Wednesday, March 03, 2010

An Eight-Team, Five-Game League

First off...even though I'm discussing this in the context of our curling league, this situation could apply to any league, sports or not. So just because you don't care about curling doesn't mean you won't find this interesting, at least if you like math and/or problem solving. This post isn't really about curling, per se.

I don't know if I've really spelled this out before here, but over the last six months, I have been the official Triangle Curling Club League Coordinator. This means I'm in charge of creating and maintaining league schedules and standings. Considering that I've been making up my own sports leagues since I was 8 years old (give or take), I think this job is a good fit.'s the deal. Starting in late March, our club is conducting two concurrent leagues. Each league will have eight teams, and each team will play five games. Here's the question: given the eight-team, five-game restriction (which can't be changed), what's the best way to format the league and determine the champion? (And yes, there HAS to be a champion. Otherwise, what's the point?)

Our previous league was an eight-team, four-game league. Here was my format for that league, which worked out pretty well:
- Teams were randomly separated into two groups of four teams each (Group A and Group B).
- The first three weeks, each team plays the other three teams in its group.
- The fourth and final week, the 1st place teams from each group played for the league championship, the 2nd place teams from each group played for 3rd place overall, the 3rd place teams played for 5th place overall, and so on.

Moving forward to the eight-team, five-game leagues, here are two formats I'm considering. Format #1 is similar to the four-week format, except with an extra week of "playoffs". Format #2 is a simpler round-robin format; best record after five games wins.

--Format #1--

- Teams are randomly separated into two groups of four teams each (Group A and Group B).
- The first three weeks, each team plays the other three teams in its group. (Note that teams play one game per week, so the terms "week" and "game" can be used interchangeably in this context.)
- "Playoffs" start the fourth week with the following four games:
Game 4A: 1st place Group A v. 2nd place Group B
Game 4B: 1st place Group B v. 2nd place Group A
Game 4C: 3rd place Group A v. 4th place Group B
Game 4D: 3rd place Group B v. 4th place Group A
- The season concludes with the fifth week of games:
Winner Game 4A v. Winner Game 4B for 1st place overall
Loser Game 4A v. Loser Game 4B for 3rd place overall
Winner Game 4C v. Winner Game 4D for 5th place overall
Loser Game 4C v. Loser Game 4D for 7th place overall

--Format #2--

- Each team will play five different teams over the five-game league. The team with best record over the five-week season wins the league.
- In order to prevent a college-football-like situation where we end up with two undefeated teams at the end, Week 5 matchups will not be determined after Week 4 is complete. Week 5 matchups will be set this way:
-- The 1st place team will play the highest ranked team they have yet to play.
-- The 8th place team will play the lowest ranked team they have yet to play.
-- The remaining two games will also be chosen so that nobody plays the same team a second time, with preference given to matching top teams with other top teams and vice versa.
(Note that it is possible to set up the schedule for the first four games ahead of time so that there can be no more than two undefeated teams after Week 4.)

So, there you have it. Which format is best? Let's look at the 'pros' and 'cons' of each.

- Format #1 is a more exciting, tournament-style format, and since we are trying to capitalize upon the "Olympic Rush", it may be best to have an Olympic-style league. On the other hand, Format #2 is easier for non-sports fans to understand, even if the matchups for the final week aren't set in advance. Format #1 will also give us a definitive, winner-take-all league championship game; Format #2 may or may not give us that.
- With Format #1, everyone will walk out of the rink the final week already knowing exactly where their team finished in the league. I think teams like to know that sort of thing. ("Yeah, we finished 4th!") With Format #2, most teams won't know where they finished until they look up the league standings after the fact, and they'll probably forget to do that. Even so, while Format #1 is a fair way to get a champion, it's not necessarily fair when determining the middle places. For example, it is mathematically possible for a 1-4 team to finish in 4th place, while a 4-1 team finishes in 5th. You won't get that in Format #2, since the only thing that determines the final standings is final league record.
- With Format #1, four teams will be eliminated from championship contention after the third game, but will still have two more games to play. This may discourage some folks on those four teams from showing up the last two weeks. Teams will be systematically eliminated from championship contention in Format #2 as well, but it's less dramatic and not as demoralizing. I think in Format #2, eliminated teams will be more likely to show up the last two weeks since they'll still be playing normal round-robin games just like everyone else, as opposed to being stuck in Loser's Bracket Purgatory.
- With Format #1, you might end up playing the same team twice, even though there are still three other teams you haven't played at all. With #2, you'll play a different team each week, guaranteed; that might be better given the social nature of our club.

"So, Chris...I see this is obviously a tough decision. Why not compromise and have a four-week round-robin followed by one week of definitive playoffs?" For some reason, that format just didn't sit well with me. The three-week round-robin plus one week of playoffs was nice, because each team played a balanced schedule, and nobody played the same team twice. Adding in an extra week of round-robin play would unbalance the schedule and allow for the possibility that you'll play the same team twice. From a mathematical and practical standpoint, Formats #1 and #2 are both better, in my opinion.

So, I think both Format #1 and Format #2 are perfectly legitimate ways to determine a league champion. Really, I think it comes down to this: Format #1 is more competitive and exciting; Format #2 is more laid-back and friendly. Which is more appropriate for our club's purposes? As much as I like Format #1, right now I'm leaning towards Format #2. But I still have three weeks to decide, so until then, feedback is more than welcome.

1 comment:

James Allen said...

Format #1 = NFL
Format #2 = BCS


Decision made.