Statistical Plus/Minus Using Logical Rates
by YaoPau on Mar 23, 2009 6:16 PM CDT
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I mentioned on the Hollinger's Opinion of Rose's ROY Chances thread that I'd been working on rate-based Statistical Offensive APM that rated Rose at a +1.69 this season. Oddly enough, fundamentallysound told me he'd been working on his own Statistical APM system and we agreed to post our methods this past weekend. I got lazy about it.
I like stats that I can fully understand and calculate myself, because that makes them useful to me. As for the first part, TS% makes sense to me, plus/minus makes sense to me, adjusted plus/minus makes sense to me. I can see Joakim Noah's .562 TS% and know he scores 1.124 points every time he goes to shoot, and I know that's about .06 higher than league average. I can see Joakim Noah's -0.60 offensive APM and +2.71 defensive APM last year and know that (noise aside) he's about half a point below average offensively and nearly three points above average defensively per 100 possessions.
Some stats, though, I don't understand. PER is one of them. Noah's 15.5 PER I know is above average, but does that mean he's 3.3% better than a 15 PER player? How does that translate to points? How in the hell is PER even calculated? And while I can use TS% for deeper analysis (how many points is Joakim adding by taking 5.4 offensive attempts per game at an efficient rate?) I can't use PER for anything else but... PER.
So in making a Statistical APM, I wanted to keep things as simple and logical as possible. I liked the output of fundamentallysound's system - the defensive numbers especially seemed right on point - but if I don't understand why his system rates Drew Gooden at a -1.06 this year, all I can do with his system is see how much it matches my own perceptions.
The method I used
Instead of finding Offensive and Defensive APM, I'm focusing on just the offensive side. Dan Rosenbaum might've found a relationship between free throw attempts per 40 and defensive success, and he might've found a relationship between steals and offensive success, but neither one makes sense to me as a logical cause. Especially defensively, where I can't be confident a Statistical APM is accurate when it's only using stats like steals, blocks, free throw rate, and personal fouls.
The categories I used are logically correlated: TS%, OREB%, AST%, TOV%, USG%, and you can find all of those statistics in the "Advanced" section of any basketball-reference.com player or team page. I used rates because they're adjusted by opportunites. OREB% is the % of available offensive rebounds that a player grabbed. AST% is the percentage of teammate field goals a player assisted. USG% is the percentage of team possessions that ended with a player's action (by shooting or turning the ball over). So not only are these stats adjusted for opportunity differences (per 40 stats used by Rosenbaum are not), but also
they tell me how much a player is impacting his team, rather than how he plays in a vacuum.
To determine the formula, I used '07-'08 Offensive APM as my dependent variable and the five rates above as my independent variables and ran a linear regression on excel. The formula is...
Expected OPM = -18.2057+30.2201*TS%+0.128564*OREB%+0.183697*AST%-0.31078*TOV%+0.136568*USG%
You can see all the results for the 2007-2008 season, along with how they compared to Offensive APM here: http://spreadsheets.google.com/ccc?key=peZQH7tnbE07s0HlWipWiUg
As for the Bulls this season...
Ben Gordon: +1.90
John Salmons: +1.89 (+2.43 with the Bulls)
Derrick Rose: +1.69
Brad Miller: +0.99 (+2.07 with the Bulls)
Kirk Hinrich: +0.46
Larry Hughes: -0.05 with the Bulls
Tim Thomas: -0.63 (-1.20 with the Bulls)
Luol Deng: -0.65
Drew Gooden: -0.85
Joakim Noah: -1.04
Andres Nocioni: -1.15 with the Bulls
Tyrus Thomas: -2.43
Aaron Gray: -2.57
Thabo Sefolosha: -3.16
A couple notes from quick glance...
1) Noah, Tyrus, and Gooden all have AST% under 8%. It's bad enough that we didn't have a post scorer, it's even worse that we didn't have a post passer either. Luol (9.1%) and Noc (7.4%) were equally awful.
2) The turnover rates for Noah (15.3%), Tyrus (14.4%), and Hinrich (17.4%) are all high, especially considering they aren't big scorers.
3) John Salmons has been shooting above his head with the Bulls (.644 TS%), but his passing has been much worse (dropped from 15.1% overall this year to 6.9% (!!) with the Bulls).
