I've never spent any great deal of time looking at, reading, or researching the analytics. On what are they based?
I'm not a huge analytics head, but the basic premise is that we have hundreds of thousands of historical actual plays, so we have the data to see the results of those plays and the impact they had on winning. Score, time remaining, field position, and likelihood to to convert the situation are all factored in to calculate expected points derived from a decision and increasing/decreasing the percent chance to win. It's based on masses of real game data.
So, like let's say that you've got 4th and 2 and the opponent's 30 yard line. Based on a gazillion previous instances, we know the expected points per drive for each decision. I'm just making these up, but it might be something like:
Punt: -.12 expected points (zero points expected and the chance your opponent scores on a return or block)
Field Goal: +1.7 expected points (3 points x 60% chance of making the kick - chance it's blocked/returned)
Go: + 2.7 expected points (75% chance of making it x expected points from 1st and 10 at the 28)
Having the ball 1st and 10 at the 28 might have an expected points per drive of 4pts, so with a 75% chance of making it, the go for it call yields +2.7 expected points.
And it extrapolates out to ensuing possessions. So if you are 4th and goal at the 1, part of calculation is that if you fail, the opponent gets the ball at their 1. And that yields its own expected points down the line, between the chance of a safety or turnover for a touchdown, plus the expected points of getting your next possession around midfield. So the calculus changes at the end of the half, because if there are 30 seconds left, you do NOT get the additional expected points on your next possession. (That's why I was surprised the 1st half 4th and goal was a GO by the book, there was only like a minute left, so you lose the expected benefit of your next possession field position. I would have no problem if Norvell overrode the book there (like he does plenty)).
Now, you obviously still have to know your team. Is your kicker great, so making a field goal is more like 80%? Have you had no answers to short yardage all day so you don't think you can convert the historical average of that down and distance? What's the weather like? Is your starting center hurt? All those things have to be factored in as a coach.
What it AVOIDS having factored in are things that shouldn't be. Such as they way the game was coached when you were coming up. What the talk radio guys are going to say about it. What happened last year in a similar situation. Your natural tendency toward risk avoidance or swashbuckling. Soft/fake factors like momentum or confidence. Tradition.
Many of the results of this have already been mainstreamed. 30 years ago, you might have a team like UGA churning up 6 yards per play for two quarters, and then punt without a thought at 4 and an inch at the 50. Nobody expects that anymore. Nobody would decline a roughing penalty on a 30 yard made field goal today, but a few decades ago any coach that would "take the points off the board" was considered dangerously reckless.
Other game situations are not as normalized...
but they will be. This is as inevitable as the shift in baseball and the three point shot in the NBA. Literally ALL the momentum is toward analytics.
A couple caveats...I believe that if you go by straight computing, there are situations that do not have enough of a base size for "the computer" to be accurate. Like, 4th and 12 from your own 30 in the second quarter. The "computer" might call that a go...I would imagine that there simply isn't enough base size of teams going for it there to have a reliable base size, and it probably has mostly fake punts factored in. Pretty much nobody would go there, you still have to use your brain.
Also, its going to take some time, but the masses of data reflect pre-analytic times, and eventually DEFENSIVE response to analytics will change numbers. So, for say 4th and 2 from your own 45...the massive balance of data reflects situations in which the defensive players and coaches were almost certainly caught at least somewhat off guard by the offense staying off the field. They probably had to rush a defensive call in, they might not have had their preferred personnel, etc. In today's game, when that situation comes up, the staff is no doubt prepared for the possibility of a go call. So the book might say 50% chance of converting, but you have to know that it's probably more like 45% today or whatever.