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## About

There are 8192 different ways to fill out an NFL playoff bracket. This tool helps you guess how your friends will fill out their bracket so you can pick a bracket that exploits their shortcomings and give you the highest probability of winning.

### Assumptions

## Scoring

Scoring is hardcoded as:
1 point - correct wildcard round winner
2 point - correct divisional round winner
4 point - correct conference round winner
8 point - correct superbowl winner
## Game Outcomes

Game outcomes are modeled using FivethirtyEight's QB adjusted ELO rankings. See their methodology here. The ELO values used were pulled on January 12, 2023.
## How to

### Step 1 - Model Friends

Take a stab at modeling your friends' selection strategies you expect them to follow while completing their brackets.
Each friend can be modeled as a linear combination of the following pre-set strategies.

## Random

Your friend cannot be modeled.
She flips a coin on every decision, so all 8192 brackets are equally likely.
## Chalk

The favorite is picked in each matchup.
All the probability mass ends up assigned to the most likely branch (branch 129, to be precise).
## Pick Underdog

Your friend likes to mix it up, but rather predictably.
They decide in advance how many games (out of 13) they are going to go with the underdog.
This is operationalized by giving the underdog in each game an x/13 chance of being selected.
## Favorite Team

Your friend is for sure going to pick team x to go all the way.
For all games that do not involve team x they apply the Extremify algorithm (see below) to make their picks.
## Tossup

Your friend decides some games are too close to call, so they flip a coin.
The tossup games are identified with the parameter x.
If the probability of a team winning is within the range [0.5-x, 0.5+x], they will pick randomly.
Otherwise, they will pick the favorite.
## Extremify

Your friend looks at the odds, and let's them influence him (either a lot or a little).
Probability of picking a team is an extremified version of the probability of team winning through the equation P_pick = (P_win^x) / (P_win^x + (1 - P_win)^x).
Values greater than 1 mean more likely to pick the favorite, values less than 1 mean less likely to pick the favorite.
For example, if a team is 65% likely to win they are:
x = 0.5; 58% likely to pick them
x = 1.0; 65% likely to pick them
x = 2.0; 78% likely to pick them
### Step 2 - Calculate

The tool will take some time to model all of the possible ways your friends will fill out their brackets, all the possible brackets you could pick, and all the possible ways the games might actually play out. It will then show you the 5 best brackets with the highest probability of winning outright (ties are not considered a win).

### Step 3 - Implement

Pick the bracket you feel best about and use it at your own peril! Feel free to click around to change the brackets up and see what the repercussions are.

Some information on what's behind the curtain:

jacobw.xyz/projects/bracket_sim
Note: This site is not well written. Things probably won't work if you click while the calculations are running.