Adjusted Plus/Minus (+/-) (Basketball Prospectus)

[jgisland]

I know at least a few people on here have been reading the new Basketball Prospectus that came out the other day. One of the articles really interested me, "The Statistical Holy Grail:Combining Usage and Efficiency" by Nathan Walker. I am familiar with Nathan's work on his blog Basketball Distribution, he has some interesting posts on there from time to time. Adjusted +/- is highly debated in basketball, from strong advocates like Wayne Winston (author of Mathletics and former consultant to the Dallas Mavs) to Ken Pomeroy once an advocate now not so much. I have always thought that adjusted +/- was interesting concept but largely a misleading stat and often didn't pass the eye test. Somehow it would tell me that last years Buffs played Burks too much and Ben Mills didn't play enough (+/- didn't actually say that but such extremes do exist). I have always been a big fan of what David Barri and Martin Schmidt do with Win Shares on their site and in their books. (i think they overrate defense and rebounding a little but, but all of their stats always say Melo is overrated which makes me smile).

But Nathan Walker's article goes a little deeper with +/- than I have seen, he actually accounts for offensive efficiency with % of possessions used adjusted for strength of schedule. I plan on running his formula through last years Buffs stats and see what comes out, I just hope it passes the eye test. I will post my findings this weekend.

 

[Goose]

Very cool. I'm curious to see what your numbers show.

I LOVE win shares, but agree 100% on the rebounding and defense being overrated there. That said, I think it's probably the closest thing we have to a definitive number to rely on right now.

 

[Darth Snow]

please do this!

 

[Buffnik]

This would be very interesting to me.

One problem that's inherent to basketball stats like this is that they aren't able to account well for whether the player is on a good team. They also tend to do a straight line progression on what a player would produce if he played 30 minutes per game instead of 15. The real world doesn't work that way.

When I look at the NBA, some of the worst decisions that GMs make come from ignoring those two factors. A leading scorer on a ****** team does not come close to maintaining his numbers when he moves to a good team. A role player on a good team who becomes a starter on a ****** team isn't going to come close to maintaining his per-minute production.

 

[jgisland]

This would be very interesting to me.

One problem that's inherent to basketball stats like this is that they aren't able to account well for whether the player is on a good team. They also tend to do a straight line progression on what a player would produce if he played 30 minutes per game instead of 15. The real world doesn't work that way.

When I look at the NBA, some of the worst decisions that GMs make come from ignoring those two factors. A leading scorer on a ****** team does not come close to maintaining his numbers when he moves to a good team. A role player on a good team who becomes a starter on a ****** team isn't going to come close to maintaining his per-minute production.

Can we call this the "renaldo balkman problem?" it always kills me when +/- or even win shares to a degree says he should be playing more or would be an elite player if he played more. Just because he gets a couple hustle rebounds and maybe a steal or two during garbage time that doesn't mean sh*t. There is a reason he plays 3 mins a game and is in during garbage time.

 

[Goose]

Can we call this the "renaldo balkman problem?" it always kills me when +/- or even win shares to a degree says he should be playing more or would be an elite player if he played more. Just because he gets a couple hustle rebounds and maybe a steal or two during garbage time that doesn't mean sh*t. There is a reason he plays 3 mins a game and is in during garbage time.

And a large chunk of it is because he's higher than hell on the bench.

 

[Buffnik]

Yep.

Baseball is a bit more accurate with the advanced stats. You still have things with platoon players where they only face left-handed pitching or a middle reliever who comes in for specific types of matchups. But the VORP (value over replacement player) stat is actually very good. I don't know that basketball will ever be able to do as well on measuring that. It's harder to quantify matchups and things like tempo, system and teammates make a huge impact that is really hard to measure.

 

[bbstats]

Hola peoples.
My essay "The Holy Grail" refers to estimating adjusted plus-minus numbers (this is the theory behind statistical plus-minus) by using Offensive Ratings + Usage.
The basic idea is that Offensive Rating is a very accurate statistic, and this helps us convert offensive rating+usage into relative values for players.

PS: Since the values you get will be per 100 possessions, be sure to multiply by Minutes% (Minutes Played / Game Minutes) if you would like to also see overall offensive value.

 

[Darth Snow]

Hola peoples.
My essay "The Holy Grail" refers to estimating adjusted plus-minus numbers (this is the theory behind statistical plus-minus) by using Offensive Ratings + Usage.
The basic idea is that Offensive Rating is a very accurate statistic, and this helps us convert offensive rating+usage into relative values for players.

PS: Since the values you get will be per 100 possessions, be sure to multiply by Minutes% (Minutes Played / Game Minutes) if you would like to also see overall offensive value.

Basketball season is gonna be AWESOME this year.

 

[RumblinBuff]

Did I miss something, or did the real Nathan Walker just drop some knowledge on us?

 

[Goose]

Did I miss something, or did the real Nathan Walker just drop some knowledge on us?

