It was another Raptors legendary moment. Down by one. Seconds left in the game. Facing playoff elimination. A little desperate.
RJ Barrett puts up a three-point attempt. It's slightly long, and bounces off the far rim. Meters up in the air. Floating for an eternity. Before finally falling back to Earth, and ... could it be ... landing right in the hoop. Raptors win!
The Raptors surely put up one hell of a game, and showed a lot of talent and skill. But that last shot? That crazy bounce? Did they maybe get just a little bit lucky, too?
As a statistician, I think in terms of margins of error. If Barrett's shot had been just 23 centimeters shorter, then it would have been a swish -- all net, no rim -- and left no room for doubt. Simple enough.
But suppose the had been just a little bit shorter, i.e. closer to the middle of the hoop. Not close enough to be a swish. But close enough to hit that far rim at a sharper angle, and bounce back a little bit more towards the shooter.
Could that sharper angle be enough for the shot to miss, and land back on the court with a big clunk and an even bigger Raptors loss? Yes, absolutely. So how much shorter would the shot have had to be, to miss in that sad way?
This is where I get calculating. That shot was measured to have bounced a whopping 2.1 meters high. The ball's radius is nearly 23 centimeters. And the diameter (width) of the rim is 75 centimeters. So, what does that tell us?
Well, if the shot had landed just over two centimeters shorter, then it would have bounced from that far rim at a slightly sharper angle -- about 1/2000 of a degree.
Over the course of the huge 2.1 meter bounce, that slight angle would make all the difference. It would shift the ball back towards the shooter, more than 75 centimeters back. And what would happen when it finally returned to rim height?
Yes, it might still hit the rim. But this time it would hit on the rim's near side, with the ball's center hanging out over the edge. The next bounce would then push it further from the net, not closer. No basket. Raptors lose. Playoffs over.
So, the next time you're wondering how lucky were those Raptors to snatch victory from the jaws of defeat with Barrett's shot last night, wonder no further. The answer is simple. They were 2.1 centimeters lucky.
Jeffrey Rosenthal is a professor of statistics at the University of Toronto, and the author of the bestseller Struck by Lightning: The Curious World of Probabilities.