you are really referring to the linemaker and there are several of them out there that nobody knows about. kenny white is probably at the very top of the list or close to it and his abilities are in the genes as his father, pete white, was a premier linemaker. he works just as hard as any handicapper plus years and years of experience helps him put out as accurate a number as you could hope for. this is more of an art than a science as there are so many variables that enter into making a line. there are also other guys out there that are linemakers and nobody knows their name but they have a great deal of talent and work very hard at their craft.
They have information that we dont....they no how the public is going to react to a line.thats all they need to no. It’s not about players, coaches,refs, its about what line will get us to play the way they want.they no exactly what a line of 6.5....7.0 and 7.5 on a game will get the bet they want.lets say they actually knew that a game was going to end 21-14.making the line 7 means nobody wins and nobody looses. So why do they make the line 6.5 or 7.5? That’s is what they no and we dont.
I'd be curious to know how many original lines are within 1 score. I'm sure that's an easy stat for someone to dig up.
The distribution of point differentials or overall scoring for totals and how close they are to the number doesn't really matter though.
All that matters is if the line is as efficient as can be or not. Where it is the # that leaves no value for the bettor to suck any EV out of. That's the goal.
But to answer your question, I know for totals if it goes over/under then it does so by about 7pts each way on average. For sides, I don't recall ever reading any data on that but I'd guess like 4-5pts. Again, not really what to look at either way but the overall premise that "the oddsmakers always get so close" is a little bit mythical.