4) I'm encouraged to see that my results matched up closely to fundamentallysound's even though we used wildly different categories and even different APM years to find our coefficients. My system rated Rose and Gooden a bit higher and Hinrich a bit lower, but almost everybody else was within half a point of one another. So you can trust these numbers, people!!!! :)
I've made my Excel spreadsheet available for download here, along with some additional notes. I'd be interested to hear your thoughts.
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As far as your 1st point goes.
It’s much more that we have don’t offensive system that allows passing by anybody, but the guards. Gooden and Nocioni have always sucked. Deng and Tyrus had huge drop offs this year, and Noah is down from last season as well. Since Brad Miller came and a little bit before that even, the front court players were finally starting to get a chance to create. Salmon’s decline in assists reflects this as well. The Bulls have one of the best set of passing bigs in the league now in Miller, Noah, and Tyrus.
I think that's the best argument I've seen for changing coaches
You’re right about Deng and Tyrus, I had no idea the dropoff was that severe.
The consensus seems to be that Deng had a great season two years ago and then fell off hard last year, but his EOPMs (+1.52 in 2007, +1.00 in 2008) are pretty close. And even though most think Tyrus is having a mini-breakout season this year, his EOPM was actually better last season (-1.73 compared to -2.43).
Well done, YaoPau. The other useful aspect of this metric is that you don't have to calculate
pace adjusted per 40 minute numbers. The rate statistics are already calculated for you. So that makes it much easier to calculate.
I agree with Scotter’s conclusions above that a lot of the AST% numbers have dropped for the Bulls players because they essentially run a playground “my turn” offense that is dominated by the guards going to the rim and the bigs scrapping for whatever’s left over.
Vinny discovers frontcourt by accident. Someone re-smash Gooden’s groin!
- your friendly BullsBlogger
by fundamentallysound on Mar 23, 2009 9:35 PM CDT reply actions
that should read "not going to the rim and taking jumpshots"... don't know what I was thinking.
Vinny discovers frontcourt by accident. Someone re-smash Gooden’s groin!
- your friendly BullsBlogger
by fundamentallysound on Mar 23, 2009 9:36 PM CDT up reply actions
The lack of need to do pace adjusted per 40 stats is very nice
Following up on this. I understand YaoPau’s reasoning for just doing offense, but using all the rate stats against the overall APM from that study would be interesting to still get an overall picture. If you did include all the rate stats would you just regress them against the defensive APM to get DSPM. I think there’s some value in DSPM, but I’m not sure if steals, blocks, and rebounds alone provides enough of a basis for DSPM. Personally, I can buy the logic of a player’s offensive profile shedding light on their defense.
Fundamentallysound, how much did the team adjusts change your results? Would you still do a team adjust with YaoPau’s numbers?
the team adjusts didn't change the rankings of players within the team and were relatively small
for the Bulls each year. For a few players they took them from being mildly negative to mildly positive and vice versa depending on the year (the Bulls all looked better on defense in 06-07 after the team adjustment which makes sense because the team was so good on offense.)
As far as using the team adjustment for YaoPau’s numbers, you could certainly do it as the methodology for it is rather crude. You just figure out the minutes weighted sum of the team’s numbers and divide by 5, then you figure out the difference between the actual ORtg or DRtg of the team versus League Average ORtg or DRtg and then divide by 5 and add that number to each players’ numbers. It’s obviously not a perfect way of doing it, but it does help make the numbers sum to the actual efficiency differentials while leaving the rankings of players within the team in tact. I see no reason why you couldn’t apply the same method to YaoPau’s numbers. I don’t know if it’s necessary to do so, though.
DSPM using rate statistics is something I would be interested in seeing. I know YP’s qualms about it, but I do think that some things really do serve as proxies for other things and there is some value in looking at those things, but as a matter of logic I understand YP’s reluctance do use offensive numbers to predict defensive contributions.
Vinny discovers frontcourt by accident. Someone re-smash Gooden’s groin!
- your friendly BullsBlogger
by fundamentallysound on Mar 23, 2009 10:12 PM CDT up reply actions
so good on defense*
Vinny discovers frontcourt by accident. Someone re-smash Gooden’s groin!
- your friendly BullsBlogger
by fundamentallysound on Mar 23, 2009 10:13 PM CDT up reply actions
What I like about this...
You can see exactly where a player’s numbers affect his OAPM (or are you calling it OSPM?). And w/ the rate stats, you can infer, as Scotter has, how much the system has affected the players. Obviously, that’s debatable on an individual basis, but it’s at least something that can be discussed. I think here, when you see a systemic drop-off from all the front-court players, it’s… interesting.
