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Just did some quick math with easily attainable data from ESPN. There have been 808 attempts in 2018 to catch a punt. 506 have resulted in a fair catch and 6 have resulted in a touchdown (no team has more than 1).

Since you can't get a TD on a fair catch that brings us down to TDs divided by attempts so 6/302 for 1.99% chance of a touchdown. Not great. Probably about what I expected. BUT what we're really debating is field position VS the chance of a turnover or a dumb penalty which negates the field position in the first place. Given that the average return is 8.42 yards, it's possibly the data would support not fielding punts for teams without a dynamic returner and/or a reliable punt return catcher.

There's nothing more devastating than this type of turnover to a team for a few reasons - field position, psyche (your defense just got a stop), and momentum, so if you could value this type of turnover against the expected value of a punt return you may find it would be wise to do nothing.

That said, if you have a reliable person to make a fair catch, then I would advise a fair catch to my player every single time.
     
 
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