With that in mind, it’s interesting to read J.A. Adande’s recap of Game 4 with a scorecard on hand. What we see is that Kobe Bryant, who scored 38 points on 66% shooting in 39 minutes, ended the game with a +4 rating, the same as Luke Walton, who chipped in 9 points on 50% shooting in 19 minutes. Sasha Vujacic had a +9 for his contributions of 9 points on 33% shooting in 17 minutes. The guys who fare the best are Lamar Odom (10-15-6 line on 40% shooting in 41 minutes, for +20) and Pau Gasol (13-10-1 in 41 minutes, for +15). Clearly, those numbers are all over the place, but what’s weird is how Kobe ended up with just a +4, given how much everyone insists he dominated the game. The following excerpt from Adande’s article helps to explain this:

Bryant came out firing. … He scored the Lakers’ first 11 points and 13 of their first 15, hitting 6-of-8 shots in the first quarter. … But the rest of the Lakers went 2 for 10 and Utah led, 25-20. The turning point actually came when he was on the bench at the start of the second quarter and the Lakers fielded a lineup of Shannon Brown, Sasha Vujacic, Luke Walton and starters Lamar Odom and Pau Gasol. It was the reserve players who hit three consecutive 3-pointers to take the Lakers from a seven-point deficit to a two-point lead.

A-ha! Kobe, may have scored a full one-third of the team’s points over the course of the game, but he was sitting out during a key stretch. Worse, while he was lighting it up in the first quarter, everybody else’s ineptitude was costing him in the +/- stakes.

This situation captures almost perfectly the beauty and the shortcomings of +/-: on the one hand, it zooms in on what matters most — winning — without ascribing arbitrary weightings to individual statistics like points, rebounds and assists while still incorporating the value of intangible contributions. On the other hand, the value of the individual is so tightly tied to who is on the court with him that +/- as a comparative tool becomes worthless, since it reflects more the overall quality of the team and the ability of the coach to construct effective rotations. It’s sort of the classic curse of single-number metrics.

One is tempted to abandon +/- as the ‘holy grail’ statistic at this point, but it’s really a very good idea in as far as cutting out the pseudo-science of sports statistics and focussing on what actually leads to wins. One wonders if the problem is ’snapshotting’ +/- ratings at the end of the game, which necessarily throws out all the information that a real-time +/- score would have. Behold:

Utah-L.A. Game 4, Playoffs 2009 - Selected Plus-Minus Ratings

What you’re seeing is a graph of realtime +/- ratings for the teams (ie, overall) as well as for various players over the course of the entire game. The overall team rating is just the point differential between L.A. and Utah (I’m a Lakers fan); for the individual players, you can see how their +/- rating was related to that of the team through time. The flat regions (eg, Luke Walton from the beginning of the game until about 7:30 in) are periods when the player’s +/- didn’t change — ie, he was either off the court, or he was on, but neither team scored. You’ll also see some periods when everyone’s rating moves together — eg, the plotted players’ +/- ratings all fell between 10:30 and 14:30 — which implies that they were all on the court (in the 10:30 – 14:30 period, the falling ratings mean Utah made a run).

The plot makes it immediately apparent how, for example, Luke Walton ended up with the same +/- rating as Kobe: he simply sat out the last 10 minutes of the game, when Utah was cutting L.A.’s lead. This, of course, raises some interesting questions, such as how starting and ending games ends players’ +/- ratings; from this example, it looks like garbage time can hurt the winning team’s ratings (though conversely, Utah’s players’ ratings benefited from garbage time), while starting can be good or bad for one’s score depending on who starts the game stronger (ie, there’s no bias there, whereas there is for garbage time).

Of course, since one now has a nice time-series describing the players’ contributions (as encapsulated by +/-), one can try computing a single-number metric of performance (though, obviously, YMMV*) by simply computing the correlation between the team’s overall +/- and the players’ individual ratings. Note that this number really only makes sense in the context of the team’s performance — ie, a player with a perfect score on the Kings is clearly worse than a player with a perfect score on the Lakers, since correlation doesn’t differentiate between covariance that leads to team success or failure. That said, let’s take a look at what this ‘+/- correlation’ metric looks like for Game 4:

