NFL Survivor Pool Pre Week 1

Recently I got an offer to join an NFL Survivor pool.  The rules are simple:

1. Pick 2 teams to win each week.  Straight win, no spreads.  
2. In order to be eliminated, you must get 2 selections incorrect (in aggregate) during the duration of the pool
• Not to be confused with only being eliminated by getting 2 incorrect selections in same week
3. You cannot pick the same team twice in a season until all teams have been picked twice.  
4. Winner take all (all participants must be paid up before week #1 begins)

The problem I built a MILP to solve this and used ESPN's FPI as a sort of ranking method. 

I determined the 'odds of winning' for team A vs B as 

where HFA is a home field advantage if team a is the home team (HFA'=0 if the team is the away team).  FPI was also zeroed because there was some teams with a negative FPI.  Also because Oakland would have a zero FPI, I added HFA and a factor to 'bump up the score'

A mathematical integer program was developed to solve the conundrum surrounding rule 3: you cannot pick a team twice in basically a season.

The model is set up as a way to defer riskier picks (i.e. lower probabilities) to later weeks using the same idea of a discounted cash flow.  The model I came up with dictated I should pick CAR (@JAX) and CIN (@OAK) in week 1 versus a sure thing such as NE or GB.

The following table is the the overall picks I would make if I had to pick all 17 weeks in week 1.  

Week	Team 1 Pick	Opponent	Team 2 Pick	Opponent
1	CAR (60%)	@JAX	CIN (61%)	@OAK
2	BAL	@OAK	NO	TB
3	NE	JAX	SF	CHI
4	CHI	OAK	IND	JAX
5	BUF	@TEN	DEN	@OAK
6	GB	SD	MIA	@TEN
7	SD	OAK	WSH	TB
8	ATL	TB	HOU	TEN
9	NYJ	JAX	PIT	OAK
10	DAL	@TB	MIN	@OAK
11	DET	OAK	PHI	TB
12	NYG	@WSH	TEN	OAK
13	JAX	@TEN	KC	@OAK
14	ARI	MIN	CLE	SF
15	SEA	CIN	STL	TB
16	OAK	SD	TB	CHI
17	IND	TEN	KC	OAK

Of course as more information becomes available and the season progresses, we will get more information (updated FPIs and/or the possibility of new rating schemes) and be able to refine my choices for week 2 and beyond.

Note: this blog post was written before yet posted after week  1's games.  My bad.