What do you think of this stat idea?

[Dr Positivity]

I came up with this stat idea a few months ago. I'm not a strong stats guy technically, so I've been lazy to follow up upon it.

My concept is this: I wanted to compare the efficiency of a possession to team defense. This is because the team's defense, or the other team's offense, is the break even point for the value of a possession. What I mean is that if a player uses a possession more efficiently than the opponent as a team, that possession by definition contributes positively to the efficiency differential. Likewise if they use a possession less efficiently than the opponent, it contributes negatively to it.

Here is what I do. I'll use Kenneth Faried as an example. I start with the Oliver individual ORTG on bball-reference, which for Faried is 116. I then subtract on-court DRTG from that. The Nuggets D with Faried on is 106, for a difference of +10. I rewrite this as 1.10. Next, I calculate how many possessions Faried uses with FGA + .44*FTA + TOV. Faried's possessions is 11.45. I multiply the 11.45 number times the 1.10 one, which equals 12.6. I then subtract 11.45 (implying the opponent comparison is 11.45 * 1, 1 as an average opponent), the difference equals +1.15 "points above the other team". Next, I multiply that by 2.7, a rough Pythagorean estimate for points=wins, which gives me a number of +3.1 Ws above average. I can then take this one step farther by adding 3.4 Ws to this, a rough estimate of average wins for a player, therefore the new number of +6.5 isn't wins above average, it's wins period. Finally, I prorate for games played. Faried plays 80 of 82 which is 97.5% of games, so he only drops to +6.3 Ws prorated.

I did the same calculation for the rest of the Nuggets

Danillo Gallinari - 7.1 Ws
Kosta Koufos - 7.1 Ws
Kenneth Faried - 6.3 Ws
Ty Lawson - 5.6 Ws
Andre Miller - 5.3 Ws
Javale McGee - 4.5 Ws
Andre Iguodala - 3.7 Ws
Wilson Chandler - 3.0 Ws
Corey Brewer - 2.8 Ws
Evan Fournier - 2.1 Ws
Timofey Mozgov - 1.6 Ws
Jordan Hamilton - 1.3 Ws
Anthony Randolph - 1.0 Ws
Julyan Stone - 0.3 Ws
Quincy Miller - 0.2 Ws

That adds up to 51.9 Ws. Denver's pyth was a 55 W team so it's not a perfect match however it's in the ballpark. As for the numbers themselves, it likely doesn't capture Iguodala's value very well, expectantly as a stat measuring the value of a player's offensive possessions to the win, while Iggy's value is defense. Iggy does help himself by lowering his on-court DRTG, however considering he had a poor offensive year, his ORTG (105) is still barely above his on-court D (104). Iggy last season punched out as closer to a star player, with an ORTG of 108 and on-court of 98.3 which with his possessions punched out at 7 Ws. Kosta's number is very high, however as the most efficient player on his team (122 ORTG) with an on-court 103.7 DRTG, that creates a powerful difference.

What do you think? I think this does a fair job of giving some credit to offensive players who are doing it on teams where high defensive energy is expended (eg. Paul George still ends up looking like a strong player even with a 104 ORTG because his on-court DRTG is 99.3, whereas on the other end the value of Anthony Davis' 113 ORTG is muted by his on-court DRTG being as high as 111), while also giving credit for players who use a lot of possessions. Players who are strong defenders help their score by lowering the team DRTG, though it still doesn't distribute that credit perfectly. I've also found for the most part the total wins ends up within a few of the real pyth. number. Most of the time it's lower, I'm trying to figure out if there's a way to rectify that. Are my 2.7 and 3.4 numbers for pyth. wins and average wins, accurate?

Overall, not bad?

[Crow]

I would first look at how many of the total team wins are fairly attributable to the difference between the team's overall offensive and defensive efficency and league average and then give the defense its fair share of the total wins. In your model the offense appears to be getting all the credit. It should only get its share and then an rough estimated share ould be distributed out to the players by your method or another. (Long ago I did this team win division at the offensive and defensive efficiency levels and at the factor levels. I could not quickly find a link for that but it may still be here somewhere in a recovered thread.)

You are also mixing Oliver's offensive rating with raw team defensive efficiency with a particular player on instead of using Oliver's defensive rating, right? That mix of metrics will account for some of the win discrepancy. I think using raw team defensive efficiency with a particular player on is a very crude way to estimate a player's defensive impact. Not necessarily worse than the crude Oliver defensive rating but neither is good in my opinion.

Another option would be to turn your output into % share of just the offensive credit using your method. E/g., Galinari gets about 12% of the team's offensive win credit. That way you can leave the defensive side out of it.

[Dr Positivity]

I would first look at how many of the total team wins are fairly attributable to the difference between the team's overall offensive and defensive efficency and league average and then give the defense its fair share of the total wins. In your model the offense appears to be getting all the credit. It should only get its share and then an rough estimated share ould be distributed out to the players by your method or another. (Long ago I did this team win division at the offensive and defensive efficiency levels and at the factor levels. I could not quickly find a link for that but it may still be here somewhere in a recovered thread.)

You are also mixing Oliver's offensive rating with raw team defensive efficiency with a particular player on instead of using Oliver's defensive rating, right? That mix of metrics will account for some of the win discrepancy. I think using raw team defensive efficiency with a particular player on is a very crude way to estimate a player's defensive impact. Not necessarily worse than the crude Oliver defensive rating but neither is good in my opinion.

Another option would be to turn your output into % share of just the offensive credit using your method. E/g., Galinari gets about 12% of the team's offensive win credit. That way you can leave the defensive side out of it.

Well put it this way. With the stat I am trying to capture value on a purely statistical level. Clearly when it comes to any on paper stat, there will be context to consider after the output.

For example take the Pacers, the numbers for their big 4 are Hill - 10.4, West - 8.4, George - 5.9, Hibbert - 4.3. Now it's easy to see the reason Hill puts up a superstar number owes itself to the defensive play of George and Hibbert more than this stat can show. The gap between Hill's ORTG and on-court defense is just about the exact same as Chris Paul's, but clearly Paul deserves more individual credit for creating that gap by being responsible for his sky high ORTG, more than Hill for his rock bottom DRTG

At the same time however, it's reasonable to accept that on paper, Hill's numbers may be where the value is on the Pacers. Even if what led to those Hill stats, was a team effort beautifully constructed by the franchise. The combination of the team effort leading to the defense the Pacers play when Hill's on, combined with the much higher efficiency he uses his 14 or so possessions, just buries opponents in the efficiency differential

[Crow]

In your model the offense isn't getting all the credit. I was interpeting it wrong. Strong offense and defense (using your methods) both contribute to a bigger net difference. Most of what I said thus was not applicable. Sorry for my error.

[colts18]

Sounds a lot like Win Shares