I think the knowledge was dropped. Hopefully he sticks around to continue dropping it.

 

[btbuff]

Did I miss something, or did the real Nathan Walker just drop some knowledge on us?

Something just happened. :wow:

 

[jgisland]

I think the knowledge was dropped. Hopefully he sticks around to continue dropping it.

After i post the buffs numbers i am sure he will be back to correct my work.

 

[Nor Cal Buff]

Yep.

Baseball is a bit more accurate with the advanced stats. You still have things with platoon players where they only face left-handed pitching or a middle reliever who comes in for specific types of matchups. But the VORP (value over replacement player) stat is actually very good. I don't know that basketball will ever be able to do as well on measuring that. It's harder to quantify matchups and things like tempo, system and teammates make a huge impact that is really hard to measure.

You are right that baseball is easier to analyze for players and that is because the sport is a series of individual battles and performances instead of a team performance. It's also easier because each pitch is a discrete event with a definitive outcome whereas basketball is free flowing. However, just as in baseball and any other sport on the planet, the best and brightest at analyzing individuals and teams are in the sports betting field (betting side NOT bookmaking/initial line setting side). You can be sure the top pro sports bettors have far better metrics for valuing a player than anything in APBR because their valuations have very real outcomes for them: winning or losing money. And as others discover what they have discovered, they'll be on to superior metrics because that is what is required in such a competitive field. Unfortunately for the fans of the game, it will be years before those metrics are ever figured out by others because there is a very real disincentive for them to share their research.

 

[jgisland]

Results are in and actually seem to be calculated correctly (for those of you that have Basketball Prospectus, the numbers are slightly different for Burks because I calculated 1 more decimal place to the right than Nathan Walker did, hence the discrepancy). All of my numbers came from kenpom.com and statsheet.com

Player	YR	Ortg	% Poss	Off PM	Adj Off P/M per 100 poss	Total Value per 40 min
Burks	So	115.7	32.2	8.319044	8.587844	6.674461167
Higgins	Sr	110.3	24.8	3.716704	3.985504	3.172824683
Relphorde	Sr	103	22	1.012	1.2808	0.891136417
Knutson	Sr	131.2	16.2	3.984584	4.253384	2.823581952
Roberson	Fr	118.3	16.3	1.964914	2.233714	1.232544468
Default	Jr	115.9	15	1.0205	1.2893	0.709744951
Sharpe	So	97.3	12.2	-2.2202	-1.951404	-0.633093936
Tomlinson	Jr	108.3	10.1	-1.71212	-1.443322	-0.645028594

*Nathan Walker caveats about his adjusted +/- in Basketball Prospectus*

1) This number is an estimate of how a team’s offense
improves per 100 possessions. A +5 player
who plays more minutes than another +5 player
will contribute more in a given game.
2) These numbers tell us absolutely nothing about
half of a player’s game (remember “defense”?).
OK, that’s not really true. In fact there is a very
significant negative correlation between a player’s
offensive output and defensive output. Suffice to
say: the more involved and successful a player is
on offense, the less they are usually involved and
successful on defense.
3) I have been very careful to not use a large team
adjustment. If we simply used a team’s SOS to adjust
with, it looks more intuitive perhaps: far less
mid-majors show up, Tyler Zeller makes the list,
and so on. But in doing so, SOS ends up explaining
60 percent of the variation in the data…which
would really just tell us “which players played
against difficult teams.”


Let me know if you have any questions on how this was calculated, I really do recommend buying Basketball Prospectus (the pdf is only $9.95) and reading Nathan's whole article and explanation.

 

[jgisland]

However, just as in baseball and any other sport on the planet, the best and brightest at analyzing individuals and teams are in the sports betting field (betting side NOT bookmaking/initial line setting side). You can be sure the top pro sports bettors have far better metrics for valuing a player than anything in APBR because their valuations have very real outcomes for them: winning or losing money. And as others discover what they have discovered, they'll be on to superior metrics because that is what is required in such a competitive field. Unfortunately for the fans of the game, it will be years before those metrics are ever figured out by others because there is a very real disincentive for them to share their research.

This can't be said enough, people who say that the sports books want to have balanced books and they set the line to get balanced action and simply rake in the vig are living in the 80's. There are too many syndicates using advanced stats to analyze teams and games that simply isn't possible. Sports books HAVE to try put out lines they believe to be a correct prediction of the game. If they put out a line to balance the books the syndicates will swoop in and kill their bad number. There is a good paper called "Understanding Price Movements in Point Spread Betting Markets: Evidence from NCAA Basketball" that does a study and proves that line movements aren't to balance books anymore, they typically happen with the spread is large and they are trying to hone in a good #, that line movements when the spread is narrow is very rare. Hence you can see line bet % where there will be a number at -6 for example with 80% of $ on that number and the line will move to -5 because they are getting hit by syndicates on the other side.

Advanced stats and gambling have a complicated and very connected relationship, this will only continue over time as the processes get better.