Vance Joseph was wrong to kick the field goal, but it wasnt the worst choice

As Denver lost  a game that they should have won yet again, the talk amongst Bronco's country centered on a key 4th down decision near the end of the game.  With fourth and one to go, down by four, Vance Joseph sent out the Field Goal unit to bring the game to within one and hope his defense could get a stop.  It worked to a degree, as Denver did in fact get another possession, but it ended as it has far too often this season with a Case Keenum sack on fourth down.

Vance Joseph made a mistake in kicking the field goal.  I do however not think this was the Largest Play Call Error sine 2011, as EDJ Sports put it.  Their analysis was a -33.3% chance to win.  But this is largely based on some incorrect analysis of the actual decision game states.  Let's look at the table below, a compilation of game states and their win percentages as produced from the Pro Football Reference Win Calculator.  Please note these values were taken before all the stats were updated on PFR for this week, so new calculations will be updated to have these game values in it, so percentages will be slightly different if you run it now.   

Denver Win %Before Play	47.20%
Denver Win Percentage After FG	42.20%
Denver Win Percentage at 1:49	27.40%
Denver Win Percentage Convert 4th Down	57.80%
Denver Win Percentage Miss 4th Down	30.75%

At the moment Denver ran the failed third down play, they still had a 47.2% chance of winning the game.  Any play after that then will end up affecting the win states. 

The coaching staff took time to decide what to do, and ended up taking a delay of game penalty burning nearly a minute off the clock. This left just 4:35 on the game clock, giving Denver a 42.2% still to pull things out.  A defensive lapse that allowed Nick Chubb to run for 40 yards meant that Denver got the ball back with 1:49 to go, resulting in only a 27.4% win chance. This is where the EDJ sports analysis goes wrong.  The field goal kick only dropped the Win Chance by 5%.  The rest of the drop was by Denver's poor resultant play. Imagine for an instant that Denver kicks the field goal, and Cleveland fumbles the ensuing kick off at their own 1.  Denver's odds to win are pretty high at that point.  That possibility for that is contained within Denver's immediate win chance after the kick.  As was the possibility that Cleveland uses up all the remaining clock and the game ends.  This is why we have to look at this decision at the moment the Field goal was kicked, not the resultant play after that.

Let's look a little closer into why that choice was likely wrong for Vance to have made though.  Kicking the field goal, as we said before left Denver with a 5% less chance to win.  Denver going for it and converting it increased their odds by 10%, while going for it and missing dropped their odds by 17%.  That would almost lead us to believe that Denver should not have gone, as their odds to win go down by much more than they go up.  This is where some meta analysis is required as well.  Over the past three weeks Denver has faced one yard situations to go thirteen times,  picking up the first or scoring a TD on eight of those plays.  That trend continues let's say, and Denver ends up with a 61% chance to convert 4th and 1.  The two probabilities then, of Denver winning by going for it, are 35.3 (by converting) and 12% (by failing).   Denver having a 47.3% win chance by going for it. This is why it was wrong to kick the field goal, because in the end, going for it gave Denver the best chance to win.

If we are looking to critique a coach, its better to get the analysis right than to be outlandish.  The mistake in kicking really resulted in a 5% drop.  I would argue the choice to run the ball on 3rd and 1 was actually worse, since it allowed nearly a minute to run off the clock was far worse in retrospect, since that gave Denver a full minute less to work with.