Given the debate about whether a punter is ever worth a 4th round draft pick, I'm going to do some back-of-the-envelope sums on how big an effect a punter can have on expected wins per season. If someone wants to do this more rigorously, they are welcome to....
Step 1: What's the difference between a good punter and a bad punter?
There are lots of different metrics here. Punts inside 20 versus touchbacks. Punts blocked. Does the punter kickoff and if so, how well? There's also holding on field goal attempts. I'm going to ignore all of these and look at yards per punt.
There are 36 punters with at least 250 career punts who have played in the last 5 years. The best third averaged between 45.8 and 47.6 yards per punt. The worst third averaged between 42.4 and 44.7. This implies a difference between good and bad punters of maybe 3 yards. Of course, the very worst punters aren't on this list, because they don't make it to 250 career punts. My guess is that the real difference is significantly more than 3 yards, but I will take this as a conservative estimate.
Step 2: How does this translate to yards per game?
There were 2198 punts in 2018, or 4.3 per team per game. If we multiply this by our 3 yards per punt, then our good punter is worth 13 yards per game.
Step 3: How does this translate to points per season?
According to the Expected Points statistic, every yard of field position is worth about 0.06 points, provided the team with the ball is in their own half and not right up against their own goal line. Multiplying that by our 13 yards per game gives about 0.8 points per game, or 12 points per season.
Step 4: How does this translate to wins per season?
We can use the Pythagorean Wins statistic to convert expected points into expected wins. For a team that scores and concedes points at a typical rate (300-350 points per season), 12 points per season are worth about
0.7 wins per season 0.35 wins per season.
So, if you've got a bad punter (or no punter), then you can expect that getting a good punter is worth maybe one win every three seasons. Maybe that every-down player that you wanted in the 4th round - say, a depth defensive back - is worth more. I doubt it though.
This still leaves open the question of whether drafted punters do better than undrafted free agents, or rejects from other teams. I'll let others try to answer that. But don't listen to anyone who claims that punters aren't worth it.
EDIT: thanks to sarf_london_niner for spotting the error in the wins per season calculation. All the comments below were before the error was spotted.