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Mike Beuoy and Reuben Fischer-Baum have created an interesting post at fivethirtyeight.com that uses Vegas odds over the course of the season to create a ranking that is then used as the basis for multiple simulations of the remaining season, in order to quantify the playoff implications of each game this week, to each team in the NFL. The link itself has already been submitted to /r/nfl, but I nonetheless thought it might be helpful to display some of that information in table form in a self-post. I also added some additional information to the table, including betting lines (per footballlocks.com) and game times.
All Remaining Games of Week 7, ranked by influence on playoff picture
*Note that this portion of the OP was not updated after Thursday night's game, so these percentages are somewhat out of date.
Points of Interpretation about the above table
"Cumulative Influence on Playoff Picture" corresponds to what the authors of the original post called "Leverage". The authors of the OP did not go into detail on how this percentage is calculated, but it probably corresponds to the differences between any two playoff scenarios A and B, weighted by the likelihoods of each given scenario occurring. The OP claims to take playoff seeding into account as well, but I'm not sure precisely how that fits into the picture.
Games that are featured by the schedule to one degree or another (i.e. the non-1:00 games) have their times bolded in the above table.
It's important to note that ranking was taken into account in the simulations that this table was based on. Thus, for example, Denver is considered to have better odds of making the playoffs than San Diego, despite being below them in the division standings, because the betting public has rated them a better team over the course of the season thus far.
The above explains some otherwise odd results, such as why San Diego's game matters very much to San Diego and Kansas City, but very little to their division-mate, Denver. Note that for purposes of deciding how much it cares about the other games, Denver assumes that it will probably win its next game, but for purposes of deciding how much they care about the game they are playing, SD and KC cannot make the same assumption, since their next game is the game in question.
Similarly, "Cumulative Influence on Playoff Picture" reflects the difference between the playoff pictures if team A wins and if team B wins, but does not take into account the probability of each outcome. This suggests the possibility of another ranking that ranks games, not simply by the net impact they have on the playoff picture, but the impact they can be expected to have on the playoff picture, taking into account the likely outcome of that game. Alas, the OP did not include this information. Perhaps some future week.
Points of Interest about the above table
GAMES
MOST/LEAST IMPORTANT: The most important game of week 7 is New Orleans (2‑3) vs. Detroit (4‑2), in which 12 different teams have a rooting interest. The least important is Tennessee (2‑4) vs. Washington (1‑5), which matters only to those hapless teams, and not very much to them. However, there are no truly irrelevant games in Week 7.
MOST IMPORTANT TO ANY ONE TEAM: While the above two games are also respectively the most and least cared about, in general, the number of teams that care about a games outcome does not strictly correspond to its overall importance to the playoff picture. For instance, Kansas City (2-3) vs. San Diego (5-1) is the third-most-important game, despite only having an impact on 4 teams, presumably because of how much it means to the teams playing it. This game is more important to San Diego than any other game to any individual team.
MOST CARED-ABOUT IN BOTH DIRECTIONS: The second-most-cared-about game, which 11 fanbases have an interest in, is Miami vs. Chicago. This is also the game with the most teams rooting for the less-popular side: 4 teams are rooting for Chicago in this game, with even more rooting for Miami.
MOST-HOPED-FOR OUTCOME: Assuming that a team always roots for itself, even when it has nothing to gain by winning the game, 10 teams are rooting for Oakland to beat Arizona this week, with only Arizona rooting for itself.
TEAMS
LONERS: In addition to abovementioned Arizona, the following teams are all loners this week (i.e, nobody but themselves is rooting for them): San Francisco, Seattle, Cleveland, Buffalo, Houston, and Dallas (ordered by how many teams are rooting against them). As a rule these are pretty good teams (since those tend to pose threats to the rest of the league), so if your team is on this list, you can pat yourself on the back. Yes, the entire NFC West besides St. Louis is on the list. Before their game was played, New England was a loner as well. Washington and Tennessee are technically loners too, but only because neither of them poses any threat whatsoever to the rest of the league and they are playing each other.
POPULAR: Counting this as "# teams rooting for/# teams rooting against", the most popular teams this week are/were Oakland, Denver, Saint Louis, Jacksonville, Minnesota, Pittsburgh, NY Jets, Indianapolis, and NY Giants, in that order.
COULDN'T CARE LESS: Oakland (0‑5) and Jacksonville (0‑6) share the dubious distinction of having no reason to care about the results of any games played this week, even their own, as they have virtually no chance of making the playoffs at this point in any case. Tampa Bay (1‑5) doesn't care about any of this week's games either, but is not playing a game of its own.
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