So let's go in order of depth.
First, basic probabilities: teamrankings.com has some phenomenal pre-selection simulation projections for the tournament, giving individual probabilities for each team making it to round X.
From these we can find AVERAGE PROJECTED WINS: simply sum together each of the 6 probabilities to find the mean-expected wins each team will have in the tournament.
From this, we can do some theory: given that team x wins at least y games, how many wins will they THEN be projected to have; I call this "Average Projected Wins with X games secure." This would be estimated like so:
=Y games won + sum(probabilities of the rest of the tournament)/(probability of winning Y games)
So for two games secure, the math would be:
=2 + sum(probabilities of winning the 3rd,4th,5th, and 6th games)/probability of winning in the second round)
From this, we can get a hybrid statistic, that I like to call Volatility: this is the marginal wins gained from winning any specific round of the tournament, TIMES the probability of winning that round. We do this by subtracting "X games secure" from our starting average (zero games secure).
For example, one team's volatility in the first round would be:
=[(2-win secure average wins) -( 0-wins secure average wins)] * odds of winning those first two games
From this, we can get a hybrid statistic, that I like to call Volatility: this is the marginal wins gained from winning any specific round of the tournament, TIMES the probability of winning that round. We do this by subtracting "X games secure" from our starting average (zero games secure).
For example, one team's volatility in the first round would be:
=[(2-win secure average wins) -( 0-wins secure average wins)] * odds of winning those first two games
The first three rounds are the ones that tell us the most information, later rounds are skewed by higher-quality teams having much higher odds of winning the games beforehand. On the right are the top ten teams by "first round volatility," considering the projected fielding of teams.
This tells us, roughly, which team will benefit the most if they can overcome early obstacles. A better utilization of this method would be to subtract from the ESPN National Bracket "average wins" rather than my statistical "zero wins secure average." This gives us a better picture of which team will do better than expected by most, and therefore, which team will help you destroy everyone in your office pool!
This tells us, roughly, which team will benefit the most if they can overcome early obstacles. A better utilization of this method would be to subtract from the ESPN National Bracket "average wins" rather than my statistical "zero wins secure average." This gives us a better picture of which team will do better than expected by most, and therefore, which team will help you destroy everyone in your office pool!
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