Should the Cowboys have gone for 2 on the 1st or 2nd TD?

Smashin222

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Information is just another word for data points....

The word information is imprecise here. It's not a statistical question. Statistics takes a series of data and assesses probabilities of outcomes. Whether you go for 2 first or second isn't a matter of success rates (data question), it's a matter of strategy (it is better to know whether you need to score once or twice as early as possible to inform your strategy). Game theory looks at strategy and logical structure independent of "statistics" related to outcomes. The only way success rates matter would be as inputs for determining the dominant strategy.

In this case, success rates for 2 point conversions is literally irrelevant because you have to go for two at some point.
 

JD_KaPow

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Let's move out of the realm of football and into other games. Some, like poker, are driven almost completely by math and analytics.
We're not talking about whether analytics is the right way to go, we're talking about how to properly apply it. In football, the goal is not to maximize your expected points: the goal is to have more points than your opponent when the clock runs out. The two goals are not the same. You must apply the math/analytics in the correct context. You must understand that information has value. You used poker as an example: information is key to the strategies in that game,and the correct strategies change as each card comes down and you acquire more information (thinking about Texas Hold'em and similar games in this case). In football, the clock and the current score matter: your decisions are not independent of those factors.
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.
Holy cow. If you're down 6 and score a TD as time expires, the game is tied and you have one untimed extra-point play left. If you kick the extra point, there's a 97% chance you win and a 3% chance you lose (assuming OT is 50-50). If you go for 2, there's a 74.25% chance you win and a 25.75% chance you lose. If you can't figure out which the better play is there, I don't know how we can have a serious discussion about it.

Similarly, if you are down 6 and score a TD anytime in the last let's say 5 minutes, the 1-pointer is clearly the better play. Why? Because being ahead by 1 point or 2 points are identical if the opponent can get only one more possession: they beat you with a FG. The second point adds virtually nothing to your win expectancy, but missing the 2-pointer and getting 0 points has a massive effect on it. You have sufficient information to make a more informed choice than just "the 2-pointer is the higher EV play." And yes, you can work this out mathematically, but you must factor in information such as the likelihood of the other team scoring with the time left, the likely length of such a drive, etc. The EV of that particular play is only one piece of data.
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.
No, that's not at all why analytics exist. It exists to find the best strategies and tactics that maximize your chance of winning the game, not scoring the most possible points over 3 seasons worth of games. Let me give you an example. I'm ahead by 2 points, there are 100 seconds left in the game, I have the ball 1st-and-goal at my opponent's one-yard line, and my opponent has no time outs left. I basically have two choices. Take a knee for 3 straight plays, or try to score the TD. Trying for the TD clearly has a higher expected points value for me than taking a knee. It is also clearly the wrong play, because it increases the chances of losing the game (via turnover). The tail of the distribution where I lose is much much bigger than if I take a knee. It's the distribution of outcomes that matters, not the expected value of the play.

Actually, there's a third option in the scenario I just described: kick a FG on 1st down. That play has a much higher EV than taking a knee, but it's just about the worst possible thing I could choose to do. I just gave the opponent back the ball, down 5 points, with 90+seconds left. It's an awful idea despite the EV, because I failed to take the clock and the current score into account.
 
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LovinItAll

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We're not talking about whether analytics is the right way to go, we're talking about how to properly apply it. In football, the goal is not to maximize your expected points: the goal is to have more points than your opponent when the clock runs out. The two goals are not the same. You must apply the math/analytics in the correct context. You must understand that information has value. You used poker as an example: information is key to the strategies in that game,and the correct strategies change as each card comes down and you acquire more information (thinking about Texas Hold'em and similar games in this case). In football, the clock and the current score matter: your decisions are not independent of those factors.Holy cow. If you're down 6 and score a TD as time expires, the game is tied and you have one untimed extra-point play left. If you kick the extra point, there's a 97% chance you win and a 3% chance you lose (assuming OT is 50-50). If you go for 2, there's a 74.25% chance you win and a 25.75% chance you lose. If you can't figure out which the better play is there, I don't know how we can have a serious discussion about it.

Similarly, if you are down 6 and score a TD anytime in the last let's say 5 minutes, the 1-pointer is clearly the better play. Why? Because being ahead by 1 point or 2 points are identical if the opponent can get only one more possession: they beat you with a FG. The second point adds virtually nothing to your win expectancy, but missing the 2-pointer and getting 0 points has a massive effect on it. You have sufficient information to make a more informed choice than just "the 2-pointer is the higher EV play." And yes, you can work this out mathematically, but you must factor in information such as the likelihood of the other team scoring with the time left, the likely length of such a drive, etc. The EV of that particular play is only one piece of data.No, that's not at all why analytics exist. It exists to find the best strategies and tactics that maximize your chance of winning the game, not scoring the most possible points over 3 seasons worth of games. Let me give you an example. I'm ahead by 2 points, there are 100 seconds left in the game, I have the ball 1st-and-goal at my opponent's one-yard line, and my opponent has no time outs left. I basically have two choices. Take a knee for 3 straight plays, or try to score the TD. Trying for the TD clearly has a higher expected points value for me than taking a knee. It is also clearly the wrong play, because it increases the chances of losing the game (via turnover). The tail of the distribution where I lose is much much bigger than if I take a knee. It's the distribution of outcomes that matters, not the expected value of the play.

Actually, there's a third option in the scenario I just described: kick a FG on 1st down. That play has a much higher EV than taking a knee, but it's just about the worst possible thing I could choose to do. I just gave the opponent back the ball, down 5 points, with 90+seconds left. It's an awful idea despite the EV, because I failed to take the clock and the current score into account.

Sorry, my mistake. I was thinking '..down by 7...'. Yes, down by 6, score, kick the extra point, drink some bubbly (Ginger Ale, obv).
 
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