Viva la nuance! Reading comprehension rules!!!
Just an FYI, which I'm sure you know.
For your formula, you use the decimal form of TS% (say, 0.511) but then the percentage form of everything (5.0, 22.2, etc.) but refer to all of them as “percentages”. I understand this is how B-R.com has it set up, and this is just semantics, but I wanted to play around with it and couldn’t get the same number for Deng until I realized the decimal goes in two different spots. Obviously, this is taken care of by how the coefficients are set up differently, and maybe this is standard, but I thought I’d point it out if not.
Viva la nuance! Reading comprehension rules!!!
This is a bit random
but where are the sites where you get stats like points in the paint and all that
the main one is:
Vinny discovers frontcourt by accident. Someone re-smash Gooden’s groin!
- your friendly BullsBlogger
by fundamentallysound on Mar 25, 2009 2:20 PM CDT up reply actions
or
Basketball-reference.com
(the “advanced” part of player-pages)
or
Viva la nuance! Reading comprehension rules!!!
I like nba.com Hot Spots
I rarely see anybody linking to it here, but I think it’s a great site and I can learn a lot from looking at each player’s page.
I wish you could copy/paste the hot spots like a regular photo
Confusion breeds success. If they don't know each other, opponents can't have strategy. GENIUS.
by Ozzie Montana on Mar 31, 2009 1:55 PM CDT up reply actions
It's complicated, but can be done
Push print screen on your keyboard
Paste into paint
Use the select tool to get the section you want (print screen is going to copy everything you can see), and copy it
Go to File→New in paint, and paste the section you copied
Save as a jpeg.
yeah, that's just a pain in the ass though
Stats with contextual observations, good. Stats with no context, bad. Anecdotal observations unsupported by data, the worst.
by fundamentallysound on Mar 31, 2009 6:09 PM CDT up reply actions
Blame it on Adobe
Not me, I don’t make flash. Or blame it on the NBA for not using javascript to generate a jpeg to begin with, instead of using flash.
or if you have a mac
use grab, it’s even easier than those steps. ;)
"They should. They better. I'm Vinny Del Negro!"
Macs rule!
PC’s drool!
:P
Joakim Noah: Better than you.
PCs seem to be winning the
Marketing war….well at least commercials.
Anyways thanks for the link peoples.
Oh well,
I own a Mac, it’s better than the PC I had. Weee. GarageBand is awesome.
Joakim Noah: Better than you.
I really can't choose between the two
I went to this computer library or whatever and all the Macs had like 17 viruses each and they had to close for a week it was crazy. But even with those viruses it was still faster than what I got.
I just can’t take those keyboards in garage band. Its hardly 2 full octaves if even. Well the one I’ve been using; not sure if they have others.
I use my Yamaha YT-300, it has the full range. :P
Though there is a broken key.
Joakim Noah: Better than you.
I'll post something that shows it off on my website if you want :P
Joakim Noah: Better than you.
Et Voila:
Joakim Noah: Better than you.
It was actually only $100,
and that was a long time ago … and I bought a MIDI input thingie off of Amazon for $20.
Joakim Noah: Better than you.
See I need to get one of those
They have me using this mini keyboard. Though I can switch between octaves its still 2 octaves at a time.
I was eying a new keyboard that was like 200-300. Its a much better feel than some of these others.
Hmmm I might try and get that if I can find it that cheap.
Amazon is not being helpful, they have it for $150.
:/
Maybe it was $150. I remember ordering a stand and adapter and stuff, too … mmm.
I bought it in the middle of my first year of college … it had to have been pretty cheap, since I didn’t have too much money …
I did find this:
http://www.amazon.com/Yamaha-YPT210-Full-Size-Keyboard-Bundle/dp/B001FSJC46/ref=pd_bbs_sr_2?ie=UTF8&s=musical-instruments&qid=1238889710&sr=8-2
It’s the 210. No sequencing, but if you’re using GarageBand or any DAW with it you don’t need that. You will need a MIDI cord … I got the E-Mu, because it seemed like the easiest … It’s like $34 with shipping from Amazon. Boo.
Good luck, either way. I just started using it for digital recording myself. :P
Joakim Noah: Better than you.
Or, you know, you've been recording with a mini-piano thing,
you probably know vaguely what you’re doing. Or at least moreso than I do. :P
Joakim Noah: Better than you.
