Plus/Minus Goes Roland

Dylan Burkhardt

Update: I’m an idiot and had messed up the off/40 column. It’s been fixed now so the numbers have changed a pretty significant amount. Sorry.

Thanks to a little research about how to utilize plus/minus statistics, Greg Simms and I are going to refine the plus/minus data a little bit. I was exchanging e-mails with Josh (of The Big Ten Geeks) and he referred me to The Hoya Prospectus, a Georgetown blog that is also tracking +/- data. The Prospectus takes the +/- concept one step further, taking into account the margin while a player is on the court and while the player is off the court to combine them into a “net” amount which is also called a Roland rating in the NBA.

So for example, Stu Douglass posted an “on” score (formerly the plus/minus number) of +13 versus Indiana however while he was off the court Michigan outscored Indiana by 11, giving him an “off” score of 11. His final Roland Rating is calculated by subtracting the off score from the on score which gives us a Roland Rating of 2.  DeShawn Sims posted an on score of 27 and an off score of –3 giving him a Roland Rating of +30. Etc. Etc.

The idea behind the Roland rating is to gauge of how valuable a player is to the team. In this case it tends to make it clear how big of a drop off you are dealing with when a player goes to the bench.

Here are the Roland ratings for Michigan players within conference play (and UConn):

Player Min On Off Roland On/40 Off/40 Roland/40
Sims 208 46 -11 57 8.85 -13.75 22.60
Harris 215 43 -8 51 8.00 -12.80 20.80
Novak 200 39 -4 43 7.80 -4.00 11.80
Morris 132 35 0 35 10.61 0.00 10.61
Lucas-Perry 149 28 7 21 7.52 3.08 4.44
Wright 41 3 32 -29 0.00 6.43 -6.43
Gibson 33 -11 46 -57 -13.33 8.89 -22.22
Vogrich 26 -11 46 -57 -16.92 8.60 -25.52
Douglass 195 4 31 -27 0.82 27.56 -26.74
  • This sort of ratings system does guys like Manny Harris and DeShawn Sims a lot of justice. This shouldn’t come as a surprise to anyone that has watched Michigan play because they essentially carry the team.
  • Stu Douglass has just been brutal by this scale. He has struggled in conference play and even yesterday he posted by far the worst numbers on the team.
  • Laval Lucas-Perry has decent numbers but they are about what I’d expect. Definitely not great but he has been a part of many Michigan runs versus Indiana, Penn State, and Connecticut.
  • Vogrich, Gibson, and Wright’s poor numbers emphasize just how bad the bench has been. There is a significant drop off from Harris, Novak, and Sims to their backups.
  • Darius Morris has an impressive +10 total and he seems to post positive numbers even when it seems like he is playing poorly.
  • Looking at these ratings, they really seem to make more sense than the original plus/minus scores but I’d love to hear your thoughts. They certainly aren’t a perfect measure but they are at least interesting.
  • Indiana and Connecticut game-by-game numbers after the jump

Michigan 68, Connecticut 63

Player Min On Off Roland Roland/40
Lucas-Perry 30 9 -4 13 28.00
Morris 17 9 -4 13 28.13
Harris 38 5 0 5 5.26
Gibson 13 4 1 3 10.83
Wright 12 3 2 1 7.14
Novak 28 2 3 -1 -7.14
Sims 27 1 4 -3 -10.83
Vogrich 2 0 5 -5 -5.26
Douglass 33 -8 13 -21 -83.98

Michigan 69, Indiana 45

Player Min On Off Roland Roland/40
Sims 38 27 -3 30 88.42
Harris 33 26 -2 28 42.94
Novak 32 22 2 20 17.50
Morris 32 21 3 18 11.25
Douglass 20 13 11 2 4.00
Lucas-Perry 24 13 11 2 -5.83
Wright 8 2 22 -20 -17.50
Person 1 0 24 -24 -24.62
Vogrich 10 -1 25 -26 -37.33
Gibson 2 -3 27 -30 -88.42
  • maxwell’s demon

    Very nice. This method seems very obvious in hindsight. This Roland sort of analysis could easily be extrapolated to offensive and defensive efficiency as well, correct?

    One thing that could never be captured but maybe worth considering is that a given bench player is often more likely to be played at the same time as the opposing team’s corresponding bench player. Therefore, any non-starter always has a slight inherent advantage.

