Summer Hat League
- Field Permits
- Swiss Scoring
- Other years: 2006 2007 2008 2009 2010 2011 2012
We are going to try using a Swiss scoring system to schedule the “regular season” games and for the seeding into playoffs this year. The goal is to maximize the number of challenging games against evenly matched opponents and to improve the accuracy of seeding into playoffs.
This season there will be six regular season games and three weeks of playoffs. At the end of the regular season, the teams will be ranked for seeding into the playoffs. The playoffs will be a 12-team modified single-elimination format. All teams will have a game each week of playoffs (a few teams will have double-headers on some days.)
This swiss scoring scheme is a combination of the scoring scheme commonly used for chess tournaments, with ideas from various other places, including the Windmill Windup tournament in the Netherlands.
For the first week, games will be assigned randomly. After each week, teams are ranked (according to scoring rules described below), and paired to make the matchups for the next week. In general the top ranked team will play the second-ranked team, and so on down the line. (The pairings may be shuffled, however, in order to avoid repeat match-ups.)
Since this scoring system is an experiment, worthwhile modifications to these rules may become apparent as the league progresses. To this end, the league coordinators have to power to modify these rules as they see fit.
Also, wherever there is ambiguity in these rules, the league coordinators have god-like final word in their interpretation.
Each week, teams will be ranked first by the total number of games that they have won so far (ties count for one-half.) After total wins, the tie-breakers are, in order:
- Opponents Wins: The total wins scored by all of the teams opponents so far. (Again, ties count for half a point.)
- Victory Points: The total number of victory points (VPs) earned by the team. Victory points are a modified version of the game point differential. See below for more.
- Opponents Victory Points: The total number of VPs earned by the teams opponents.
- Head-to-head record. In a two-way tie, if one team has beat the other in a game, they win the tie-breaker. See below for details on how multi-way ties are handled.
- Coin flip. If/when it comes down to this, the league coordinators may introduce additional tie-breaking criteria in order to avoid the arbitrariness of the random tiebreaker. (See "LC Rule", above.)
After the first week’s games, scores will be tabulated, and teams ranked and paired for the next week’s games.
Similarly, after the second weeks games, teams will be ranked and paired for the week three match-ups. And so on...
In general, the top-ranked team will be paired against the second-ranked team; the third-ranked will be paired against the fourth-ranked; and so on, down the line. No repeat match-ups are allowed during the regular season, however, so as the season progresses, some shuffling of the pairings will be necessary.
The pairing procedure to be followed is:
- Pair the top-ranked with the next-highest ranked team which has not yet been met.
- Pair the highest ranked unpaired team with the next-highest ranked viable team. (Here, viable means the team has not yet been played, and is unpaired for the current round.)
- Repeat step 2 until all teams have been paired.
If, during this process, one gets stuck, back up one step and redo the previous pairing skipping one extra viable team in the rankings.
After each game, teams are assigned “victory points” (VPs) based on the point differential of the game.
In the case of a forfeit, the winner gets 20 victory points, the loser (forfeiter) gets one less than the minimum number victory points scored by all other non-forfeiting teams that week (with a minimum of zero — a team can never lose victory points.)
(Captains: When reporting scores on the web site, please score forfeits as 1–0.)
On the Head-to-Head Tie-breaker
In the case of multi-way ties the head-to-head results can be ambiguous with respect to tie resolution. In order to avoid confusion, here’s the procedure.
- Construct the directed-graph of all the head-to-head matchups pertinent to the tie be resolved. (The nodes of the graph correspond to teams, the edges correspond to games.)
- Identify any cycles in the graph (e.g A beat B, B beat C, C beat A).
- Discard from consideration all matchups involved in those cycles.
- Infer any unambiguous ordering from the remaining matchups. For this step, transitivity can be assumed to hold. I.e. if A beat B and B beat C, A can be assumed to have beat (or be able to beat) C.
Three-way tie, A>B (A beat B), A>C → A>[B,C] (A wins, B and C still tied. (Go to next tie-breaker to resolve B-C tie.
Three-way tie, A>B: not enough information to rank C with respect to A or B; ignore this tie-breaker.
Many thanks to Steven Kwan for extensive email discussions which led to a great improvement of these rules over their originally proposed form.