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Introducing (For the Last Time?) The Plus-Minus/40 Salvation Scale

 

A personal fact about me is that I really like plus/minus. It’s noisy and messy and often a little stupid, but I like that it offers a measure of performance without any individual counting stats. I don’t think it’s a great metric, but it can supplement a larger evaluation and it’s fun to talk about.

Plus/minus per 40 minutes (that’s what I’ll be using here, with raw figures from the glorious Hoopdata) can entertain us in a number of ways. It can help us confirm things we already know, like that Pau Gasol is the best player on the Lakers (outscoring opponents by 11.03 to Kobe’s 7.93) or that Dwyane Wade (5.83, zero or below in all four Heat losses) is ruining everything for LeBron (9.55). It can also offer a few surprises, like that Chris Bosh has the highest plus/minus of the Miami guys (10.83) or that Kevin Durant is being outscored by 3.21 points when he’s on the floor this season. Eesh.

Let’s take a look at the C’s plus/minus per 40 spectrum, presented here in chart form as a gift to your eyeballs.

Is there anything of value that we can take away from this chart, other than the comforting knowledge that there is beauty in the world? Maybe not, but we should probably blow a few hours discussing it anyway. Here are a few things that jump out at me:

  • Overall this chart ranks the C’s performance this season pretty much as you would by sight. For example, the starters have been outplaying the reserves by a pretty wide margin. Not great for a team that, you know, gave its bench a name, but also not a huge surprise. Among the non-starters, it appears that the earlier you get into the game (Glen, Marquis) and therefore the smaller a percentage of your floor time you spend with Nate Robinson, the higher your plus/minus value is. The C’s bench situation could be worse; this isn’t Miami. But we should nonetheless be thankful for the neck-tattooed Christmas elf who’s about to rejoin the team.
  • Glen is probably the one guy whose position on the chart jibes the least with his perceived performance so far this season. He looks like he’s been succeeding with the starters and likewise failing with the bench, with an end result of general mediocrity. Glen had five games with a plus/minus of exactly 1, including a bizarre four-game stretch from  Milwaukee to Dallas. He’s still been good, he just spends time on the floor with a lot of different lineups of varying quality. He doesn’t hurt the good ones, but also doesn’t do much for the bad ones. Nothing to call the cops over.
  • The Nate-Semih combo has been getting absolutely torched. It’s not a given that bench players come with a low or negative plus-minus: they’re usually on the floor with the opposing team’s bench players, guys they should be at least capable of outscoring. And they’ve posted a couple of huge games: they were big in last week’s Memphis win and basically won the OKC game on their own. But Nate’s had negative scores in 7 out of 10 games and the two of them were almost solely responsible for the loss in Dallas. Overall you can look at this as a referendum on Nate’s shooting, which will probably improve, and his ability to run an offense, something he’s never been at all interested in doing anyway and that seemingly nobody has ever demanded of him. Cool. By the way, how happy is Nate to have three days off right after Call of Duty: Black Ops came out?
  • Marquis is a pleasant little surprise here, but not a huge one, as he’s looked good so far. He posted two big plus/minus games against Chicago and OKC, and has been pretty consistently in the positive. Looking back at the chart, I think we can all agree that that is the face he would make in reaction to this or any score.
  • No surprise that Rondo’s leading the team in this metric, even though he’s also leading the team in minutes and spends a decent chunk of his floor time with bench guys. If not for that Cleveland game, where everyone posted a pretty bad plus/minus except KG, Rondo would have outscored the opposition in every game.
  • I find Ray’s middling performance here to be a little curious. The prevailing wisdom with Ray is that he provides a floor-spacing element that makes every lineup he’s in better. But his plus/minus this season generally comes in substantially lower than the other starters, and he’s posted a negative value in three wins, including a -12 in the Chicago game. I have a feeling this has something to do with A) his defense and B) the fact that he historically plays a few more minutes with the bench than, for example, KG and Pierce do.
  • As if Jermaine wasn’t giving you enough to be disheartened about, the C’s have barely outscored the opposition when he’s on the floor even though he started 5 of the 7 games he played in and the starters generally performed very well in those games. The Milwaukee game, for example, saw Jermaine get outscored by 5 while all the other starters ended up with a plus/minus of at least 9. This seems like a good place to end this discussion.