I'm pretty sure I just vaguely know anything
My teacher…..well he seems to be new to it as well. So originally I thought I could only use that mini keyboard.
I just got my sisters keyboard its a Yamaha PSR 270. I don’t have any other hook ups to it though.
But I’m guessing the MIDI comes separate in most.
Anyways thanks :D
Though I should keep trying on that mini keyboard to get use to voicing chords.
It should have a midi hookup in the back:
you just need a midi to USB cord, and hook it up, and then it should automatically connect if you’re using Garageband [or you need to put it in ‘PC mode’].
If you’re using Audacity or some Windows program [I was trying to use FLStudio and Audacity], prepare to run into a lot of problems with it being recognized. … Well, I ran into problems, anyways. That’s part of the reason I got the Mac in the first place.
Joakim Noah: Better than you.
Hmmmm
Audcactiy has already been giving me problems too. Though I think it was because of the virus.
I’m gonna have to find someone with a Mac
I think it's just because
it’s more confusing on other systems. Garageband+the cord and it was recognized instantly, and I was beating out melodies in seconds.
Joakim Noah: Better than you.
Sorry, my sense of elitism only goes so high :)
Confusion breeds success. If they don't know each other, opponents can't have strategy. GENIUS.
by Ozzie Montana on Apr 1, 2009 1:14 PM CDT up reply actions
Thanks!
Stats with contextual observations, good. Stats with no context, bad. Anecdotal observations unsupported by data, the worst.
by fundamentallysound on Apr 1, 2009 10:51 AM CDT up reply actions
yes, yes it is. He lives underneat the bucket.
Stats with contextual observations, good. Stats with no context, bad. Anecdotal observations unsupported by data, the worst.
by fundamentallysound on Apr 1, 2009 11:57 AM CDT up reply actions
underneath*
Stats with contextual observations, good. Stats with no context, bad. Anecdotal observations unsupported by data, the worst.
by fundamentallysound on Apr 1, 2009 11:57 AM CDT up reply actions
He knows his strengths.
Joakim Noah: Better than you.
I know Tyrus is trying to add new elements to his game
but his jumpshooting bugs me. I see a 30.6, 31.4, 32.4% among his 2-pt jumpshot zones – at some point Vinny or Bernie should tap him on the shoulder and say “we’re in a playoff race, enough is enough”.
well you can't really have Tyrus AND Joakim sitting underneath the bucket.
Joakim does it because his jumper is even uglier than Tyrus’s. Tyrus should roll and cut to the bucket more, but he has to be able to take that shot sometimes because it spreads the floor and makes it so people can’t just completely camp in the paint against him.
Stats with contextual observations, good. Stats with no context, bad. Anecdotal observations unsupported by data, the worst.
by fundamentallysound on Apr 1, 2009 2:38 PM CDT up reply actions
I agree he should take an occasional jumpshot
especially since so much of his game is driving to the hoop and drawing fouls. The problem is, he’s taken 302 jumpshots this year (compared to 301 shots in the paint), and he’s made 35.7% of them.
We talked about Rose using the jumpshot to set up his driving. I think Rose settles for jumpshots too much too, but at least it made sense because he can be a prolific scorer at times. Tyrus, though, isn’t. If he’s going to stand 15 feet from the basket, then fine, take 100 (not 300) jumpshots a year, and those other 200 times, pass the ball off for a higher percentage shot. His AST% dropped from 11% last year to 5.6% this year. Part of the reason is Vinny’s offense, but part of that I think is that Tyrus believes he can shoot now. 8% more of his FGA this year are jumpshots compared to last year, and it should be going the opposite direction. Say what you want about Vinny not putting in Joakim, but Tyrus’ shot selection killed us in OT against Toronto.
Yea, Tyrus should probably shoot less jump shots, at least until
he becomes more accurate at that shot, and even then, he’s more likely to be successful driving to hoop and dunking or getting fouled. On the bright side, he’s gotten back to finishing inside like he did when he was a rookie, whereas last year he was pretty bad at finishing inside. So, there’s that.
Stats with contextual observations, good. Stats with no context, bad. Anecdotal observations unsupported by data, the worst.
by fundamentallysound on Apr 1, 2009 3:13 PM CDT up reply actions
it seems wrong though
iirc he made one of those outside jumpshots and missed one. both were taken recently. :P
"They should. They better. I'm Vinny Del Negro!"
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