Up 30-27 with 2:27 left in the fourth quarter, the Baltimore Ravens faced a 4th-and-4 from the San Diego Chargers 13-yard line. Both teams had one timeout remaining so a first down would mean the Chargers could get the ball back with 24 seconds left, assuming the Ravens did not score or convert a second new set of downs. With a field goal, the Ravens would be up only six points, meaning a touchdown would all but win the game for the Chargers. Avid football analytics readers know that in some situations, being up four to six points is worse than being up three points. This is because opposing offenses are forced to be more aggressive, and as a result, more efficient by passing the ball, rather than settling for a long, game-tying field goal (a.k.a. The Jason Garrett).

With a successful conversion, the Ravens' win probability would jump to 97.3%; a failure means 77.6% chance to win. The probability of converting on 4th-and-4 is roughly 43.6%.

E[WPGo-For-It] = 86.2%

A 31-yard field goal converts at 94.0% (probably higher for Tucker), resulting in a win probability of 82.1%; a miss means the Ravens would have a 77.1% chance to win. Tucker has only missed one field goal under 40 yards in his career, so let's be generous and say there is a 98.0% chance he makes the field goal.

E[WPField Goal] = 82.0%

That makes the break-even point a 22.5% conversion rate on fourth down - essentially half of the actual league-wide conversion rate.

Brian's original win probability model has it as an even greater difference, so much so that there is no break-even point (although his field goal success rate is admittedly low):
After the field goal, Philip Rivers led the Chargers on an eight-play eighty-yard touchdown drive, culminating in the game-winning score to Eddie Royal. The Chargers actually scored touchdowns on each of their final three drives.

The fact that the Ravens ultimately lost is not grounds for criticizing John Harbaugh's decision to kick the field goal - it is the process that is important, not the result. And, to be fair, many different factors can sway these probabilities in game. That being said, the league baselines are a great place to start the analysis and there is such an enormous gap in expected win probability that the Ravens likely made the incorrect decision.

Keith Goldner is the Chief Analyst at numberFire.com - The leading fantasy sports analytics platform - and creator of Drive-By Football.  Follow him on twitter @drivebyfootball or check out numberFire on Facebook. Check out numberFire's new iOS App in the app store now.

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• ### Keith Goldner

In reply to: Guest - meep_42

In order to avoid sample biases like that, we use third down conversion rates in situations where teams would not be trying to go for it on fourth down -- in similar field position. Obviously, this is not perfect, but it is a much better estimation of true 4th down conversion rates.

• ### Guest - Tom1978

> ... Both teams had one timeout remaining ...

The Chargers actually had no timeouts left, and the Ravens two. San Diego used their last timeout on 2nd down. On 4th down, the Ravens lined up to try a fake field goal, then called timeout when the Chargers didn't fall for it, hence they only had one left for their final drive.

So, a Ravens 4th down conversion would have ended the game (provided that they didn't go out of bounds).

• ### Hugh Nightingale

I cannot remember if I have posted this before but a necessary rule change IMHO the NFL ought to consider is that if Defense foul after the 2MW in Q4 when losing, then if the play itself was sufficient for a FD (not the penalty), the GC stops only is Def can be charged a TO. Otherwise GC is started with the PC from 40secs.

Suppose this scenario. Off are leading by 3 and successfully rush for a FD to their 20 at 1:50. Def have 1 TOL. They foul with (deliberate) illegal use of hands. It costs them an extra 5yards stopping the GC but retain a TO. If they had not fouled, Off would have comfortably run out the GC. Now Off have to make plays rather than take a knee and Def have at least a chance of a blocked or short punt and perhaps a couple of pops at the EZ.

A similar logic applies when Def foul on an Off TD play - say RTP. It is no penalty! Unless the scoring team come up with a cute KO from the 50 or even try an onside kick, it's still a yawn-bore TB to the 20. Make the ruling that if the KO is out the back of the EZ from the 50, it is a TB to the 10 (or even 15) instead..!

• ### Guest - SlackerInc

I think it's so interesting that your win probability can go down if you increase your lead from three to six points. I totally understand the logic behind it. But if teams always used the most optimal strategy against each other, this advantage would go away, and more points would always be better (or at least just as good), right? I just can't accept that this is a mathematically persistent paradox if human error is taken out of the equation.

• ### Keith Goldner

In reply to: Guest - SlackerInc

Exactly, it's inefficient human behavior that causes the abnormality. If all teams acted optimally, it would not exist because teams down three points would be just as efficient as those down six.

• ### Guest - Mark M

The failure of the field goal attempt seems to give a slightly higher winning % than the failure of the 4 th down (77.6 vs 77.1) You definitely give up yards on a field goal failure so how is that possible? Typo?

• ### Guest - roger

I disagree with the statement that there is an "enormous gap". We are looking at derived values of 86% and 82%. (The break even point is irrelevant, we only care about WP of the two decisions.)

If the input numbers vary by a few percent (say the WP of a made field goal was 85% instead of 82.1%) then the two decisions are much closer. Based on this, I'd say its a wash, either FG or GoForIt are acceptable decisions. If Harbaugh's reading of that particular game situation of the chargers O against the Ravens D on that drive with that weather/wind, and he though he have a favorable chance of stopping the TD, then kicking was the right decision.

• ### Guest - roger

Both."

Where is the "both" part? Your response is that it is entirely based on historical results, (along with your 3rd down proxy used for 4th down.). And it is league wide multi-year historical averages as well, as I understand it.

It would be great to see the std deviation of these averages (in fact, critical!). I suggest showing us the team by team stddev. For instance, TDs in the red zone can vary from ~70% for the broncos, to ~20% for the jags, so reporting the mean of TD in red zone is almost meaningless. In your hypothetical example of 600 successes out of 1000 tries, how much does that 600 vary team by team? I would think it would be very large.

• ### Guest - Pritesh

I think it's so interesting that your win probability can go down if you increase your lead from three to six points. I totally understand the logic behind it.

Meanwhile you guys can read my recent blog post about GSA SER

• ### Guest - Pritesh

Hi keith I fully agree with you that it is the process that is important, not the result.

Meanwhile you guys can read my recent blog post about article spinner for mac