This article is an example of something I’ve seen slowly becoming more common which is a little frustrating: acting like you are using science to explain something by just throwing out random measurements and misunderstanding the formulas they’d be used in. Here Rhett Allain writing for Wired clearly is very frustrated that Lebron is once again being called a flop artist after this lovely play in last weeks evisceration of the Cavaliers by Durant and his Warriors. Lets walk through this.
So we start off with a brief writeup of the most basic principle in physics, a description of force between two objects colliding. We get a quick humble brag and then him showing a lovely little graph which he’s created based on knowing the frame rate of clip and using the known dimensions of an NBA court as reference points. He gives no explanation of what we’re seeing, or even what the units are. The axes are helpfully labeled x and t so at least we can guess it’s a position versus time graph if he’s following conventions.
He gives us one verifiable data point, the listed weight/mass of the players. From there, he uses the equation for momentum (Momentum = mass times velocity) to derive the relative momentum of each player before and after the collision.
“Before the collision, the total momentum for the two players was 910 kg*m/s and after the collision it was 554 kg*m/s. The total momentum decreased. Does this mean there was a flop on the part of LeBron? Not necessarily. It does mean that there must at least be an external force during this collision. It’s possible (and even likely) that Draymond was pushing significantly on the floor in the negative x-direction and this would change the total momentum of the system (Draymond plus LeBron).”
Does it mean that? Turns out humans are not frictionless point masses. As animate beings, humans can exert force in a number of different directions and at different angles and rotations. The whole question is not just if Lebron deliberatedwas adding an external force to the equation, but if he was doing so in a fashion which would accentuate the contact and make it look excessively violent. To put this in some perspective, the amount of variables introduced by the seams of a baseball make it impossible to accurately predict the trajectory of a curveball due to the complexity of how the atoms in the space we consider empty are interacting with those seams. Nothing of value can be derived about this situation using just the four “measurements” we’ve been given so far.
“OK, so here’s what I think. Yes, Draymond hit LeBron (that seems clear). Draymond used his foot to exert a force on the system of both players and this changed their momentums. Did LeBron throw up his hands to emphasize the hit? Maybe, but it doesn’t matter—he was still hit. The end.”
Well, of course there was contact! He says himself that seems clear. This was deemed a flagrant foul. From the rule book: “A flagrant foul-penalty (1) is unnecessary contact committed by a player against an opponent.“ How much change in momentum is unnecessary contact? Are those concepts even related? So these “calculations” have really been a waste of everyones time.
“THIS IS ONE of my jobs. When there is something that happens, I have to do an analysis—the internet needs me. In this case, it’s a hit between Draymond Green and LeBron James. Was it a hit, or did LeBron flop? I’m not the judge, I’m just going to present evidence.”
Brutalizing physics and the game basketball is not presenting evidence.