Create Pairwise calculation

[grjanke]

I'll jumpstart this.

Pairwise Criteria

My proposed criteria are based off of college hockey. Ties are broken with ELO.

• ELO - 1 pt for winner (replaces RPI)
• Sum of win-pct vs common opponents - 1 pt for winner
• Head to head wins - 1 pt per win

Issues to Address

• Who makes up the comparison pool? In college hockey it is simple, since there's a clear boundary between Division 1 and other divisions. We don't have that benefit. I propose that our comparison pool consists of all teams that display in the ELO ratings, but we have to be comfortable with that pool changing over time.
• How are ties broken if ELO is also tied? ELO uses integers, so it is more likely that ELO ratings are tied than it is that RPI ratings are tied. I propose that there is no second tiebreaker. If teams are still tied after ELO comparison, they are considered equals, and neither gets a PWR point.

[matttrenary]

Elo doesn't use integers. We just display them in integers for easier viewing. So ties are unlikely. However, if there is a tie, I'd assume both teams would get a half-win, rather than giving neither team a win.

[matttrenary]

As for determining who is included in the comparison pool, I agree that it should be anyone included in the Elo list.

We should consider a minimum number of games to be included, but Pairwise doesn't need to wait.

FIDE uses a 5-game minimum. Current 15s game breakdown for <= 5 games: 5 games: 14 teams 4 games: 5 teams 3 games: 11 teams 2 games: 6 teams 1 game: 25 teams

[grjanke]

I don't know exactly how FIDE works, but I imagine there's an element of randomness in game selection, so they feel confident in giving players ratings after 5 games. I think 5 games would be enough for us, but only if teams have played a variety of teams / some non-conference games in that sample.

California Lutheren has played 5 games, but all are against conference opponents who have also played <= 5 games. No way should they be included.

I bet 5 games is enough if its required that one of those opponents is connected to the "broader web" of Division 1 teams?

[matttrenary]

I'm pretty open to whatever works here. I'm not too concerned since this issue will become less of an issue over time, and generally only impacts lower-rated teams. But having clear criteria (and code) is going to help.

[grjanke]

I'm going to finally take a crack at implementing this.

Timeframe There should be a new Pairwise Ranking each school year. This gives teams a fresh start. Note that ELO still won't reset each school year (unlike RPI), but that's okay.

Tiebreakers I've changed my mind on this. Instead of using ELO as the end all be all tiebreaker, we should use the following order:

1. Head to head wins
2. Sum of win-pct vs common opponents
3. ELO

I think it's best to reward teams on what they've accomplished against each opponent that year. If two teams are next to each other in the rankings, let's bump up the one who has the head to head win!

With more than 100 teams and only a dozen games each year, ELO still has a ton of say in the rankings.

Obviously we can experiment with this after implementation. I'm just documenting my thought process.

[matttrenary]

Sounds good. We should even consider using your order outright. i.e., if team A went 1-0 vs team B during the season, that's it, team A wins the pairwise. If they didn't play, then you just look at win pct vs common opponents. If no common opponents, Elo.

Or... You use Elo ratings gained/lost for all of these.

1. Elo gained/lost in head to head games
2. Elo gained/lost vs common opponents
3. Elo

This gets a little bit away from "most deserving", so is just a thought for experimenting.

[grjanke]

This is almost done!

• Right now we apply the criteria in order outright!
• However, if two teams are tied in final PWR, ELO is the tiebreaker there.
• All ineligible teams are listed below eligible teams in the rankings, which makes sense since they have 0 PWR.
• We still have to separate out rankings by each season.
• I'm going to test my code for bugs later when I'm not tired.

[grjanke]

I fixed the final PWR tiebreaker. Now, we run a mini pairwise between the tied teams. If they are still tied (rare), then ELO is the last resort.