Utah-L.A. Game 4, Playoffs 2009 - +/- correlations

I’ve shown both team’s players on this one chart, so what you’re seeing is who contributed to what ultimately proved to be a Lakers’ win as a normalised score based on players’ full real-time contributions. So if you were to say a dude is absolutely indispensable to a team’s success (ie, the MVP), you would expect him to have, over the course of the season, a +/- correlation of almost +1. We see that, for example, for Pau Gasol, implying he was on the court for almost every significant period of the game (even if he didn’t contribute as much as Kobe in raw numbers). The implications for Andrew Bynum are also interesting, since a correlation that low means he basically didn’t matter much as far as the team’s ultimate success is concerned. I’m really itching to see what it says about Shane Battier ;)

Unfortunately, it’s not the end-all, be-all of metrics because by construction the amount of playing time a player receives will bias it, and because it’s basis in the overall winning ability of the five players on the court means it doesn’t break down how much of that success is attributable to any individual player. However, it does roughly put players where we expect them in the pecking order, and gives a rudimentary sense of how much responsibility a team’s results individual players should be ascribed. And there are ways to improve this metric, a topic which really deserves another post (although here’s an obvious extension: define the overall team +/- to always be in favour of the team that wins).

In summary, what complaints we have against +/- ratings might be resolvable by analysing players’ +/- ratings as they evolve through time. In abstract terms, +/- seems a much more objective metric than the weighted-average metrics in more common use (eg, PER, Wages-of-Wins), which make assumptions that borne out only by a couple of decades’ history.

I’m attaching the spreadsheet containing my data as well in case anyone’s interested in taking a look at it. If I get time — and if there’s interest — I might compile this sort of data for all the games next year and put it on the web. Let me know what you think.

Utah-L.A. Game 4, Playoffs 2009 – Data

Utah-L.A. Game 4, Playoffs 2009 – Scorecard

• I have trouble using this phrase in polite conversation now, but hopefully we’re all on the same page as to why I’m using it!

All I want right now, is for someone to look at Tim Thomas’ line in the March 28 Bulls-Pacers game and restate the value of +/-, basketball’s statistic of the moment:

                        MIN  FGM-A  3PM-A  FTM-A  OREB  DREB  REB  AST  STL  BLK  TO  PF  +/-  PTS
Tim Thomas, PF  6   0-3     0-1        0-0      0   1   1   0   0   0    0    2 +8  0

Yes, for the 6 minutes in which he netted 1 rebound, 3 misses and 2 fouls, he was rewarded with a +8 rating.

I’ve been defending Kobe more or less since 2000 now. I’ve never been a full-on fanboy, but in a sport populated by egotistical megalomaniacs, I admired his rabid desire to win, and most importantly the pressure he put on himself to excel. His detractors argued this was just a manifestation of his ego, that he was only interested in bolstering his legacy; I didn’t care, as long as he won.

And that’s why this hurts. It’s not the first time Kobe’s lost in the Finals (2004, when he, along with Shaq, Payton and Malone managed to lose to the Pistons), but it is the first time that he’s the sole leader of a team that has been bounced out of the Finals. He was frequently doubled by the best defensive team in the league, but that’s not a good enough excuse. His teammates absolutely disappeared, but after doing enough to get Kobe to the Finals, they can’t be blamed. The Finals are when the Jordans of the game take over and deliver victories, no matter how or what or why or who. It’s only fair that Kobe is the face of the team when they’re winning and when they’re losing. We demand that of our Jordans just as well.

The thing is, Jordans, plural, don’t exist. There was one Jordan, an icon who fortuitously came along at that period between eras where destiny offers individuals the opportunity to immortalise themselves. Magic and Bird were winding down, and the league had no one to rival the sheer athleticism and bloody-mindedness of Jordan. The two ingredients did exist, but separately, in the Drexlers and Isiahs of the world. True, the rules were tighter and players were more skilled, but a little thought reveals these facts cut both ways.

Maybe that’s why, in retrospect, I’m not all that surprised Kobe lost. He’s never been Jordan, not since he was drafted at the unlucky thirteen spot by a team he refused to play for. Not when he was labelled a copycat rather than an iconoclast as Jordan was. Not when forced to be second banana for several years, and having to learn leadership at 26 when Jordan started learning at 21. Not in being reviled by the public for an accusation that was later dropped where Jordan’s indiscretions (which many claim equalled Kobe’s) were carefully handled by Stern. Not in playing before people were willing to replace their basketball god, Jordan. And not in playing in a league where the level of athleticism has caught up to the point that other than Dwight Howard and Lebron, no one has an outright athletic advantage over others.

No, Kobe is not Jordan. But Kobe is Kobe, a guy who has conquered all the odds and the roadblocks fortune has thrown his way, willing himself into a position where the comparisons with Jordan, that most untouchable combination of talent and destiny, have at times not been unreasonable.

