recently.

We have offensive usage%, which tells us how many possessions a player uses when he's on the floor, through FGA, TO, or FT. How about a defensive usage%? How many defensive possessions does a player end when he's on the floor?

First off, would this stat even be useful? What would it really tell us?

Second, how do we calculate it?

Per basketball-ref, the formula for offensive usage is: 100 * ((FGA + 0.44 * FTA + TOV) * (Tm MP / 5)) / (MP * (Tm FGA + 0.44 * Tm FTA + Tm TOV)). So, FGA, FTA, and TOV are ways to end an offensive possession.

How would you end a defensive possession? Defensive rebound, steal, block, or foul are pretty much it, I think.

I'm not the best at statistics, so I would appreciate some help here in generating a formula that works.I have some questions. Would it be better to include DREB%, ST%, BLK% and such, or just raw numbers? I don't know if this is the right method for it, but I'll give it a try to generate a formula based off the offensive usage formula.

100 * ((DREB + ST + BLK + PF) * (Tm MP/5) / (MP * (Tm DREB + ST + BLK + PF))

I'll use Dwight Howard as an example and use his numbers.

100 * ((603 + 57 + 120 + 228) * (16925 /5) / (2284 * (2365 + 523 + 404 + 1418))

=31.7177373475966848 = 31.7%

So, according to my formula (which isn't necessarily the right formula, just a preliminary one), Dwight Howard ends 31.7% of his team's defensive possessions through either a rebound, steal, block, or foul.

Another example: LeBron James

100 * ((385 + 108 + 22 + 111) * (16710/5) / (2489 * (2010 + 627 + 314 + 1373))

= 19.4388333644910873 = 19.4%

DeAndre Jordan:

100 * ((691 + 73 + 170 + 235) * (17115/5) / (2517 * (2308 + 611 + 337 + 1525))

= 33.2521285711044837 = 33.3%

So, thoughts? Comments? Is this a useful stat? Did I get the formula right? What changes would you make? What do you take away from the 31.7% defensive usage of Howard, 19.4% of LeBron, and 33.3% of Jordan?

There might even be a stat out there already for this. If there is, let me know please.

[ceiling raiser]

Are you looking for something similar to the Stop% Dean Oliver uses for individual DRtgs?

Defensive Rating

Just as Oliver's Offensive Rating represents points produced by the player per 100 possessions consumed, his Defensive Rating estimates how many points the player allowed per 100 possessions he individually faced while on the court.

The core of the Defensive Rating calculation is the concept of the individual Defensive Stop. Stops take into account the instances of a player ending an opposing possession that are tracked in the boxscore (blocks, steals, and defensive rebounds), in addition to an estimate for the number of forced turnovers and forced misses by the player which aren't captured by steals and blocks.

The formula for Stops is:

Stops = Stops1 + Stops2
where:

Stops1 = STL + BLK * FMwt * (1 - 1.07 * DOR%) + DRB * (1 - FMwt)
FMwt = (DFG% * (1 - DOR%)) / (DFG% * (1 - DOR%) + (1 - DFG%) * DOR%)
DOR% = Opponent_ORB / (Opponent_ORB + Team_DRB)
DFG% = Opponent_FGM / Opponent_FGA
Stops2 = (((Opponent_FGA - Opponent_FGM - Team_BLK) / Team_MP) * FMwt * (1 - 1.07 * DOR%) + ((Opponent_TOV - Team_STL) / Team_MP)) * MP + (PF / Team_PF) * 0.4 * Opponent_FTA * (1 - (Opponent_FTM / Opponent_FTA))^2
Also necessary is the calculation of Stop%, which is the rate at which a player forces a defensive stop as a percentage of individual possessions faced (essentially the inverse of Floor%, but for defenders):

Stop% = (Stops * Opponent_MP) / (Team_Possessions * MP)
With those numbers in hand, individual Defensive Rating can be computed:

DRtg = Team_Defensive_Rating + 0.2 * (100 * D_Pts_per_ScPoss * (1 - Stop%) - Team_Defensive_Rating)
where:

Team_Defensive_Rating = 100 * (Opponent_PTS / Team_Possessions)
D_Pts_per_ScPoss = Opponent_PTS / (Opponent_FGM + (1 - (1 - (Opponent_FTM / Opponent_FTA))^2) * Opponent_FTA*0.4)

source: http://www.basketball-reference.com/about/ratings.html

So you could just plug D_Pts_per_ScPoss into the DRtg formula, and solve for Stop%.