What do you guys think? About the chart, I mean. Awesome, right? I guess you can also talk about plus/minus if you want. Also feel free to let me know if you never want to talk about any of this ever again.

  • BrendanJackson

    What have we done….

    • I_Love_Green

      My thoughts exactly.

  • Cool Hand Luke

    Small sample for Ray, he usually leads the team or is very close to the lead (check past years) in the (adjusted or not) plus minus stats.

    He regularly also puts up fantastic plus minus with the bench, has that not continued so far this year? Must be, as raw +/- time for the starters will be the same when they're on the court together and only be different in the time they spend with one and one off.

    Yeah, looking a bit deeper the bench+1 starter that has had the most time is robinson-allen-daniels-davis-erden. It'd make sense that he'd have lower numbers if he's spending more time with that group than the other starters.

    The last few years he's been great with the bench. I wonder if it's just the small sample.

    • hdavenport

      Right, it's Ray's historical plus/minus numbers that made this seem a little odd. Probably just the sample and how badly the rest of the bench is playing.

  • Batman

    where did you ever get such an epic picture of semih?

  • Berkcelt

    Not sure how I feel about +/- but that was an interesting post.

    And yes, that chart is awesome. Please update it from time to time, many thanks.

  • zebulon

    Couple of problems with this analysis:

    The C's have unusual substitution patterns – we regularly use lineups of four or five bench players at a time, while most coaches keep at least two starters in for the vast majority of the game. So even though Erden/Davis/Quis/Robinson/Allen or Rondo doesn't do well in raw plus minus, they shouldn't really be expected to, playing against lineups with multiple starters.

    Also, Ray has played lots of minutes with the bench (as you mention). But this has a HUGE impact on plus/minus numbers. In terms of raw plus/minus, a player is only responsible for about 20% of their individual rating, as they are only 1/5 of a given lineup. On the other hand, Ray's adjusted plus/minus (which attempts to factor in the respective ratings of the lineups a given player plays with and against) is terrible this year. He's at -9.6, ahead of only Nate (at -15) for the season (both numbers courtesy of 82games.com).

    On the other hand, the raw numbers you present here are really interesting. Rondo is the best on the team, despite playing extended minutes with the bench. Shaq is way ahead of Jermaine or Baby, despite missing so many looks at the rim and being too slow to play defense. Quis has a good raw plus/minus despite the lineups he plays with, which is backed up by his ridiculously awesome adjusted plus/minus of +15. And the graph is just awesome.

    • hdavenport

      Excellent point on the substitution patterns, but this is supposed to be one of the deepest teams in the NBA, which should theoretically allow Doc to throw a few more bench guys out there at once without losing a lead. This is totally anecdotal, but Alvin Gentry went with two lineups of five in Phoenix last year and they made it look pretty good, so it's not impossible. Meanwhile, Nate was outscored in the Detroit game.

      I saw that about Ray's APM. Almost makes me feel like the algorithm couldn't sufficiently wipe out the bench's influence. You're not really asking me to defend this, but I went with unadjusted plus-minus because the standard errors at this point in the season are monstrous for adjusted, while the raw numbers at least are what they are.

      82games hasn't updated all of its figures, I guess because it started this season's analysis a few weeks late? I generally use Basketball Value for that stuff.

      • zebulon

        You're right – I've been using basketball value too, but somehow have the bookmark listed as 82games. Total mistake on my part.

    • greyberger

      Adjusted +/- comes with a standard error. At this point in the season one standard error will usually be larger than the +/- rating. Even in cases where it's not, the rating is found by comparing lineups to find out who is contributing what… so the more stints the better.

      In short adjusted +/- is for one season or more. Half a season is pushing it. Eight games in the results are nonsensical.

  • Morpheus

    Meh, i think JO's +/- WILL improve once his knees are 100%.

    Personally i do not like +/-

    • Eric

      Your plus/minus opinion I understand and respect. Not certain, however, that JO's knees will ever be 100%.

