When do NFL teams go for it on 4th down? I did some analysis using play-by-play data from nflsavant to find out.
(Click for full-res)
Data includes 2013 regular- and post-season, but not the Super Bowl. Data for 2014 is current through November 13. There were 851 plays in the data set where a team went for it on 4th down (including fakes).
None of the conclusions are that surprising: most 4th down attempts come near the end of the game, on short-yardage, or near the endzone. Game margin wasn't included in the data, but would have been really interesting to have as well.
I also considered each dimension independently and binned them:
By yard line
One minorly interesting bit is the width of the 'dead zone' - the range where you are too far away to kick a field goal, but too close to the opposing end zone to punt it. I always thought of it as narrow, but here it looks like it's almost 10 yards wide, starting at roughly the opponent's 42 (shown here as the 58 yard line). And then the huge drop in 4th down attempts between there and the opponent's 20 (likely, but not shown here, to attempt field goals).
By time left
Beyond the obvious 4th quarter increase, there is a neat little blip at the end of the first half.
By yards to gain
There is a visible spike at 10 yards to gain, from teams that were unsucessful at doing anything on their first three downs. Many, but not all, of the 10 yard 4th down tries come in the 4th quarter, per the opening chart above. And since there were so few of them, I grouped all of the 4th and 15+ plays together, but the biggest value in the data set was a 4th and 35.
It wasn't successful.