Based on opponent-adjusted generic win probability (GWP), the number of expected wins can be estimated for each team. Teams that have won more games than expected can be considered lucky, while teams with fewer wins than expected can be considered unlucky.
The list of NFL teams sorted from luckiest (positive numbers) to unluckiest is posted below. We would expect most teams to be within +/- 1.0 wins. So teams outside that margin can be deemed significantly lucky or unlucky.
| Team | GWP | Wins | Exp W | Luck |
| GB | 0.68 | 12 | 9.6 | 2.4 |
| CLE | 0.48 | 9 | 6.7 | 2.3 |
| SF | 0.14 | 4 | 2.0 | 2.0 |
| NYG | 0.50 | 9 | 7.0 | 2.0 |
| DET | 0.29 | 6 | 4.1 | 1.9 |
| ARI | 0.31 | 6 | 4.3 | 1.7 |
| NE | 0.88 | 14 | 12.3 | 1.7 |
| CHI | 0.25 | 5 | 3.5 | 1.5 |
| CAR | 0.33 | 6 | 4.6 | 1.4 |
| NO | 0.42 | 7 | 5.9 | 1.1 |
| DAL | 0.78 | 12 | 11.0 | 1.0 |
| BUF | 0.47 | 7 | 6.6 | 0.4 |
| MIN | 0.54 | 8 | 7.6 | 0.4 |
| SEA | 0.63 | 9 | 8.8 | 0.2 |
| OAK | 0.27 | 4 | 3.8 | 0.2 |
| PIT | 0.63 | 9 | 8.8 | 0.2 |
| HOU | 0.49 | 7 | 6.9 | 0.1 |
| TEN | 0.58 | 8 | 8.1 | -0.1 |
| IND | 0.86 | 12 | 12.1 | -0.1 |
| JAX | 0.73 | 10 | 10.3 | -0.3 |
| SD | 0.67 | 9 | 9.4 | -0.4 |
| WAS | 0.54 | 7 | 7.5 | -0.5 |
| KC | 0.32 | 4 | 4.5 | -0.5 |
| CIN | 0.41 | 5 | 5.8 | -0.8 |
| BAL | 0.35 | 4 | 4.9 | -0.9 |
| STL | 0.29 | 3 | 4.0 | -1.0 |
| TB | 0.76 | 9 | 10.6 | -1.6 |
| DEN | 0.55 | 6 | 7.7 | -1.7 |
| ATL | 0.36 | 3 | 5.0 | -2.0 |
| PHI | 0.61 | 6 | 8.6 | -2.6 |
| NYJ | 0.44 | 3 | 6.1 | -3.1 |
| MIA | 0.31 | 1 | 4.3 | -3.3 |
"Luck is just my shorthand for a random process, and I admit using the word luck may be misleading."
I think you should do away with this "stat" and report. This seems to be the difference between your predictions and the actual results. Writing this difference off as "luck" or unaccountable random events conveys the message that your model is perfect and any outcome that differs is because of random events.
I have a prediction model too. It's throwing darts at the schedule. Whenever my model is wrong it is because of a series of random events which I'll call luck.
Either that or you've found statistical proof that God is a Packer fan. I'm OK with that.
You just don't like it because the Packers look so lucky!
But you're absolutely correct--the model's error can't be written off completely to randomness. But certainly some of it can. The question is how much. I think the answer is 'at least most of it.'
All outcomes in sports are partially affected by random processes. If they didn't, we'd almost always have at least one undefeated team and one winless team every year.
From previous research (not just my own), we know that on average the "better" team (however you reasonably choose to define that) wins about 75-80% of the time in the NFL. (We can basically test how much the actual win distribution differs from a true binomial distribution. The difference is the "true performance" component and the binomial component is the "luck" component--no models necessary, perfect or otherwise.)
If my imperfect model can predict outcomes correctly at a 70% rate, that leaves about 5-10% of outcomes not accounted for by other factors, and 20-25% of outcomes accounted for by randomness. These things would tend to even out over a long season, but the NFL season isn't long. It's only 16 games, so we should expect some teams to benefit more than others by luck.
Loosely put, the luck value I calculate is an estimate with a margin of error. The Packers really could be +2.0 "lucky" or +2.8 "lucky." But we do know that throughout recent NFL history, accounting for opponent strength, teams with the same level of in-game performance won 2.4 fewer games than the Packers have so far.
There are statistical methods to test and verify the random component. The error is uncorrelated with other factors, comprises a Gaussian distribution, and is homoskedastic.
Actually, Favre has carried my fantasy team almost all year. I'm in my league's championship game this weekend, so I need some of that luck to keep coming in the late-December Chicago weather.
Good luck with your darts. Let me know how that's been working for you.