That’s saying something. That’s saying there’s good reason to keep watching as Kobe plots and attacks this latest roadblock to his only goal: winning.

What really rankles me, though, is the quality of writing. Spot my problems with this paragraph:

But the principles they are now employing eventually may be considered the new “LeBron Rules.”

The Wizards are playing rough, invoking the Detroit “Bad Boys” on more than one occasion and not saying they’re sorry for knocking James on his backside as much as possible. Have other teams tried to send messages to James with hard fouls before? Sure. But not to this level and with this much apparent conspiracy, according to the man himself.

“I’ve been put on the floor before, but it has been a little different this year,” James said. “Hard fouls happen, but this is a difference.”

I bet you’re thinking I’m pissed off at Mr. Windhorst regurgitating the tired notion of “<Insert superstar’s name here> Rules”, a pointless multiplication of a single idea: to knock said superstar down as many times as possible. No, although his perpetual effort to parallel LeBron with Michael Jordan is transparent even to the blind; what bothers me is the simultaneous elevation of LeBron to hero status and the verbatim quote, which underscores his shortcomings off the basketball court.

(And let’s be clear, LeBron can’t plead Ebonics here — that sentence is just plain wrong.)

This isn’t an isolated incident, particularly given how poorly-spoken today’s sports superstars are. And that Mr. Windhorst is trying to convey LeBron’s thoughts exactly as he expressed them is hardly surprising given that he is a journalist. The problem is that raining hosannas upon LeBron’s head even as he is shown to be committing verbal faux pas galore (and without hesitation and without remorse — without even realising what the problem is!) is exactly why English, the language, sits on a slippery slope today. A slippery slope whose gradient we are ever-increasing by irresponsibly (even if it’s inadvertent) communicating that savaging English is OK.

Understand this isn’t a moral issue to me: I’m not talking about what we’re teaching our kids, I’m saying that the quality of the English we see and hear around us, on TV and in newspapers, is more or less the zenith of what we ourselves aspire to and will ultimately attain. So returning to the point, Mr. Windhorst and others like him would do well to either cut out the hero-worship and present their subjects as normal human beings rather than ideals that we should all admire and dream of emulating in all things, or employ the same artistic license they so happily abuse while serving up cliches and edit their subjects’ soundbites. For the sake of their subjects. And us all.

(Note that I feel bad about hammering Mr. Windhorst this way when more or less all media types are to blame. But I’m sure he understands I’m not trying to target him. And that this problem is bigger than us all. <Cue ‘Gladiator’ theme.>)

It’s probably not surprising, given Brown never played professional ball and has no qualification other than that he’s worked in the league for over a decade, starting off as a video coordinator and scout. You wonder why Dan Gilbert hired this guy, whose only real function seems to be to put out soundbites like, “LeBron stepped up and put us on his shoulders. He said, ‘Come along for the ride.’ And we all hopped on.” I mean, honestly, what else does this guy provide? He’s got too obvious a mancrush on LBJ to tell him to fix his jumper, his rotation is completely unsettled — vets like Marshall and Jones are rustry from not playing enough and guys like Gibson who’s better than Snow NOW, as a rookie — and he’s forced this team into a defensive style that it clearly isn’t equipped to play. His idea of playing to LBJ’s strengths is to give him the ball every time up and let him decide whether he feels like shooting fadeaway 3’s or passing the ball to teammates who spend most of the shot clock watching LBJ and bracing for the inevitable clanger from 25 feet out. Oh, and he’s let Larry Hughes develop into a volume shooter at 33%. Yech.

Comparing LBJ to Shaq has been a staple for sportswriters since LeBron got to the NBA. The idea normally is to point out how physically superior both players are compared to other players at their positions, but it’s a valid comparison in as far as both players’ tendency to coast unless pressed. There are huge holes in LBJ’s games — his shooting form is horrendous, his midrange game is poor, and his post game is limited to overpowering his defender — but the last couple of years are enough to figure out that those aren’t going to be plugged unless someone with credibility and authority steps in to provide some guidance.

The team’s offense and defense need attention too: the Cavs aren’t quite as bad as people make them out to be, what with Ilgauskas (a former All-Star), Varejao and Gooden anchoring the frontline, and lots of (one-dimensional) role players in the backcourt to provide specific things like shooting and defense. They still need to make some upgrades, particularly at point guard, but their biggest shortcoming by far is the guy making the calls from the sidelines.

(And it’s a massive shame they didn’t get a chance to talk to Adelman. He would have been perfect for a team fronted by a pouting superstar and lots of role players.)