I think you are trying to hard to make a distinction that really isn't all that meaningful. Missing a field goal is luck but stepping out of bounds isn't? Nonsense. The reality is that sometimes field goals get missed, even easy ones. Things like that happen in each and every game by both teams. Bad calls, strange bounces, uncharacteristic mistakes. They seem out of place in the context of that one individual player or game but overall the "lucky" plays are probably fairly consistent from game to game.
The loser's lament of "well that isn't going to happen again!" is probably true in the sense that that particular circumstance won't happen again, but chances are some other "luck" based adversity will. The question is how you react and recover from it. Good teams tend to deal with them better.
In truth, not only are "lucky" plays not consistent from game to game, they can actually remain skewed for large chunks of the season -- it can sometimes take 2 or 3 whole seasons for aberrant luck to revert to the mean. That said, assuming reversion to the mean is still always a more effective model for prediction.
The Jets, actually, have long been the poster-boy beneficiaries of this kind of luck. At some point last season, there was talk about Sanchez having shown improvement, as demonstrated by a dramatic drop in interception percentage. Someone at FootballOutsiders noticed that there had been a corresponding increase in passes defensed, went back and looked at the tape from the games, and determined that opposing defenders were getting their hands on Sanchez' passes just as often, they just happened not to be catching as many of them -- something that the Jets had no control of, and thereby, as far as they are concerned, luck.
Another example of quantifiable luck is opponent's adjusted FG%. Not counting blocked or tipped FG's, a team can expect opposing kickers to hit their field goals at a certain rate, depending on their avg. distance. A team whose opponents have made their field goals at a much lower-than-average rate over the first 8 games have been lucky, and have usually seen their points allowed per game go up a bit over the second half of the season. When evaluating a defense, the fact the distance of the field goal they force is important; whether that field goal gets made is not.
Another example of measurable luck is fumble recovery. As it happens, forcing fumbles is a repeatable skill -- recovering them is effectively random. I know commentators like to praise coaches for teaching awareness and drilling players to jump on loose balls, but there's no evidence that this has any actual affect. No team has ever been consistently better at recovering opposing team's fumbles. Every fumble has a certain likelihood of being recovered by the defense based on who fumbled and where. Strip-sacks are recoverad at a certain rate, bad snaps at a different rate, running backs' fumbles at the line at another rate, receivers' fumbles when being tackled at another. A team that fumbled the ball five times in a game and recovered all their own fumbles isn't better at recovering fumbles, they just got lucky. Conversely, after half the season, a good way to spot defenses that are bound to improve are ones that have forced a lot of fumbles, but been very unlucky in recovering them.
What's more, while interceptions are produced by skill, NFL history has demonstrated that what happens after them is effectively random. Now, an INT on a quick out is returned for a TD more more often than an interception on a hail mary, but for every 'type' of reception, there is an expected number of return yards depending on where on the field it occurs, and no NFL team has been consistently better at maximizing INT return yards than any other -- except one team, or more accurately, one player: Ed Reed. Ed Reed is the only player who has consistently gained more yards or scored more TDs off of interceptions than the predicted average in the last 15 years.
So, looking at the Jets/Pats game in terms of things that have been demonstrated to be luck, we see that the Pats recovered all the fumbles by either team, benefited from a surprising missed FG, and had an INT returned for a TD that (albeit one with a high expectation of being returned for a score.) In terms of the types of luck that can be quantified in the NFL, the Patriots were undeniably the luckier team in Sunday's game.
Equally undeniable, however, is that they seriously out-played the Jets. It wasn't bad luck that the Jets couldn't protect Sanchez or that he folded under the pressure. It was a combination of the Pats' actually rushing the passer well, and the Jets not blocking well. The Pats may have been fortunate to have 25 extra seconds on the clock before the half, but it sure wasn't 'luck' that they were able to drive down the field for a TD in a minute and half, and it wasn't luck that made the Jets unable to stop the Pats in the second half.