[magicmerl]

Part of the problem is that something like gathering the rebound acts as a proxy for the defense played which caused the miss. But it's not the defense at all (just look at Kevin Love).

I think that defense is better captured by the team-wide stats like plus/minus and on/off numbers.

[bondom34]

I like the thought, but a tweak at least I could see would be to change the rebounding portion to account for available rebounds. I think the NBA player tracking stats offer some info on contested/uncontested rebounds. Positioning could account for some rebounding numbers to act as a filter for guys who just aren't in the area for a defensive rebound (guards would inherently have a lower % due to position alone for example). I can't think of another way to adjust it off the top of my head, maybe the stats board could help though.

[ceiling raiser]

Just on my phone so someone might want to check this, but here's the formula for Stop%:

Code: Select all

Stop% = 1 - (5 * (DRtg - Team_Defensive_Rating) + Team_Defensive_Rating) / (100 * Opponent_PTS / (Opponent_FGM + (1 - (1 - (Opponent_FTM / Opponent_FTA))^2) * Opponent_FTA*0.4))

I put the three players mentioned in the OP into this sheet:

https://docs.google.com/spreadsheets/d/ ... xE7PnJ2ekU

Here's a copy if you guys want to play around with it and add some names:

https://docs.google.com/spreadsheets/d/ ... 7UzzP5KT3k

All the numbers can be accessed from team pages, i.e.:

http://www.basketball-reference.com/teams/HOU/2014.html

[bondom34]

Another one to factor in you can get from NBAWowy, they have a percentage of blocks rebounded by your team. Since you're looking at how many possessions end w/ the defender, a block should only count if it is retained by the defense, so technically you would multiply blocks by fraction of blocks rebounded by the team.

[RSCD3_]

I like the thought, but a tweak at least I could see would be to change the rebounding portion to account for available rebounds. I think the NBA player tracking stats offer some info on contested/uncontested rebounds. Positioning could account for some rebounding numbers to act as a filter for guys who just aren't in the area for a defensive rebound (guards would inherently have a lower % due to position alone for example). I can't think of another way to adjust it off the top of my head, maybe the stats board could help though.

Yeah definitely have to have contested rebounds in there

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[MisterHibachi]

Gonna take me some time to get my head around that formula, fpliii.

I wanted to add those numbers, about which blocks are recovered by your team and stuff. Wasn't sure where to find the numbers tho. I also wanted to add a penalty to the formula, to make it a better estimation of good defense but not sure how to do that. Maybe make fouls a negative? But some fouls are good fouls. Missed steals?

I think this is all captured by that formula in fpliii's first post, actually.

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[ceiling raiser]

Gonna take me some time to get my head around that formula, fpliii.

I wanted to add those numbers, about which blocks are recovered by your team and stuff. Wasn't sure where to find the numbers tho. I also wanted to add a penalty to the formula, to make it a better estimation of good defense but not sure how to do that. Maybe make fouls a negative? But some fouls are good fouls. Missed steals?

I think this is all captured by that formula in fpliii's first post, actually.

