07-19-2016, 09:49 AM
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#52
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MVP
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Re: What do you do?
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Originally Posted by CM Hooe |
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Yes, absolutely. Let's do the math!
tl;dr - the math says go for it and call a pass play.
Let's start by agreeing on some facts. If we convert for a first down on 4th and 5, our win probability (herein WP) is 100%; we don't have to run another play before time runs out and our opponent can't stop the clock, so we are guaranteed to win. In addition, if there is any outcome which results in our opponent getting the ball back, including scoring points to increase our lead, our WP necessarily cannot be 100% because the ridiculous scenarios I outlined are still in play; it is still possible to lose, even if it takes an act of God to do so.
Using ProFootballReference's win probability calculator and some models from Advanced Football Analytics: if we turn the ball over on downs and somehow lose six yards doing so (unlikely, but let's say we get sacked), our WP is still 95.59%. More realistically, we simply throw an incomplete pass or throw the ball away to avoid a sack, and our win WP after the turnover is 95.71%. Let's be reasonable and go with the second number. To get both these numbers, I also ran five seconds off the clock for the time it takes to run the play, regardless of the result.
If we miss the field goal, that's an automatic seven yard loss for the spot of the kick and five seconds lost, which leaves us a WP of 95.57% for us after the turnover. If we make the field goal and immediately kick a touchback (best case scenario, so no possible kick return but no additional time run off the clock beyond those same five seconds), our WP is 99.86%. The odds of making a field goal from 47 yards out, all things held constant, is 67%, per Advanced Football Analytics. The odds of missing are in turn 33%. Again being reasonable, we will assume for this scenario that if the field goal is blocked, it is not returned; it is same result as if it were simply missed, a seven-yard loss and a turnover.
We then calculate expected WP for each scenario using proportions. For the field goal scenario, the expected WP is:
Code:
99.86% * 67% + 95.57% * 33% = 98.44%
Similarly, to get the expected WP for going for it:
Code:
100% * P(1stDown) + 95.71% * (1 - P(1stDown)) = expectedWP(GoForIt)
The break-even point in the go-for-it equation - what you have to set P(1stDown) to for both equations to have the same result - is 63.7366%. If you think you have exactly that chance of gaining at least five yards, the decision between going for it and kicking a field goal is a wash. If you think you have better than 63.7366% chance of making it, you should go for it. If you think you have a worse chance of making it, you should kick the field goal.
In 2015, all 34 statistically qualifying quarterbacks averaged greater than 6.0 yards per pass attempt, and of those 14 of these quarterbacks completed passes at a rate greater than 63.7366% - Kirk Cousins, Drew Brees, Russell Wilson, Ben Roethlisberger, Matthew Stafford, Matt Ryan, Philip Rivers, Andy Dalton, Teddy Bridgewater, Alex Smith, Sam Bradford, Tom Brady, Joe Flacco, and Jay Cutler. So if you go for it with a passing with one of these 14 quarterbacks under center, your P(1stDown) is necessarily greater than the break-even point, meaning that mathematically it is correct to go for it. Further, not included in those are two more who average greater than 7 yards per pass attempt and greater than 63.7366% completion percentage for their careers - Aaron Rodgers and Tony Romo, giving you fully half the league which should go for it in this situation rather than kick a field goal on the strength of quarterback play alone, based on the simple math of "I have at least this percentage chance to gain five yards or more".
If simple math isn't good enough for you and you want to use the same proportional math to calculate proportional yards each quarterback will move you forward, you have to switch over yards-per-completion. You do this so you don't double-count the negative result of an incompletion going zero yards (yards per attempt is yards / attempts, which necessarily factors in incompletions and interceptions). So our formula for this is
Code:
yardsPerCompletion * completionPercentage + 0 * (1 - completionPercentage) = proportionalYardsPerCompletion
When you do this math using career yards per completion and completion percentages for all active quarterbacks, every single such qualifying active quarterback - from superstars such as Aaron Rodgers and Tom Brady to more marginal talents such as Matt Cassel and Mark Sanchez - posts a proportional yards per completion value greater than 6.0 yards.
In conclusion: go for it, and call a pass play.
EDIT: I should note that in calculating the WP for the "made field goal + touchback" scenario, I spotted the ball at the 20-yard line following the touchback. With the new NFL rules placing the ball on the 25 yard line, your WP is instead 99.81%, which will reduce the break-even point and result in more quarterbacks qualifying as good enough to justify the "go for it" decision.
EDIT 2: for completeness - if you punt and down the ball on the 1-yard line, your WP is 98.7%. Let's call a failure a touchback which puts the ball on the 20-yard line following punts - this puts your WP at 97.02%. If your punt team can down the ball on the 1-yard line at an 84.7% clip, you can match the break-even rate of the field goal scenario. It gets more complicated than that depending on what you call a success for a punt, but generally speaking I'd guess it's the worst decision to make in this scenario, compared to going for it or the field goal attempt.
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Your calculation for completing the pass is based on general passing stats and not situational passing stats. The defense knows you have one chance, and they know you have to pick up 6 yards, and they know you have to pass to pick up those yards. That probably lowers the success rate.
Edited to add: of course we are talking about Madden, in which money plays exist and pass rush is virtually non -existant. If this were real football I would point out the situation matters, as does the roster. But it's Madden so...
Case in point:
Last edited by ForUntoOblivionSoar∞; 07-19-2016 at 09:56 AM.
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