The Eagles Got It Right By Going For Two Points Down Eight in the Fourth Quarter – Six Is The New Seven

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There is no doubt that the Eagles two-point try led to a horrifically bad beat. (The spread was +6.5) Many people argued that they should have kicked the extra point and then gone for two, and the win, on the subsequent (fictional) touchdown. The rationale for this is understandable. The Eagles will have to kick an extra point and go for two to win, so the order does not matter. You might as well kick the extra point first. While understandable, the rationale is incorrect mathematically. 

Two distinct logical errors are occurring in this thought process. First, order always matters in probability. Always. Second, the error exists by failing to understand the entire sample space. Sample space always matters. These errors can be most easily demonstrated by referring to a common problem called the oldest child problem. 

Suppose I told you that your new neighbors have two children, one of which is a girl. Then I asked you, what is the probability that the oldest child is a girl? You might reasonably respond that the odds are 50%. They are not. Here is why. 

We know that the neighbors have two children, one of which is a girl. So to attack this problem, we must layout the sample space. The sample space of multiple events will always depend on the ordering. Your neighbors could have had their two children in the following sequences: 

  • Boy – Girl
  • Girl – Girl
  • Girl – Boy

Since we know that one child is a girl, boy-boy is not an option. As a result, we have three possible outcomes in our sample space. In two of the possibilities, the neighbors oldest child is a girl. Without any additional information, the odds that the oldest child is a girl is not 50%, but 66.66%.

Applying This To The Eagles

In the same way, the sample space mattered when the Eagles had to make their decision. The argument to kick the extra point first is based on the idea that they will need both an extra point and a 2 point conversion to win the game. Therefore, the order does not matter. 

While you may mentally exclude the fact that going for two after the first touchdown includes the option to go for two again after the hypothetical second touchdown, the odds do not. You only exclude that possibility because your mind is tricking you into assuming they make the first try. After all, they did. The order of events matters. Most people believed the sample space facing the Eagles was:

  • Extra point/ Two-Point Try
  • Two-Point-Try/ Extra Point, and
  • Extra Point/ Extra Point

It wasn’t. It also included:

  • Two-Point Try/Two-Point Try

As in the oldest child problem mentioned above, this final part of the sample space changes the math.

If the Eagles are going to go for 2 points at all (which they absolutely should), then here is why it is more logical to go for it on the first attempt. One side note, before I begin. I will be using the following percentages to work the problem.

  • Percentage of made extra points 94%
  • Percentage of made two-point tries 49.4%

These percentages are generally accepted. Ultimately, the math is not even close, so use any percentages you wish. 

If the Eagles kicked the extra point after the first touchdown, here is what they would be facing after the second (fictional touchdown): 

  • The Eagles would have a 46.43% chance to win (Made EP% x Made 2 pt conversion%)
  • The Eagles would have a 2.9% chance to tie (missed EP% x Made 2 pt conversion%)

If the Eagles went for the two-point conversion after the first touchdown:

  • The Eagles would have a 46.43% chance to win (Made 2 pt Conv% x Made EP%)
  • The Eagles would have a 74.39% chance to tie (Make one of two, 2 pt conversions. The probability of making one of two tries equals the probability of success on the first try, plus the probability of success on the second try, minus the combined probability of missing both, or 74.39%)

The value of going for two after the first touchdown should become apparent from the preceding. The win percentage remains identical, while the tie percentage increases by 71.4%. 

The counterargument is that if they made the first 2 point conversion, they would never go for the second. So really, the Eagles should only be 49.4 to tie the game. That is correct, sort of, and still way higher than the tie percentage they have by kicking first (2.9%). Also, it is worth noting that they would have a zero percent chance to win if they failed on the first two-point conversion. However, if they made the first one, they would be 94% to win the game with an extra point. There would not be a second attempt. The point is the odds of one event occurring increase as the number of attempts increase. 

We all understand this intuitively. If we were to bet on the flip of a single coin, we would agree on even money. However, the odds that you get at least one head in two flips of the coin are far superior to the odds of getting a single head in a single flip of the coin. The Eagles gave themselves more “flips” by going for two after the first touchdown. 

Of course, old-school NFL thought says kick the extra point both times. In that case, you have:

  • an 88.36% percent chance to tie.
  • an 11.64% chance to lose.
  • a zero percent chance to win.

