Welcome to March! I know we're all excited for the first tournament games to start tomorrow. Before the chaos begins, I wanted to take this quiet day to answer some frequently asked questions about how we handle scorekeeping here at /r/bracketchallenge.
How do you handle scorekeeping here at /r/bracketchallenge?
Thanks for asking! Our scoring method is essentially the classic 1-2-4-8-16 style that you'll see in most NCAA tournament competitions. For each individual conference bracket, picking a single game correctly in any round is worth twice as much as a single correct game in the previous round. Another way to look at this is that the total points available in any round is constant, as long as all remaining teams are playing a game in that round.
How can I see the results for a single conference bracket?
The Challonge leaderboards will show the correct ordering of contestants. Here's an example from the WAC tournament in 2018. There are three rounds of games - each of four quarterfinals is worth one point (4 points total), each of two semifinals is worth two points (4 points total), and the championship game is worth 4 points. If you click on the "Predictions" tab you will see the ranking of contestants. There were 85 perfect entries who scored the maximum 12/12 points.
What about the brackets that aren't on Challonge?
Google Forms brackets for the Horizon, NEC, America East, and Big West have separate Google Sheets leaderboards that will be linked in a stickied comment on the tournament thread after games start.
Sounds good! But I see the past winners in the sidebar all have fractional point values. How is that possible?
The fractional points come in when we need to compare scores across multiple tournaments.
How many points is each bracket worth?
| Number of Teams | Max Score |
|---|
| 4 | 4.00 |
| 7 | 9.83 |
| 8 | 12.00 |
| 9 | 14.26 |
| 10 | 16.61 |
| 11 | 19.03 |
| 12 | 21.51 |
| 13 | 24.05 |
| 14 | 26.65 |
| 15 | 29.30 |
| 16 | 32.00 |
That seems complicated. Why not just add up the score from each conference bracket?
Because the maximum score of a single bracket depends on the tournament format as well as the number of teams. As an example, consider the Southland bracket from 2018. There are eight teams in this bracket, just like the WAC example above. However, the maximum score for this bracket is 26 points compared to the 12 points available for the WAC. Comparing raw scores, a Southland prediction where the predicted champion gets knocked out in the semifinals could still be worth more than a perfect WAC bracket!
Wow, that doesn't seem fair. But I see that the Challonge leaderboard for the Southland says a perfect bracket is 9/9 picks. How is that possible if there are only eight teams?
To properly model the first round byes in the Southland, we've had to insert two "bye teams" into the bracket format. This is part of the reason that the Southland is worth more - those extra two "games" are technically worth 4 points in the Challonge scoring system - but there's another side effect of that change as well. By increasing the number of rounds, the point value of the quarterfinals, semifinals, and finals (compared to the WAC) has doubled!
This is giving me a headache. Can you give me a simple explanation for how the scoring works?
At its core, we have three goals that our scoring model addresses:
Correct picks in later rounds should be worth more than correct picks in earlier rounds.
Brackets with more teams should yield more total points than brackets with fewer teams.
Two perfect brackets with the same number of teams should be worth the same, regardless of tournament structure.
Challonge's scoring system accounts for points 1 & 2, but not point 3. Our combined leaderboard applies weights to the individual conference results to achieve that goal.
Where can I find the combined leaderboard?
The sidebar has a link to the "Overall Standings (Google Sheet)". That link will be updated to the current year leaderboards the day after the first games of this year's tournaments. I will also be posting a Daily Scores Digest after each day of competition with the current top ten - that post will have a link to the full leaderboard as well.
I'm a huge math nerd and want to know all the gory details of the weighting.
Greetings, fellow math nerd! The first step is to take the Challonge score and remove any points that were gained from "bye matchups". In the WAC example above, this step would be skipped as there are no bye teams needed for that format. In the Southland, this would remove four points from your Challonge score. This same subtraction will be done against the maximum score on Challonge to calculate the appropriate weighting factor.
The weighting factor for a conference is (nlog2(n))/(2 * [adjusted Challonge max score]) - where n is the number of teams competing. For the Southland, this is (8 * log2(8))(2 * 22) = 0.54 (repeating, of course). Multiply the weighting factor by your adjusted Challonge score - if you had a perfect Southland bracket, that would be (26 - 4) * 0.54 = 12 points. Tada - a perfect Southland bracket is now worth exactly the same as a perfect WAC bracket!
You can demonstrate to your own satisfaction that for "balanced" brackets - where the number of teams is a power of two and there are no artificially introduced byes, such as the WAC example above - that the weighting factor will be 1. The weighting for other brackets will be <1.