Never Punt. even on 4th and 15 on your own 5 yard line.
What is the likelihood that if you do punt your defense will prevent the other team from scoring? If you punt from your own 5 the other team takes over with great field position and will likely score a touch down.
These are made up numbers....
But lets say that if you turn the ball over on downs at the 5 the other team has....
90% chance of scoring a TD
5% chance of scoring a FG
5% chance of not scoring.
And if you punt the other team has.....(keep in mind punting from the 5 puts the other team in great field position and their is decent chance at a blocked punt.)
75% chance of scoring a TD
10% chance of scoring a FG
15% chance of not scoring.
And if you go for it you have a 30% chance of converting on 4th down.
Should you go for it?
Based on the laws of probability.... absolutely. Even if your odds of converting is only 15% you are still better going for it.
Keep in mind these numbers are made up but are quite plausible.
Not punting offers other advantages as well.
(1) Greater play selection on third down. You can now treat 3rd down the same way you treat 2nd.
(2) Easier to pound and ground. Rather than needing an avg of 3.3 yards per carry you only need 2.5.
(3) One more player available for defense or offense.