    Also, I knew LLP played well yesterday but surprised by his total through B10.

  • Rob O.

    I like the addition. The conference numbers are not surprising except maybe LLP. Also, I would have expected to see Morris with a negative Roland, so that was a pleasant surprise. I have to start giving the freshman more credit. I have been more comfortable when Stu is playing the point but I guess I’m wrong. It will be interesting to see how the averages play out since the individual games can vary significantly (e.g. Douglass and Gibson in the UConn and IU games.)

  • Nice work. Check out I have per game on/off numbers for every team, and they’re calculated once a week.

    -Jon Nichols

  • ZRL

    I bet that Michigan’s 6 points in the coaches poll is just Calhoun voting Michigan 19th.

  • Merlin

    Very insightful. There should be a defensive and offensive Roland number as I think was suggested above.

    I was not a fan of LLP’s play this year but I think that is changing. His play is all about confidence and I think he is starting to feel more comfortable during games.

  • From Jon Nichols’ link… Here is his Michigan data for the entire year.

    Player Team Roland On Off
    Manny Harris Michigan 11.6 7.3 -4.2
    Zack Gibson Michigan 4.7 0.4 -4.3
    Zack Novak Michigan 4.6 1.5 -3.1
    Stu Douglass Michigan 1.9 -0.1 -2.0
    DeShawn Sims Michigan 1.5 5.3 3.9
    Laval Lucas-Perry Michigan -1.7 -2.7 -1.0
    Darius Morris Michigan -2.3 1.3 3.6
    Matt Vogrich Michigan -3.5 -2.0 1.5
    Anthony Wright Michigan -4.6 1.9 6.4
  • hutch


    I LOVE the +/- stats, but I am not a real fan of this addition. I think it punishes bench players on a decent team (that generally scores more than its opponents) and would make the bench players on a bad team look better than the starters. I would just stay with the +/- for when they are in and divide by 40. In any event, you have misarranged the numbers in the “off/40” column and that skews a lot of the numbers. What you have for LLP is really Harris’s number (if the base “off” column is correct), you have Novak’s number for sims and Morris’s number for Novak. Please review those. Thanks for all you give us.

  • Ahh, shit. You are right. Updating it now.

  • jmblue

    Why is it called a Roland rating?

  • OK should be fixed… My screw up definitely skewed the data quite a bit so take another look.

    They are called Roland ratings because of the guy who “invented” the measure.

  • Giddings

    Now that the numbers are fixed it seems to make more sense. I do think you should stick with this Roland rating, but like the commenters above I really miss the Offensive and Defensive breakdowns. If these could be added in I think we would really have it down.

    Surprised to see how bad Stu’s numbers are. It looks like based on Jon Nichols’ numbers he was much better out-of-conference. I still have a lot of confidence in him running the show, he makes some great passes like the one to Peedi yesterday for the layup down the stretch. Darius makes great passes as well, but still has a few things to learn.

  • maxwell’s demon

    Baffled by Stu’s results for the UCONN game…

  • AmherstAl

    Here is one bias though, there might be others. When Gibson comes in the game, Sims (clearly one of the best players on the team) is out. Other players don’t have that. Most of the time that Novak, or any other starter, is in the game, Sims is as well. That helps Novak’s numbers. Same for pretty much everybody else. You could probably say the same thing for Vogrich subbing for Harris, although not to the same extent.

  • Kevin

    Correct me if I’m wrong but isn’t that the point? To see how the team is affected either positively or negatively by each player? So when Gibson goes in and we go even plus/minus normally, theoretically he’s hurting the team because of the production we lose by not having sims in. It shows the dropoff.

  • AmherstAl

    Well yes, but it needs to be intrepreted that precisely. Keep in mind that Darius Morris usually subs for Stu Douglass. Let’s just assume that Darius, Zach G and Matt were equally good. These stats benefit DM because he subs for Stu and most of the time Manny and Deshawn are in the game. ZG and MV are penalized for subbing for a star.

  • You guys have it right. That’s the biggest weakness of plus-minus: teammate ability. Of course, there are things such as “adjusted plus-minus,” which attempts to factor out such things as teammates, but it’s awfully complicated and filled with flaws of its own.

  • Confused

    Adjusted +/- seems like a much better stat. I don’t really understand why you’d used these Roland numbers.

  • maxwell’s demon

    It shows the effect of not having a player in the game. For people that play 30 minutes +, this method significantly clarifies their impact on the game.

