Too often we see coaches make the wrong decision even in today’s NFL when going for two points. Today, I am going to try and help explain Benjamin Morris’s great article that sums up what coaches should do based on win probability Using analytics and historical results, we can dive into why NFL teams should go for two points rather than one. Let’s start with the diagram below.
| GOING FROM A LEAD OF | … GIVES YOU THE TACTICAL BENEFIT OF | … AND A WIN PROBABILITY CHANGE OF | ||
|---|---|---|---|---|
| 0 | to | 1 | The lead | +8.4 |
| 1 | to | 2 | A generic point | +1.8 |
| 2 | to | 3 | Puts you up a field goal | +6.5 |
| 3 | to | 4 | Puts you up more than a field goal | +5.0 |
| 4 | to | 5 | A generic point | +2.9 |
| 5 | to | 6 | Puts you up two field goals | +3.1 |
| 6 | to | 7 | Puts you up a touchdown | +5.2 |
| 7 | to | 8 | Puts you up a TD with a 2-point conversion | +3.3 |
| 8 | to | 9 | Puts you up two scores | +2.9 |
| 9 | to | 10 | Puts you up by a touchdown and a field goal | +2.2 |
| 10 | to | 11 | Puts you up by a TD with a 2-point conversion and a FG | +1.3 |
| 11 | to | 12 | Puts you up more than a touchdown and a field goal | +1.1 |
| 12 | to | 13 | Puts you up a touchdown and two field goals | +0.4 |
| 13 | to | 14 | Puts you up two touchdowns | +1.0 |
| 14 | to | 15 | Puts you up two TDs with a 2-point conversion | +0.5 |
| 15 | to | 16 | Puts you up two TDs with two 2-point conversions | +0.7 |
| 16 | to | 17 | Puts you up three scores | +0.2 |
First, we must examine how much the probability changes from going from a 1 point lead to a two point lead. Obviously, 2 is better than one, but what are the chances?
If you aim for a single point, you’re likely to succeed around 95% of the time. However, if you go for two points, your success rate drops to roughly 50%, though with double the reward. Despite these options having equal expected values (approximately 0.95 points), this doesn’t mean a coach should be indifferent between the two choices. Nor should they automatically opt for the “low-risk” option, which many coaches still tend to do. Instead, the decision hinges on one crucial question:
Which option would improve our chances of winning more, the first point or the second point?
The beauty of this decision is that you don’t need to determine the exact value of each option. You only need to know which one is more valuable. If the second point increases your chances of winning more than the first, then “risking” the first point to go for two ultimately improves your chances of winning.
Since scoring in the NFL usually occurs in increments of 3 and 7 points, different point margins have varying implications for winning chances. For example, the opposing team is generally more likely to score 3 points (from a field goal) than 2 points (from a safety), making a 3-point lead significantly better than a 2-point lead. A 2-point lead, however, is only slightly better than a 1-point lead, as you would lose the lead with a field goal either way. The good news is that the relative importance of each point is fairly intuitive.
Each potential lead has different implications and benefits, such as putting the leading team ahead by a field goal or a touchdown. The marginal value of a point is simply the difference between neighboring scenarios (like the value of being up 3 points instead of 2). Let’s imagine there are 11 minutes left in a game. Consider each scenario and its benefits, and you can probably estimate the marginal value of points quite well. Here are the probabilities.
| EST. CHANGE IN WIN PROB. IF YOU GET … | EST. CHANGE IN WIN PROB. IF YOU GET … | ||||||
|---|---|---|---|---|---|---|---|
| MARGIN AFTER TD | +1 | +2 (VS. +1) | BETTER OPTION | MARGIN AFTER TD | +1 | +2 (VS. +1) | BETTER OPTION |
| -15 | 0.5 | 1.0 | Two | 0 | 8.4 | 1.8 | One |
| -14 | 1.0 | 0.4 | One | 1 | 1.8 | 6.5 | Two |
| -13 | 0.4 | 1.1 | Two | 2 | 6.5 | 5.0 | One |
| -12 | 1.1 | 1.3 | Same | 3 | 5.0 | 2.9 | One |
| -11 | 1.3 | 2.2 | Two | 4 | 2.9 | 3.1 | Same |
| -10 | 2.2 | 2.9 | Two | 5 | 3.1 | 5.2 | Two |
| -9 | 2.9 | 3.3 | Same | 6 | 5.2 | 3.3 | One |
| -8 | 3.3 | 5.2 | Two | 7 | 3.3 | 2.9 | Same |
| -7 | 5.2 | 3.1 | One | 8 | 2.9 | 2.2 | One |
| -6 | 3.1 | 2.9 | Same | 9 | 2.2 | 1.3 | One |
| -5 | 2.9 | 5.0 | Two | 10 | 1.3 | 1.1 | Same |
| -4 | 5.0 | 6.5 | Two | 11 | 1.1 | 0.4 | One |
| -3 | 6.5 | 1.8 | One | 12 | 0.4 | 1.0 | Two |
| -2 | 1.8 | 8.4 | Two | 13 | 1.0 | 0.5 | One |
| -1 | 8.4 | 8.4 | Same | 14 | 0.5 | 0.7 | Same |