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Oops sorry if I was unclear with the second post. The Stop% I calculated in the second post is the same thing that's derived in the first post. Thing is, if we use the method above, the formula is complicated as hell:

Code: Select all

Stop% = (STL + BLK * (Opponent_FGM / Opponent_FGA * (1 - Opponent_ORB / (Opponent_ORB + Team_DRB))) / (Opponent_FGM / Opponent_FGA * (1 - Opponent_ORB / (Opponent_ORB + Team_DRB)) + (1 - Opponent_FGM / Opponent_FGA) * Opponent_ORB / (Opponent_ORB + Team_DRB)) * (1 - 1.07 * Opponent_ORB / (Opponent_ORB + Team_DRB)) + DRB * (1 - (Opponent_FGM / Opponent_FGA * (1 - Opponent_ORB / (Opponent_ORB + Team_DRB))) / (Opponent_FGM / Opponent_FGA * (1 - Opponent_ORB / (Opponent_ORB + Team_DRB)) + (1 - Opponent_FGM / Opponent_FGA) * Opponent_ORB / (Opponent_ORB + Team_DRB))) + (((Opponent_FGA - Opponent_FGM - Team_BLK) / Team_MP) * (Opponent_FGM / Opponent_FGA * (1 - Opponent_ORB / (Opponent_ORB + Team_DRB))) / (Opponent_FGM / Opponent_FGA * (1 - Opponent_ORB / (Opponent_ORB + Team_DRB)) + (1 - Opponent_FGM / Opponent_FGA) * Opponent_ORB / (Opponent_ORB + Team_DRB)) * (1 - 1.07 * Opponent_ORB / (Opponent_ORB + Team_DRB)) + ((Opponent_TOV - Team_STL) / Team_MP)) * MP + (PF / Team_PF) * 0.4 * Opponent_FTA * (1 - (Opponent_FTM / Opponent_FTA))^2 * Opponent_MP) / (0.5 * ((Tm FGA + 0.4 * Tm FTA - 1.07 * (Tm ORB / (Tm ORB + Opp DRB)) * (Tm FGA - Tm FG) + Tm TOV) + (Opp FGA + 0.4 * Opp FTA - 1.07 * (Opp ORB / (Opp ORB + Tm DRB)) * (Opp FGA - Opp FG) + Opp TOV)) * MP)

once everything is combined into a single formula. Thing is, this Stop% stat is used in calculating individual DRtg, but we already know everybody's DRtg (going back to 73-74). So I just took the end stat, and solved for the stat above, which is way to complicated to put into a spreadsheet (for me at least maybe someone else has the patience to deal with the parentheses and clicking the correct cells).

But yeah, they should be the same. I'm not sure if it's exactly what you're looking for though, according to the link above, Stop% is:

The rate at which a player forces a defensive stop as a percentage of individual possessions faced (essentially the inverse of Floor%, but for defenders).

Floor% is:

As a side note, we can also calculate what Oliver calls Floor Percentage, which answers the question, "What percentage of the time that a player wants to score does he actually score?":

Floor% = ScPoss / TotPoss

To be honest, I like Floor% too (though it's also pretty complicated lol). Maybe it's worth it for someone to create a spreadsheet with both, using the long formulas. I can do that at some point perhaps, but I don't know if I have time now.

[MisterHibachi]

Yeah, I think Stop% is pretty much what I was trying to get at actually. Thanks, fpliii

[Narf]

Part of the problem is that something like gathering the rebound acts as a proxy for the defense played which caused the miss. But it's not the defense at all (just look at Kevin Love).

I think that defense is better captured by the team-wide stats like plus/minus and on/off numbers.

As Minnesota would rank a top 10 defense when Kevin Love is on the floor, I fail to see the example you're making.

People score less vs Minnesota when Love is on the floor.

[Narf]

Part of the problem is that something like gathering the rebound acts as a proxy for the defense played which caused the miss. But it's not the defense at all (just look at Kevin Love).

I think that defense is better captured by the team-wide stats like plus/minus and on/off numbers.

As Minnesota would rank a top 10 defense when Kevin Love is on the floor, I fail to see the example you're making.

People score less vs Minnesota when Love is on the floor. And defensive rebounding is actually pretty important in defensive efficiency.