GridIronMine.com's Whether Station
With the Whether Station fans can determine for themselves whether the correct call was made. The best way to show this is by example. Suppose there are 10 minutes remaining in the game, your team trails by 3, the ball at your opponent's 45 yard line with a 4th and 1. Your coach punted the ball. You know it was the wrong call, but how do you prove it. Let's, use the Whether Station.
When you first go to the Station, you will see the following:
You will now set the various fields to reflect the above situation. Then press "Calculate" to get the odds of winning (or Victory Forecast) at this point.
At this point your teams VF is 43%. But it can't stay there. So what happens on the next play. Suppose you punt and your opponent takes over on their 15 and 20 seconds ran off the clock. Enter that situation into the Whether Station as before. Be sure to set possession to defense because you don't have the ball. Now save this result by pressing "save".
Your VF went down considerably to 36%. If your coach had gone for the first down there are two possibilities: you make it or you don't. Specifically, let's look at gaining 0 yards or 1 yard on that 4th-down play. These two situations are shown in the figure below.
The Whether Station determines the VF for failing to convert is 30%, 6% worse than punting. It gives a VF of 46% for converting, 10% better than punting.
Now the VF for going for it is a combination of the these two outcomes. The NFL average for 4th and 1 is about 58%. In that case, the VF for going for it is 58% of 46% and 42% (100% - 58%) of 30%. Or algebraically,
0.58 * 0.46 + 0.42 * 0.30 = 0.39 or 39%
Now was punting the correct call? It depends on your team's probability of converting the first down. What we need to do now is determine the break-even point, which is the probability where the VF for punting (36%) is equal to the VF for going for it. Algebraically, the break-even point is the probability, P, in the following equation.
P * 0.46 + (1 - P) * 0.30 = 0.36
Solving for P we get:
P = 0.375 or 37.5%.
So either your coach thinks his team converts 4th&1 at a rate more the 20% lower than the NFL average or he is a girly man.