Why probabilities?
The [BracketMatrix] takes seriously a fact than most models ignore: basketball is a random game. In a match-up between two teams, the same team isn't always going to win; granted, one team might have a higher probability of winning, but the outcome is never a certainty.
This has a tremendous consequence: even an omniscient observer who knows the true probability underlying the game cannot know the outcome of the game. The fact that no model is more than 75% accurate is not an accident: a coin, randomly (uniformly) weighted to prefer heads or tails, can be predicted with no better than 75% accuracy by an observer who knows how the coin has been weighted.
Basketball is a weighted coin: the [BracketMatrix] does not purport to predict games, but it will tell you how the metaphorical coin has been biased toward one team or the other.
How does it work?
The mathematics behind the [BracketMatrix] are, honestly, pretty tricky, and have been developed over the course of many years.
We don't want to give away too many secrets just yet, but we do want to hear what you think of the model thus far—do you notice some phenomenon that the model seems to be ignoring? Are there ways we could improve it?
Please contact us with your ideas at .
How well does it work?
As a test, let's use 222 games played between January 3 and January 8, 2007, using the previous day's [BracketMatrix] to predict the outcome. Of these games, 154 were correctly predicted, meaning the [BracketMatrix] was correct 69% of the time.
This doesn't sound very good.
But in fact, this is fantastic, and on par with experts and bookmakers. Remember, even if the true probabilities were known, the best we could do would be 75%.
How accurate are the reported probabilities?
Unlike most other models, the [BracketMatrix] takes the randomness of basketball seriously—it reports probabilities. Working with those same 222 games played between January 3 and January 8:
- Among pairings estimated between 50% and 60%, the [BracketMatrix] guessed correctly 61.8% of the time.
- Among pairings estimated between 60% and 70%, the [BracketMatrix] guessed correctly 60.0% of the time.
- Among pairings estimated between 70% and 80%, the [BracketMatrix] guessed correctly 76.5% of the time.
- Among pairings estimated between 80% and 90%, the [BracketMatrix] guessed correctly 83.3% of the time.
- Among pairings estimated between 90% and 100%, the [BracketMatrix] guessed correctly 68.4% of the time.
So roughly p% of those games that the [BracketMatrix] estimated to be won p% of the time actually are.
