I'd love to see some kind of metric breaking down the relationship between a positive first play for the Patriots and their overall performance. It wouldn't be all that hard to do - but I'm lazy and don't feel like doing it.
-Alec Shane in his fantastic Fan Notes from the Game
Challenge accepted, hombre.
First, we can break this into two thoughts because I'm doing this behind Alec's back. He's either referring to the Patriots first play of the first drive leading to overall success in the game, or first play of the drive leading to isolated drive success. Let's look at both.
How does the first play of the first drive impact the Patriots overall success?
So right off the bat we don't see much based off of the Patriots first offensive play of the game. The losses all started with positive gains. Some slug fests started with zero yards, and there's just no real consistency here in the data. Sorry, Alec.
How does the first play of the drive impact the success of the drive?
Here's the success of drives based upon the first play, in two-yard buckets. Non-scoring includes punts, turnovers, and turnovers on downs. Scoring drives are touchdowns and field goal attempts (grouping attempts and completions together).
Of the 54 drives that started with a gain of 2 yards or fewer, 61% resulted in a non-scoring drive. Of the drives that started with a gain of 3 yards or greater, 61% resulted in a scoring drive. How's that for a mirror image.
70% of drives that start with a 7+ yard gain end in a scoring attempt. That jumps up to 75% if they start with a play greater than 10 yards.
So, Alec, I guess what I'm saying is you are absolutely correct. When the Patriots start their drive with a big play, they're far more likely to wind up with a scoring attempt.
In fact, the Patriots opening drive started with a two yard loss by LeGarrette Blount, which the Patriots managed to salvage with a field goal. That was the first time all season that the Patriots scored after losing yards on the first play of a drive.
Don't confuse these outcomes and say that a big first play will result in a score; it just makes it a far more likely outcome.
Hope this answers your question, Alec.
All the best,