I don't think those cases are outliers at all. There's a value to certainty.
First of all, let's agree on what we're talking about. From 2017 to 2019, the success rate on two-pointers was 48.5%. The success rate on extra points was 94.0%. I'm going to assume that all the two-pointers were mandatory (no choice to be made) and all the 1-pointers were optional. This is clearly off a bit, because sometimes a one-pointer is clearly the better bet (you're down 6 and you score a last-second TD) and sometimes teams take the optional two-pointer (but usually after a penalty places it at the one-yard-line instead of the two, which changes the odds). Can't be off much though, since those effects would cut against each other.
The average team attempted 37.3 extra points and 3.4 two-pointers in a season. Those 37.3 extra point attempts translated into 35.1 points. Convert those to two-pointers and those teams could have expected to score 36.1 points.
So that's what we're talking about. If you went for two instead of kicking the XP every single time, you would expect to score one more point over the entire season. There's simply no way that's more important to your decision-making than the huge increase in variance and uncertainty you'd be accepting if you adopted that strategy.
That doesn't mean nobody should do it, or teams shouldn't go for 2 more often. Bad teams, in particular, should embrace variance. If you assess that the odds are in your favor because of the matchup of your short-yardage offense vs. their short-yardage defense, sure. But in general, because you don't know how the game will play out, you're probably better off with the lower-variance play until you have more information later in the game.
Let's move out of the realm of football and into other games. Some, like poker, are driven almost completely by math and analytics:
- In poker, the play (check, bet/raise, fold) that has the highest EV is always the right play. It doesn't matter whether one wins the hand or not. Nobody will ever argue the logic of making the play that has the highest EV (setting aside some leveling strategy).
- In basketball, we're seeing the evolution of analytics within the game as more teams understand the true value of the 3 point shot.
- Baseball is now driven by analytics league wide. Are there still managers and front offices that will pursue strategies that are not +EV when compared to analytics? Yes, but they are becoming further and further apart. Managers that don't embrace analytics are dinosaurs now.
Back to football: Our minds are ingrained with what the 'right' play is based on a lifetime of watching the sport without regard for analytics. Look no further than our win Sunday.
- Though there is NO QUESTION that MM made the right call going for 2 when he did, there are people that will argue the point based on their life's experience watching the game and, as a fan, their 'suspense' emotion (I guess that's how one would characterize that).
Another example: You said, 'You're down by 6 and score a TD as time expires. Clearly the 1 point play is the better bet.' But is it? I don't know the answer, but I guarantee there's an analytic that says whether it is or isn't. Because we desire the comfort of less variance (more certainty in the outcome) does not mean that it's the best decision, just the more comfortable one.
While your example of points scored over a season may be accurate, it will begin to change as more coaches embrace analytics. There is one thing that is certain: Over the long run, converting 48.5% of 2-point plays is 'more valuable' (higher EV) than converting 94% of 1 point plays. Over 100 attempts, one would score 97 2-point attempt points versus 94 1-point attempt points. Is there a higher variance with the 2 point play? Of course, but that's why analytics exists, to measure the result over a large sample size.
I'm not going nor am I trying to change minds. People will think what they will, but math always wins in the long term.
Really, I just want my team to win.
