The Fifth Down had an interesting article this week on the importance of winning in week 1: 52% of the teams who win in week 1 make the playoffs, compared to 23% of the teams who lose in week 1.
We can break this down further by using my software. According to my software, teams that won have a 44 to 51% chance of making the playoffs and teams that lost as having a 25 to 30% chance. The reason that for the differences between the prediction of my program and the historical records is that all the teams currently have identical power ratings in my software. For my predictions, variation in each category comes from two sources. First teams that won on the road on week 1 will tend to be ranked higher than teams that won at home because they have a 8 home games remaining (each with a 58% chance of victory) and 7 road games remaining (each with a 42% chance of victory). The second source of variation is how your division foes did. Kansas City benefits because they won while all their division foes lost.
Advanced NFL Stats pointed out that the success of teams that win in week 1 can be attributed to two factors: 1) the benefit of actually winning the game and 2) the fact that winning in week 1 indicates the likelihood of winning in future weeks due to being a strong team. We can quantify these two effects as follows. Consider that at the beginning of the season, assuming all teams were equally rated, each had a 37.5% chance of making the playoffs. So based on the historical record the improvement in playoff odds during week 1 is 52-37.5 = 14.5%. Now if we take the software predictions as averaging a 47.5% chance of making the playoffs for week-1-winning teams, we can conclude that the effect of actually winning the game accounts for (47.5-37.5)/14.5 = 69% of the success of week-1-winning teams in making the playoffs. The remaining 31% of the benefit of winning in week 1 comes from the fact that you might actually be a good team.