  • Amherst makes a great point about Gibson–and by extension, everyone. But this does confirm my feelings about Douglass. Whenever I look in he is playing poorly, which baffles me. He really impressed me last year.

    The stats make the argument for still more p.t. for Morris. He is going to be a huge help to this team–knock wood–for four straight years. Given how much he contributes already, let’s have him be a tried-and-true veteran down the stretch. Once he’s really comfortable there are going to be six or eight more points in it nightly for M as he drops in layups, dishes, etc. (Three pointers will be grand once we get some shooters!)

    Hope Beilein looks in here from time to time, or has access to these stats.

  • UMIndy

    I would think with a large enough N, the question about who else is on the court would filter out.

  • Mat

    Amherst is correct to point out that Gibson is hit rather unfairly in this system. He’ll almost never get the positive benefit of playing with Sims that others (like LLP, Morris, even Wright) get. Doesn’t mean he is a worse player that those guys.

    Same goes for Douglass though. Although not as dramatic as the Sims-Gibson dynamic, whenever Manny sits down, Douglass is in the game because he is the best perimeter scorer after Manny.

    These are good stats and point to some interesting signs. But like any other stat, need to be taken with a grain of salt.

  • The best usage of the statistic would be to compare Gibson to Sims directly I would think… I’m just learning this stuff just like you guys though.

  • Andy


    The numbers for Stu really shock me. I generally consider myself pretty knowledgable about basketball and feel pretty good about my feel for things. My eyes tell me that Stu is the third best player on this team and a very solid defender and cog in the offense. I’m shocked his numbers were so bad yesterday.

    Anyway, I looked at the box score to figure out how he got to those numbers. Basically, yesterday was a game of two runs. UM had a run in the first half to take a 9 point lead and UConn had a run at the beginning of the second half to even it up. It was basically a toss up and pretty even back and forth the rest of the game. Highlights relative to Stu…

    At 9:24 of the first half, 14-14 game, Stu comes out – On = 0
    In the next 1:30, LLP hits two 3s and Wright hits one.
    At 6:22 Stu comes in, UM 23-16. Off = +7
    Plays the rest of the half, UM 32-23. On = +2

    UConn run, comes out at 15:56, UM 37-33, On = -5.
    Out for 31 seconds in which Gibson hits 2 FTs. Off = +2
    UConn grinds down lead, over next 7 mins. Out @ 8:58, 47-47. On = -6.
    Manny and DeShawn get tough, Stu back in at 5:39, UM 54-50. Off = +4
    Plays rest of the game. UM 68-63. On = +1

    So basically he was off the floor during the LLP / Ant barrage in the first half, was on for most of the UConn grind back into the game, and was off for an unfortunate 31 seconds. The central question to all of this is how much can be attributed to his (or anyone’s) presence or absence? Judging by these numbers, he was brutal to the team, but his box score (13 points, 4 assists, 2 steals, 1 turnover) says otherwise. Anyway, I don’t know what I’m trying to prove here… I think this stat is just one way to look at the game, doesn’t tell the whole story.

  • It’s definitely just one aspect, especially on a single game basis. On a single game basis it just describes who was on the court for big runs. When you increase the sample size over a number of games it becomes a little more valuable as you start to see trends emerge. But I agree that the single game numbers especially need to taken with a grain of salt.

  • Andy

    Didn’t mean to imply that I don’t like the stat. It’s actually right up my alley, logical analysis of a game and team I love. Just kind of rambling and trying to rectify what I see with what the numbers showed.

  • Mike

    Dylan –
    I like the stat, but I think the problem mentioned by hutch is still there. Douglass should have an off/40 of about 6.3 (which would make him not look as awful). I think many of the other off/40 numbers are still wrong as well. If I’m right, I think we’ll see that Morris is actually the best /40 player, interesting I guess.

  • Here are my calculations for Douglass…

    Douglass was off the court for 45 (played 195 of 240) minutes and Michigan outscored their opponents by 31 points. That’s .688 points per minute multiplied by 40 equals 26.55 “off per 40”.

  • Mike

    never mind, I get it now. like I said, good stat!

  • gpsimms

    I did send in both an “old” +/- state and a “new” roland version because I kind of like the offense/40 and defense/40 looks as well. For example, I think one thing we see is that Darius has brought a lot to the team on defense, but is still working on learning the offense. His +/- is good, but I’m pretty sure both his score/40 and allow/40 are low.