Personally, I will trade 13.97% of tie equity (88.36% – 74.39%) for 46.43% of win equity. So I would never kick twice. And I will gladly take on an additional 71.4% of tie equity by going for two the first time. 

How The Eagles Game Should Inform Your Betting

I understand that you may personally feel that mathematics is ruining the game you love. NBA fans have been complaining for years that the league is entirely three-point shots and dunks now. The NFL is changing right now and fast. Notice the Chargers’ aggressive fourth-down decision-making. Notice also the Browns dipping their toes into the water with their two-point-try decision making. Over the course of this decade, going for it on fourth down and going for two points will become increasingly common, barring a rule change.

The Chargers, for example, are currently 7 of 8 on fourth down attempts. That conversion percentage is not sustainable, but it does not need to be sustainable. Of course, the team will get hammered in the media the first time it backfires, but only by people that do not understand probabilities. It will come from the “back in my day” crowd – ok grandpa, drink your Ensure and tell me again how the forward pass ruined football.  

If teams commit to going for it on fourth down, it opens up the play calling on third down. This fact alone makes it more likely that teams will face fewer fourth downs, and succeed more often when they do. The math on this approach is beyond dispute. The NFL is a copy-down league. It is not innovative. It steals from college and even high school. They are stealing college concepts left and right, the RPOs, for example. There are already college and high school teams playing a no-punt philosophy. Not surprisingly, those teams are having incredible success. This is coming to the NFL. 

Knowing that now and knowing which teams are more likely to utilize the math to their advantage (knowing which teams will be early adopters of positive expectation decision making) will improve your betting success now and in the long term. Also know, none of this is new to the analytics crowd. They have been arguing for this approach for the better part of a decade, what is new is that teams are finally starting to listen.

If the style of play no longer appeals to you, as many NBA fans have bemoaned, do not blame the math or teams being smart enough to extract every advantage from it. Blame the rules. If the league changes the rules, I will adapt the math accordingly. The NBA could get rid of the short-corner three and move the three-point line back. The NFL can adjust extra point length or move the two-point try back to the five-yard line. 

My favorite complaint is from the MLB crowd that hated defensive shifts. To me this is so illogical, you mean you do not want the defense to be where the batter is most likely to hit the ball? Even children know this is valuable. Watch the next homerun derby and notice how the kids congregate in left-field with a right-handed, pull hitter at the plate. Notice them move with a left-handed pull hitter at the plate. “Sorry son, go stand in the opposite field where you have a next to zero chance of catching a ball. It is about the integrity of the game.” It is nonsense.

Quants do not make the rules, they just show you the best way to exploit them. I want to be precise. I do not advocate any style of play, save one. I look to bet on teams that play in the manner the mathematics deems most efficient. 

As teams advance in their use of positive expectation decision-making, we will see slightly different numbers becoming more valuable in spreads. Do not be surprised to learn in five years that the number six is the new seven in spread bets. There is a grand-canyon-sized gap between aggressive, and reckless. Smart teams, like smart poker players, are maximumly aggressive. We are way beyond a three-times-the-big-blind-bet, or simply shoving all your chips to the center of the table. This is not bully ball. This is a game-theory-optimized strategy.

Make no mistake about it, if a team scores a touchdown in the fourth quarter and is down 8, the only logical decision is a two-point try.  

Also, be sure to consider the coaching philosophy of the teams you are betting on and against. Nobody enjoys being forked into the pit by uncommon play calling. Soon, decisions like Philadelphia’s on TNF will be as common as wings sprinting to the corner, not the hoop, on an NBA fast break. You do not have to like it, but you should bet it accordingly. 

I will remind you that it has always been a unique thought that advanced our understanding. It was a 13-year-old Boby Fisher who, shocked the chess world in the Game of the Century when, in the seventeenth move, he sacrificed his Queen with the now world-famous move, Bishop to e6. His maximally aggressive decision making won the match a few moves later. And with that move, 1500 years of accepted strategy in chess went out the window. Surely, we can fix 101 years of football.

One last point, if you ever hear Troy Aikman say he disagrees with a decision, as he did before the Eagles’ two-point try on Thursday, you can bet the house it is the correct decision. 

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