OK. Take a look at 2013 week 1.
http://www.survivorgrid.com/2013/1
IND (-11) v. OAK was picked by 41% of the pool. NE (-10) @ BUF was picked by 18% of the pool. The next two were PIT (-6) v TEN and TB (-4) @ NYJ, picked by approximately 8% each.
Without going back and looking at the games, the right move would have been to put 1/2 on NE and 1/2 on IND. If we had diversified to PIT and TB, both of whom were lost - even if we had 2 picks each - we would have lost almost 1/4 of our picks, which would have put us behind the average pool.
In 2012, the top 3 picks won, and the fourth pick (picked by 5.3% of the pool) lost.
The math goes something like this. If you want the highest chances of getting all 21 picks through, you should only bet on one game. If you want the highest chance of getting 1 pick through, you should bet on all 16 games. The more teams you bet on, the less likely you will get all 21 picks through but the more likely you will get some picks through. It's really a trade-off. The question is which trade-off do we want. There is no right answer to this, but obviously people have different philosophies when it comes to this, which is why this week was such a clusterbomb in terms of voting.