  • Was just trying to keep it simple… I’ll go with a more detailed look for the next go round, we still have the data.

  • Erik

    Nice stats, I like the change.

    The one thing I think people are a little hung up on with the whole Gibson/Vogrich thing is that this stat doesn’t measure how “good” a player is. It simply measures the score differential when the player is on the floor.

    Novak gives intangibles, Gibson made a HUGE block…those are not necessarily reflected in this statistic, it doesn’t mean those plays or players are any “less good”.

    I guess it’s semantics, but I think it’s important. Regardless of how we feel about Stu or Gibson as all around players and what they can bring to the table in hustle, rebounding, height, defense, etc…this stat only measure scoring differential, not the overall “goodness” of a player.

    One thing I was wondering about for the statisticians out there is if there is a way to incorporate turnovers and steals into these formulas. For example, we know what the average point per posession was in a given game. So what if we took all of UofM’s defensive rebounds and multiplied it by UConn’s point per posession (in effect saying “What if they cleaned up all their rebounds, how many more points would it have resulted in”). Do the same for turnovers: “if they hadn’t turned the ball over at all, how many more points would it have resulted in”. Do that for both sides and see what the results show.

    I’m guessing it will be skewed by fast break points since many rebounds (and especially turnovers) lead to fast break points at the other end. But I’m just thinking out loud if there is a way to feed rebounds and turnovers into an equation along with scoring to determine how well a team played.


  • Sid

    Somebody needs to come up with a grit indicator. Loose balls recovered, charges taken, rebounds against all odds, tap outs to keep an offensive possession alive, setting picks on giants and sprinting back to foil a layup would all get a plus. Failing to box out, letting your man beat you down the court after a made bucket and remaining standing during floor scrums in your vicinity would get negs. Being bloodied would draw a double plus, bloodying an opponent would be case-by-case. Let’s get this done.

  • Andy

    @Erik – “this stat only measure scoring differential, not the overall “goodness” of a player.”

    That is kind of what I was getting at, but after thinking about it in the shower this morning, that’s really the whole point. In reality, it doesn’t matter how much hustle, grit, steadiness, or whatever adejective we can come up with a player has. Scoring differential is the only stat that matters at the end of the day in basketball (or any sport for that matter). If on a consistent basis the team is doing better with you off the court as opposed to on, you shouldn’t play as much, end of story.

    One interesting thing to add (way more work) would be to see how a players Roland Rating worked over different time frames in a game. Say a player has a great RR the first 3 minutes they’re in, but they fatigue and they end up moving back to about neutral, that would tell the coach to either play him in short spurts or get him in better shape. Or say someone has an overall solid RR, but their rating in the last three minutes of games is horrible, you’d keep him out of crunch time. Just some ideas on how it could be expanded.

  • maxwell’s demon

    Not to beat a dead horse with a stick but:

    “Teams rush floors when they do something phenomenal,” said Kansas State forward Curtis Kelly, who had 17 points and eight rebounds against one college basketball’s best front lines. “It’s flattering. They knew we were going to win. They didn’t have to rush the floor because they believed in us.”

    (In response to KSU not rushing the court last night)

  • Erik


    I guess what I”m getting at, is these stats reward guys who can create on offense, or stop on defense. It does not reward guys like Novak who do the intangibles. Novak doesn’t create on offense. He isn’t really a lock down defender. He sets up his teammates. Regardless of how well he sets up his teammates, his score is going to be heavily reflected on whether or not his teammates “cash in” when he gets them the ball.

    On the flip side, you look at a guy like Manny or Peedi, they create their own offense. These numbers are highly indicative of their play and whether or not they are creating offense. For stu, it’s about whether or not he’s locking down his man on defense.

    I can see for guys like Wright, Gibson, and to an extent Novak they are just role players who are used with the intent of setting up their teammates. Their scores are dependent upon other people more than the “stars” of the team.

    I don’t think it means Novak or Vogrich or Gibby played poorly if their score is low necessarily. It could mean they played really well, gathered rebounds, forced turnovers, passed the ball well…but their team mates didn’t make the shots when they passed the ball.

    I’m just offering one shortcoming of this method, not saying this is necessarily true. That’s why I wish there was a way to factor in turnovers and rebounds into the equation for a more complete metric.