A few comments on the Will Hill progressive:
Its not a particularly easy analysis to accurately estimate EV because with this high payout, multiple winners become much more likely. First let's look at the recent history to estimate how many will play this week. Two weeks ago, the "pot" was $57,180 and last week it was $76,815. Using Rule #4, the 80% of wagers added back rule, about 4908 tickets were played 2 weeks ago and 7622 tickets were played last week. The over $100k payout will probably attract well over 10,000 tickets, let's say around 12,000. Many of these will be mutually exclusive picks by the same person, reference FrankB above, who clearly don't want to replicate cards.
I entered the contest two weeks ago with 32 tickets (total cost $160), but hedged on 3 early dogs (took points + small ML bets) that had MLs of around +300 or so. I used all the big favorites with the strategy that the chance of multiple winning entries was going to be small. Unfortunately, I had the Texans who lost to the Rams but my hedges salvaged most of the cost of the progressive. I manually filled out the cards after creating a written table of all the possible number combinations that I wanted. I did 2 stages: first, I filled in all the static "picks" (10 games that I only ever had one side) for all 32 cards and then secondly completed the variable picks, checking off each combo as I finished that card. Overall (including running tickets through the writer) took about 47 minutes which means its roughly 90 seconds per card vs. FrankB's app entry of 15-20 seconds per card.
Now, to some math.
Let's take the fair ML approximation of each game to represent actual probability of winning the game on the progressive card. Just for classification let's say there are two Very High MLs (49ers and Broncos > -700), three High (Saints, Packers and Seahawks > -420), 4 Medium (> -200) and 6 Low. Using the fair MLs, the "fav" only 15 team parlay hits at roughly 329/1 or about 0.30% probability. Changing the 49ers pick to the Jags puts the ML parlay at 3926/1 or 0.025%. The real question for the EV calculation is not how many picked the 49ers vs those who picked the Jags, but how many more winning tickets would have had the 49ers than the Jags. We can assume that it is almost certain that, if someone gets all 14 games plus the Jags correct, they will be the only winning ticket. Now, we know that 6 games are virtual coin flips so our 12,000 entries are randomly going to produce roughly 190 tickets alive after those games. The 4 Medium favs, even if heavily distributed toward the favs, should reduce this to about 30 tickets. The 3 High and other Very High picks might reduce this to 20 tickets. So an EV (all fav) would be 0.003*107K/20 - 5 = 11 vs EV(jags + all other fav) 0.00025*107K - 5 = 21. Thus, the before tax EV return would be higher by taking the Jags with a roughly 8% chance of winning, but the after tax return (say 35% marginal tax bracket) might just be more of a push.
These assumptions and analysis are by no means complete, but just provide a starting point for some further thought.
