pseudo Smith Set

Tracking the Smith Set - 2010

© Copyright 2010, Paul Kislanko

In election methods, the "Smith Set" is the subset of all candidates that individually have an advantage against all candidates outside of that set. We define a "pseudo-Smith Set" for FBS as the list of teams that are undefeated, or whose only losses are to undefeated teams (or to teams whose only losses are to undefeated teams.)

After two weeks almost all of FBS is still in the Smith Set. You can see how this works - after week 1 every team is either 1-0 or has only lost to a team that is 1-0. After week 2, all teams are 2-0 so are in, or 1-1 with the loss being to a 2-0 team, or 0-2 with losses to the 2-0 teams or one of those and to one of the 1-1 teams whose loss is to a 2-0 team.

The (pseudo-) Smith Set can only become smaller as the season progresses, and at some point it may cease to exist. We'll track it, along with some related items here.

Division 1 Connectivity: This report summarizes the number of other D1 (FBS+FCS) teams that can be related to each team by an A↔B<↔...↔Z chain, where ↔ means "played." When every team can be related to every other team, it is said that the field is connected. The links are to the teams' pages that describe the directed games graph, where A→B→... means that A has a win over B.
D1 pseudo-Smith Set through week 2: All teams that are undefeated or whose only losses are to undefeated teams.

I'll provide updates more or less weekly, especially for the FBS version:

Week FBS pseudo-Smith Set FBS Connectivity

2 Week 2 Connectivity week 2

6 Week 6 Connectivity week 6

7 Week 7 Connectivity week 7

8 Week 8 Connectivity week 8

9 Week 9 Connectivity week 9 Down to eight teams after 30 Oct games.

10 Week 10 Connectivity week 10

11 Week 11 Connectivity week 11

12 Week 12 Connectivity week 12

13 Week 13 Connectivity week 13

Week	FBS pseudo-Smith Set	FBS Connectivity
2	Week 2	Connectivity week 2
6	Week 6	Connectivity week 6
7	Week 7	Connectivity week 7
8	Week 8	Connectivity week 8
9	Week 9	Connectivity week 9	Down to eight teams after 30 Oct games.
10	Week 10	Connectivity week 10
11	Week 11	Connectivity week 11
12	Week 12	Connectivity week 12
13	Week 13	Connectivity week 13

As more games are played, the pseudo-Smith Set can only become smaller. It is interesting to watch the progression of "good wins" becoming inconsequential, or "good losses" turning into bad ones.