Kobe Bryant’s Finger and Geometry

Kurt —  January 11, 2010

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Bill Bridges put this in the comments, but it is too good not to make its own post.

The accuracy required for a player to hit a mid-range jump shot, let alone 3 pointers is astounding. Consider this. The inside rim of the hoop is 18″ in diameter. The Ball is 9.54″ in diameter. If the ball lands exactly in the middle of the hoop, the distance between the skin of the ball and the hoop is 4.2″. Let’s assume that if the ball is more than 4.2″ away from dead center that the shot is more likely to miss than go in. 4.2″ is not a lot of room for error. Players cannot be so accurate by measuring their shots. Rather, the accuracy comes from over 10,000 hours of repetition during which the shot is generated not by intent, but by muscle memory.

Kobe’ problem is that while his muscles are making the same movements from memory (honed, in his case by well in excess of 10,000 hours), the splint/wrap is introducing volatility in the angle of the ball. Simply put, movement is perfect, yet he misses. To compensate, Kobe must adjust the shot. This adjustment completely negates the reliance on muscle memory. The shot is now aimed and adjusted and invariably misses.

To be as successful as he was shortly after the injury, he must have adjusted his grip rather than the motion. The grip + constant dimension and tension of the splint allowed Kobe to maintain the same motion with good results. But something has changed in the last few games and the shot is more volatile than before. The wrap is different. Or the splint is stiffer. Or the pain is such that Kobe cannot maintain an adjusted grip. Whatever the reason, the volatility of the shot has increased. This must mean that more of his shots are off- center. The more off-centered the shot is, the more likely it is to miss.

To refresh you of elementary trigonometry, let’s assume that that a direct line from the shooter to the middle of the basket is the adjacent side of a right triangle, the actual line from the shooter to the hoop is the hypotenuse and the distance between the middle of the hoop and the actual point of contact is the opposite length (or the “error”). (with me so far?). Then we can calculate the error resulting from an incremental drift in the angle of the shot from dead center when the shot reaches the hoop. If this error is in excess of the aforementioned 4.2″, the shot is likely to miss.

From 10 feet away (an ideal post-up turn around distance), a shot 1 degree off dead-center results in an error of 2.1″ – a make. A 20 footer, results in an error of 4.2″ – a 50/50 proposition. A three pointer of 24 feet results in a 5″ error – most likely a miss.

Now let’s assume Kobe’s shot is off center of 2 degrees. A 10 footer is off by 4.2″. 20 footer is off by 8.4″ – barely grazing the rim. A 3 pointer is an air-ball.

An error of 3 degrees turns even the 10 footer into a miss. Something has resulted in more of Kobe’s shots being 2 – 3 degrees off center.

I’ve even ignored the increased velocity that long-distance shots require. This serves to magnify the errors by increasing the kinetic energy of the bouncing ball. The same error factor is more likely to result in a miss for a long shot than a short shot.

If the volatility introduced by the splint is going to linger and be persistent, he has to change his approach.

– He needs to go back into the post and try to get more 10 footers than continue shooting from the perimeter

– On the perimeter, he needs to shoot more bank shots, ala Duncan. A bank shot serves to reduce the velocity and the net effect is akin to reducing the distance of the shot. (Newtonians note, this is due to friction, a frictionless system would have bank shots at the same level of accuracy as a non-bank shot).

He could also take a week or so off and, god forbid, let his finger heal a bit.

After the game last night, a reporter asked Kobe if it was crazy to think he would take time off. “Probably” was the response.

On another topic, Darius had these thoughts about Bynum getting touches and being more active, and if that should continue when Gasol returns.

Bynum is still a player that focuses (mostly) on how he can get his. This isn’t necessarily a bad thing (I love that he *can* get his and has developed into a pretty reliable post threat). But that (gunner-ish mentality) creates a trickle down effect for how efficient our offense can be – because even if Bynum plays at an efficient level (he does) what makes this offense elite is creating easier opportunities for others based off your own efficiency (i.e. drawing extra defenders and getting your ‘mates open shots).

So, in the end, while letting Bynum do his thing may get this team a more engaged and active player, what is the tradeoff? Less touches for a just as efficient (and even more helpful to his teammates) player in Gasol? Less easy opportunities for our guards and wings because they’re creating shots for themselves (like Farmar/WOW shooting pull up jumpers in the half court) rather than our bigs creating shots for them? I mean, this is what I’m seeing and while I’m not mad about it, I’m not ecstatic about the results either.