I disagree, mostly because you are arbitrarily deciding which factors are considered "lucky" without evaluating every aspect of the game under the lens of probability. Its like cherry picking. The fact is that everything in the game has an expected probability of success. When events with low probabilities of occurrence, like tipped interceptions or missed PATs, occur people consider them "lucky" but the reality is that it these types of events aren't really all that unusual. Go back through every game and I am sure you can find a low probability event happening in every single one even though they aren't the same. These seemingly rare events also gain attention but they aren't the only factor that may be out of whack with the expected rate of probability.
Lets take for an example the missed short field goal by Folk. That seemed like a low probability occurrence. The reality is that Folk misses from that distance 14.7% of the time. Then lets look at another event that some don't think of lucky/unlucky; the missed swing pass to Welker which looked like could go for big yards. What is the change that Brady misses that pass? Probably less than 14.7% I would imagine. Same is true for many other plays which are seemingly low probability like Gronkowski stepping out of bounds on the TD. The only way to truly gauge the "luckiness" of a team is if they went through every action by every player on every play to try and compare the success failure to the expected rate. It would be a mind numbingly impossible task.
Lets look at it another way. As we said, Folk has a career 85.3% success rate for fieldgoals between 20-29 yards. Vinatieri on the other hand has a success rate of 96.5%. What is the difference between their two success rates? If the fans on Jets Insider are to be believed, the difference is luck. Sorry, I'm just going to have to disagree with them.
At the end of the day, people use low probability events because its an easy way for fans to justify outcomes that they didn't expect. They expect things to be different the next time because that specific event won't happen again. They are most likely correct that the specific low probability event won't happen again but it is also likely that some other low probability event will occur that could negatively effect the outcome of their game.
Sure, there's a lot of invisible and/or unquantifiable luck that goes into every play of every game. This is why I didn't cite things like Santonio Holmes slipping in the red zone, or Brady missing on a short pass to Welker. Those things can't be isolated and analyzed to establish expected probabilities.
Some things can be, and have been. It has nothing to do with whether the events themselves are "low probability" or not. What matters is whether its something teams have demonstrated some degree of influence over.
A QB, such as Tom Brady hitting or missing a short pass to a WR, such as Wes Welker, is something that not only teams but individual players clearly have influence over, as evidenced by the fact that some teams/players consistently complete them more often for more yards. What's more, some defenses consistently allow fewer completions for fewer yards than others.
Some things, however, show no evidence of being something that some teams are better at than others. I brought up a few, such as fumble luck. No team has even proven reliably better at recovering fumbles than another. All variance in teams' fumble recovery rate follows patterns you'd expect from random distribution. Fumble luck has nothing to do with "low probability" events. Fumbles are pretty routine occurrences, and most fumbles are recovered by one of the teams.
The same goes for opposing FG% -- except for when balls are actually contacted, teams don't make other teams more or less likely to make field goals. So on that particular play, the Jets' missing the field goal may not be bad luck for them, but it is definitely good luck for the Pats, because they have no control over the outcome.
There's even some evidence to suggest that a teams' and/or kickers' FG% is more luck than we think. A kickers' FG% shows little consistency from one season to the next. Meanwhile, a kicker's average kickoff distance is one of the most consistent stats you could find. This strongly suggests that avg. kickoff distance is a repeatable skill in a way that kicking "accuracy" just isn't.
