Narrative stats vs. Rudy Gay

Earlier this season, the Toronto Raptors traded forward Rudy Gay to the Sacramento Kings.  At the time of the deal, Gay was second on the team in points per game and thought of as a star player.  His salary this season is $17 million.

At the time Gay was traded, the Raptors were 6-12.  Since the trade, they've gone 11-5.

What happened?  Gay's salary may be high, and his scoring may be decent, but, as Dave Berri points out, it looks like Gay just isn't very good.  He scores a lot of points, but only because he takes a lot of shots.  Berri writes,

"...Gay had an effective field goal percentage of 42.1%.  It shouldn’t take an understanding of “advanced stats” to conclude that such a player isn’t “good”."

Which makes complete sense.  A team has about 100 possessions per game in which to score.  A player who takes a shot has "used" one of his team's possessions, and, so, needs to use it wisely.  

The NBA average, last year, was that teams took shots in around 83 of those possessions, which (coincidentally) led to around 83 points on field goals.  But, if every player on a team shot like Rudy Gay, they'd score only around 70 points.  

Of course, it could be that Gay's EFG% is low because he's the one who has to take the harder shots, like desperation attempts with the shot clock winding down.  But, unless you have some reason to believe that's what's happening, your first reaction would have to be that Gay's shooting is hurting the team.

(UPDATE: I should clarify that you can't conclude that Gay is hurting the team just because he's below average; a below-average player can still have value if he's better than the next best alternative (that is, better than "replacement value").  In this case, I'm assuming that Gay is sufficiently below average that he's worse than the bench, a resonable assuption considering the Raptors' subsequent performance after the trade.)

Has any mainstream basketball journalist acknowledged Gay's poor efficiency?  Dave Berri asked on Twitter,

"Has any sports writer argued that the Raptors are better since the Gay trade because Gay is not a very productive player?"

There were only a couple of responses, pointing to online articles at Grantland and ESPN.  I did find another article that suggests teams are finally catching on, but also implies that, yes, it is indeed a fact that efficiency tends to be underrated.

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As I said, I don't follow basketball as much as I should, so I may be wrong, but it does seem to me that broadcasters and sportswriters like to concentrate on per-game counting stats: points, rebounds, and assists.  When they discuss efficiency, it's usually for the team as a whole: "The Raptors lost 100-81 while shooting only 39% from the field."  Sometimes, they'll mention a player, but only when it's something really extreme: "Player X went only 2-for-15 in the 107-79 loss."

So, why the emphasis on points, instead of actual benefit to the team?  

I think it's because, as a rule, counting stats normally "work," in a narrative sense.  It's a rare case when you see a decent-sounding counting stat that doesn't mean a good performance that game.

Take baseball batters, for instance.  In a single game, if you accumulate any significant number of anything good, you probably were one of the biggest contributors, since your opportunities are limited.  The average player gets less than half an RBI per game.  So, if you drove in two or three, that's excellent.  If you got more than one hit, that's probably a .400 average for the game, which is outstanding.  

In hockey, the best forwards may average half a goal per game.  So, even a single goal is twice as good as average.  For a one-goal performance to be inefficient, you'd have to have taken twice as many shots as normal, which I guess would be possible but unlikely (except maybe for Alex Ovechkin).  And, of course, if you score two goals, or three, you've definitely helped the team win.

What about football?  Well, maybe, for rushing yards, you have the situation where you also need to know opportunities, how often that running back was given the ball.  But for QBs, there's less of that.  QB totals usually include a completion rate, and a negative (interceptions) to go with the positives ("Andrew Luck completed 29 of 45 passes for 443 yards with four touchdown passes and three interceptions").  Moreover, the number of throws doesn't vary *that* much from game to game ... for 443 yards to be mediocre, you'd probably need to have thrown, I dunno, 75 passes or something?  And that doesn't happen much.

Even in basketball, it's not a problem if the numbers are exceptionally high.  If a player scores 40, he's probably had an excellent game.  To score 40 points and still be inefficient, you'd have to take a lot of shots.  That doesn't happen.  Last season, LeBron James had seven games of 35+ points, but had only one game with more than 30 field goal attempts.

So a high scoring game is almost certainly good.  But those middling games, the ones in the low 20s ... those are where you can't tell from just the number.  Those are the ones where what looks like a positive performance may be good, or bad, depending.  

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My guess is: in a world where every other high counting stat is a sign of a good performance, it's easier to carry the narrative along to Rudy Gay territory than to remember this rare exception.