This post is in response to Jeff's post earlier, and a conversation that has been going on on twitter and local radio waves since the end of the Chargers win over the Colts. Here's what Jeff had to say:

Let's dispense with the exception first - I didn't agree with Mike McCoy's decision to kick a 50 yard FG instead of attempting to convert a 4th and Inches with the game on the line. For a detailed explanation, refer to Bill Barnwell's Thank You For Not Coaching! article this week.

Although I'm firmly in the "go for it on 4th down most of the time" crowd, as it's generally an equitable decision in terms of total points scored, this wasn't one of those situations. The game's context played a crucial role in the decision making: a field goal makes this a two score game south of the two minute warning, while Indianapolis's two remaining timeouts can further extend the game even in the case of a successful conversion. For that reason, we only really need to examine the actual odds of conversion with a subtle consideration of the repercussions on either end. As you'll see below, the math supports Mike McCoy's decision to rely on Nick Novak's foot to put the game on ice.

Fifty yard field goals

A fifty yard field goal shouldn't be lumped together with all other 50+ yard attempts. Anyone making an argument on the odds of Novak making a fifty yard field goal by examining his career numbers from fifty and beyond is letting us down intellectually.

Let's examine the actual odds of making a fifty yard field goal. Below is a plot from a commenter at Decision Science News who plotted every single made (teal) and missed (red) field goal from 2002 through 2012 as a stacked histogram in which the field goal distance is the x-axis.

From this plot we can draw several conclusions:

There is a steep drop-off in field goal percentage in the early fifty yard range. Kickers between 2002 and 2012 made a fifty yard field goal 65% of the time.

Point one confirms what is stated above: using field goals longer than fifty yards to estimate the odds of kicking a fifty yard field goal is poor methodology, as it unfairly penalizes this decision. It's the intellectual equivalent of using 4th-and-3 conversion rates as a part of the 4th-and-1 conversion percentage.

The case-in-point is Nick Novak's career as a Charger. He's 9 of 11 from 45 to 49, 0 of 0 from 50, 4 of 4 from 51, and 2 for 7 from beyond. In other words, Novak's experience as a Charger conforms to the chart above: there is a clear difference between a field goal in the late forties to early fifties, and ones from farther out. Both for the league as a whole and for Nick Novak.

Point two can serve as the baseline for any estimate on the likelihood of Novak making the kick, but would be a lazy stopping point as there is more to consider. Like...

Kickers are much better in 2013 than they were in 2002, or even 2008

Last September, Advanced NFL Stats' Brian Burke demonstrated that kickers in the NFL continue to get more accurate all over the field. In fact, he found that kickers from 2008 through 2011 were over 10% more accurate from 50 yards out, in relative percentage points, than kickers from 2000 through 2003. Kickers from 2004 through 2007 were, as you'd expect, between those two.

It stands to reason, then, that the 65% quoted above is disproportionately weighing kicks by kickers who are less talented than present day kickers, like Nick Novak.

Brian Burke isn't the only one to point out this phenomena. CBS ran a similar article back in 2011, while Bleacher Report referred to 2012 as the "Year of the Kicker" after early season kicking percentages were on-pace to shatter NFL records.

The percentage that we should be using in this discussion is closer to 70% than it is to 65%, and that's before we consider the field and weather conditions, which were excellent.

The difference between a field goal and a first down

First things first: even if the Chargers pick up the first down, the game is not over. The Colts had two timeouts, would have used one after the Bolts picked up the first down, and would have used another following the Chargers first down run. After that, the Chargers can run the ball twice more hoping to pick up the first, while Indianapolis couldn't stop the clock.

If the Chargers wouldn't have picked up another first down, they'd be faced with a similar decision slightly closer to the Indianapolis goal-line with around 0:40 remaining. In other words, even if the odds the Chargers convert the first down is higher, we still have to consider that there'd be a meaningful chance that the Colts get the football back because we'd have to convert again.

Up seven with forty seconds remaining may seem like a slam dunk win, but it isn't. The Patriots went down the field in 1:08 without a timeout for a game-winning touchdown against New Orleans in this very week. And have we forgotten Tennessee already? Jake freaking Locker went 94 yards on us in under two minutes without a timeout.

On the other hand, a field goal makes this a two score game with less than two minutes remaining. Barring a lightning-quick touchdown and a successful onside kick attempt, the game is over if Novak makes the field goal.

The odds of converting a fourth and short

I've seen many different numbers thrown out here, but none of them seem like a proper comparison to make. Using all third (!!!) and fourth-and-short conversion numbers seems wreckless. Are we really lumping in all those other scenarios where teams still have to defend against big plays? Obviously, having to commit defenders to the possibility that the offense will use the down and distance to exploit the defense for a big play will increase the odds of the conversion itself.

The Colts had no such fear. They had one goal: do not let the Chargers convert a first down. A big play would have hurt, sure, but a big play here isn't nearly as damaging as a big play on a fourth-and-one in the first quarter. Or a big play on a third-and-one in the third quarter. In other words, the context of this particular fourth-and-one isn't the same as the third (!!!) and fourth-and-ones overwhelmingly represented in the odds quoted in Grantland's TYFNC column this week.

A better proxy for the odds of conversion would be the fourth-and-goal conversion rate from the one yard-line. In this scenario, like the one we're discussing, there really is no such thing as a "big play". Just a good outcome and bad outcome. According to ESPN, fourth-and-goal plays from the one yard-line succeeded just 41% of the time over the past five seasons. That is a drastically different percentage than the 68.8% quoted.

Even if you don't believe the play should be treated exactly like a fourth-and-goal from the one, you'd have to at least concede that the play should be treated somewhere in between that and all third (!!!) and fourth-and-ones. A blend of those two odds that is favorable to those arguing against Mike McCoy's decision to kick the field goal still gives a decisive advantage to McCoy.

Summary

Kicking the field goal was the right decision, mathematically. Not only because the odds that Novak made the field goal were higher than the odds of conversion, but because it also avoided a potential additional conversion of the same decision one minute later.

Kick or run, though, Chargers fans should all agree on one thing: it's great that Norv Turner is no longer here. He would have punted.