  • Morpheus

    Awesome graph though, that would make a cool avatar

  • chris

    Once everything shakes out (i.e., Shaq starting, Baby closing, and a healthier JO playing with Nate/ DWest/Quis/Baby), this team could be scary good. Check out how good they are with Shaq (and Baby) playing with the Big 4:

    Min Off Def +/- eFG eFGA
    1 Rondo-Allen-Pierce-Garnett-Davis 95.4 1.12 0.99 +26 .519 .447
    2 Rondo-Allen-Pierce-Garnett-J.O'Neal 82.1 1.03 0.98 +7 .435 .401
    3 Rondo-Allen-Pierce-Garnett-S.O'Neal 48.7 1.10 0.95 +17 .570 .417
    http://www.82games.com/1011/1011BOS2.HTM

    • hdavenport

      Those numbers are definitely good, but I'd like my team's best lineup to be A) the one that plays the most minutes and B) better than the 30th best lineup in the league in overall rating. I do think that the trend is upward though.

      Again, I use BV rather than 82g so I don't know if the #'s are different.

  • crizik

    Expect Nate to improve a lot with Delonte on the floor. Now he will be doing what he knows and likes to do, wich is scoring. Nate is a shooting guard, and for the first time in the season he will be coming out of the bench to do just that.

  • jasont

    i don't know what +/- means but that was a fun read!

  • koolaid

    nice graphic!

  • Rich

    Your opening paragraph just reaffirmed my hatred for +/-. Anyone with two eyes can tell Chris Bosh isn't playing well, yet he walks away with the highest +/- of any of the Miami starters? I really do hate the stat with a passion.

    • zebulon

      It gets at the lineups he plays with – always with Wade or Lebron, and usually with both of them. The heat (unsurprisingly) are a great team with all of their superstars in, and aren't that good with lineups like house/jones/ilgauskus/haslem/james. Bosh has a great +/- so far because the times he takes the floor, the Heat are dominating their opponents.

  • tkenneyjr

    I've been a big fan of the Wins Produced stats that orignate at http://dberri.wordpress.com. It looks like the best in predicting team success and revealing non-scoring productive players. And now they've got an automated site at http://www.permanent-sketch.com/WinsProduced/Main….

    According to WP48, Rondo is the 2nd best PG in the league, behind only CP3.

    • zebulon

      Wins Produced is a useful catch-all stat, but it doesn't tell the whole story. It is based entirely on box score stats, so it by definition cannot value anything outside of the box score.

      Plus/minus, on the other hand, is completely separate from other stats. It's purely a measure of how a team has performed with a given player on the floor. It obviously has its issues (such as the effect of teammates, lineups, and opponents), but it is valuable in that it provides a different lens through which to evaluate players. This chart doesn't answer all questions about who on the Celtics is playing well or why Nate Robinson has been so sub-par this year, but it does provide some interesting insights – like Jermaine's poor play and Quis' surprising productivity.

  • jang

    Is there possibly enough bronze in the world to immortalize Kevin Garnett and Paul Pierce's sacs?
    http://hoopstopia.com/?p=247

  • Tree Frog

    Using faces to represent information is a legitimate analytic technique. It's called making a Chernoff Face.

    Look at this wiki page – http://en.wikipedia.org/wiki/Chernoff_face

    • hdavenport

      Why does this not have a million thumbs up?

      • just me

        We like pictures only, words have to be read.

  • http://theultimategoldparty.com scott

    chart is awesome. i think the +/- is fairly useless for individuals especially this early. however if there is an adjusted +/- for personnel groupings that would be worthy of discussion otherwise let's leave this for the fans of teams that don't win.

  • scott

    chart is awesome. i think the +/- is fairly useless for individuals especially this early. however if there is an adjusted +/- for personnel groupings that would be worthy of discussion otherwise let's leave this for the fans of teams that don't win.
    http://theultomategoldparty.com

  • Idaho

    fairly useless statistic confounded by 9 other guys on the court.

    • Chris O

      very much so, unless it is an adjusted +/- (which for those of you who don't know is based on the quality of all players involved). still fun to look at debate and great chart lol.

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