Tourney odds are calculated using a Monte Carlo Simulation. Actually, multiple Monte Carlo Simulations.
Basically, every remaining game has a projection from the model of what percent of the time each team *should* win. The simulation then uses a random number generator to pick a winner for that game. So, if your team is a 75% favorite, when the random number is 1-75, it’ll pick you to win. If it’s 76-100, it’ll pick you to lose. It then does this for every game in the state and generates Heal Point Standings based on those results. If you do this enough times, you will end up with every possible combination of Heal Points. Of course, that’s a LOT of times. Normally, you would do 10,000 simulations, but since this is actually multiple Monte Carlo Simulations built inside of a larger one, I find my computer can do 1,000 without completely bogging down to the point of being unusable.
The process is then repeated using a 50/50 prediction for every game, which creates more combinations where the 0-14 team actually wins their final 4 games.
So, when the Tourney Odds say that you’re 42% to get the 3 seed, that means that in 42% of the simulations using the model’s predictions, you ended up in the 3 seed. Simple enough.
The Best and Worst Case Scenarios come from the 50/50 simulations, as they tend to find more of the outlier combinations.
If both simulations agree on your tourney status, it’ll say you’ve clinched. It IS possible to “un-clinch” if the next time I run the random number generator, it finds a new combo that it had previously missed. Again, there’s a LOT of different combos. Short of spending over $6K on a custom program that does all this instantly, that’s the best I can do.
Let’s use an example:
Here’s B North on 12/29/19. We’re going to focus on Ellsworth.
The Model thinks Ellsworth is in the tournament, but the 50/50 simulation disagrees. Essentially what that means is that Ellsworth is *probably* in, but if everything falls apart, they could still miss. Say the entire team gets mono or fails Algebra or their parents decide to join the circus and they have to move. Whatever really bizarre thing you can think of. But that’s probably not going to happen, so Ellsworth is essentially in. Still, coaches get paranoid about these things, which means THERE’S WORK TO DO.
The S1 6.6% means in 6.6% of the simulations, Ellsworth gets the #1 seed. In 22.3%, they get the 2 seed. And so on.
Here’s the rest of Ellsworth’s season:
The Bapst game is a great example (whenever that gets played). The Model says Ellsworth wins that 95.7% of the time, so in the 1,000 simulations, they win in 957 of them and lose in 43. In the 50/50 simulations, they win 500 and lose 500. This opens up way more bad scenarios for Ellsworth (and good ones for Bapst), so that’s what we use to say if a team clinched. But the model is pretty accurate, so if it says Ellsworth is going to win 95% of the time, they’re going to win.
The 50/50 simulations give us Ellsworth’s Best/Worst case:
But Ellsworth is currently 4-1. They *could* go 17-1 or 4-14, but the 50/50 model didn’t find any of those combinations this time around. Of course, it’s early, so it still could. Tomorrow it could find them. And that’s how a team “un-clinches”. If 5-13 was enough to get Ellsworth in, it’d call it and maybe tomorrow they’d be back out, but it’ll probably work itself out in a week or with their 5th win.
As we get closer, this gets more concrete.