#### barackdhouse

##### Footballguy

I've done a detailed analysis as best I can and will attempt to be concise here. Much had been said in the "Post Here When Coaches Do Something Stupid" thread, but I don't want to pollute that too much as there has been plenty of this there already. There are obviously some assumptions baked into my parameters here. For example, I didn't try to include the likelihood of a pick6 or fumble return6, or of onside kick scenarios. A few basic premises here:

* I am giving the Packers a 40% chance to force a punt and get the ball back with ~1 min left - furthermore I have them going down and scoring a winning FG 40% of *that* slice of the pie, and an additional 3% that they score a winning TD instead of a winning FG.

* I've got Rodgers as a 40% chance to convert the 4th and 8 for a TD and as a 67% to convert any 2 pointer

* I've got Crosby as 90% to make the FG

* There are other parameters that can be argued (for sure), but I want to try and be as inclusive as possible of every possible outcome

* In the Stupid Coaches thread there was a

Ok, to show my work. The name of the math game here is proportional weighted probabilities. If you read any further I'm going to assume this will make sense to you.

Probabilities

A = A1 + A2 + A3 + A4 where

B = B1 +~~B2~~ + B3 + ~~B4~~ where

C = C1 + C2 + C3 + C4 where

X = X1 + X2 + X3 + X4 & Z1 + Z2 + Z3 + Z4 are the same idea as A, B, C but

With me so far?

Since I have Rodgers at 40% to score the TD and another 67% to convert the 2 pointer, then it follows that:

A1 = 40% FORCE PUNT WITH ~1 MIN x (40% GET FG TO WIN IN REGULATION + 3% TD TO WIN IN REG) =

A2 = (40% FORCE PUNT WITH ~1 MIN x 57% GOES TO OT x 50% WIN IN OT) + (60% NO FORCE PUNT x 10% CLOCK TO OT x 50% WIN IN OT) ----note that I am saying if they don't force a punt, and the game is tied, that Brady will go down and win the game in regulation 90% of the time in this scenario, but 10% it goes to OT =

A3 = 60% NO FORCE PUNT x (70% GIVE UP FG + 20% GIVE UP TD) =

A4 = (40% FORCE PUNT WITH ~1 MIN x 57% GOES TO OT x 50% LOSE IN OT)+(60% NO FORCED PUNT x 10% GOES TO OT x 50% LOSE IN OT) =

B1 = THIS CALCULATION HASN'T CHANGED = STILL 40% x 43% TO WIN IN REG =

B3 = WITHOUT POSSIBILITY OF OT, THIS IS JUST 100% - B1 =

C1 = NEVER SAY NEVER BUT THE ODDS OF WINNING IN REGULATION IF THEY DON'T GET THE TD ARE PRETTY CRAPPY, GONNA SAY (2% CHANCE OF PICK 6 OR FUMBLE 6 x 10% CHANCE GETTING BALL BACK x 10% SCORING AGAIN) ALSO KNOWN AS 1:5000 =

C2 = 40% FORCE PUNT ~1 MIN x 30% RODGERS LEADS TD DRIVE x 67% 2PT x 50% WIN IN OT =

C3 = 60% NO FORCE PUNT + (40% FORCED PUNT x 70% NO TD) + (40% FORCED PUNT x 30% TD x 33% 2PT NO GOOD) =

C4 = 40% FORCE PUNT ~1 MIN x 30% RODGERS LEADS TD DRIVE x 67% 2PT x 50% LOSE IN OT =

Ok now let's add up the winning probabilities by weighted pie sections:

Chances of winning under

Chances of winning under

Chances of winning under

X1 = 40% FORCE PUNT ~1 MIN x 30% RODGERS LEADS TD DRIVE TO WIN IN REG =

X2 =

X3 = 60% NO FORCE PUNT + (40% FORCED PUNT x 70% GB FAILS TO SCORE TD DRIVE) - (X2+X4) =

X4 = X2 = I'm tired and I am pretty sure that the odds of winning in OT vs losing in OT need to be the same now matter how this is mapped out = 0.4%

Y1 = without diving fully, I'm going to say these odds are the same as C1, since they are down 8 still =

Y2 = C2 due to same logic as Y1 =

Y3 = 100 - (Y1 + Y2 + Y4) =

Y4 = Y2 If it goes to OT the odds should be the same to win/lose =

Ok now let's add up the winning probabilities by weighted pie sections:

Chances of winning under

Chances of winning under

I'll tell you right now, though, that those numbers are pliable and you can find plenty of wiggle room based on many of the assumptions I made. But perhaps more fundamentally than any of this, the difference is very marginal. That is the ultimate conclusion.

Another spin on this. If we did a little exercise where we said "what if the NFL changed the rules and said if you elect to go for a FG, that it is just an automatic 3 points and run like 4 seconds off the clock?" So Crosby's factor jumps to 100%. That changes the 11.6% number to 12.4%, still less than the TD side, according to my parameters.

Interesting and dorky thing about numbers here. 31.6% to win is a factor of

Ok well I'm going into hibernation now. @Joe Bryant let me know if you're hiring. JK but seriously.

* I am giving the Packers a 40% chance to force a punt and get the ball back with ~1 min left - furthermore I have them going down and scoring a winning FG 40% of *that* slice of the pie, and an additional 3% that they score a winning TD instead of a winning FG.

* I've got Rodgers as a 40% chance to convert the 4th and 8 for a TD and as a 67% to convert any 2 pointer

* I've got Crosby as 90% to make the FG

* There are other parameters that can be argued (for sure), but I want to try and be as inclusive as possible of every possible outcome

* In the Stupid Coaches thread there was a

**major mistake being made, which was to assume that OT is the only possible outcome for GB to win**. Some called it a negligible factor.**I've got them winning in regulation 17.2% of the time if they score the TD**, regardless of whether they convert the 2. That isn't negligible.Ok, to show my work. The name of the math game here is proportional weighted probabilities. If you read any further I'm going to assume this will make sense to you.

Probabilities

**A, B, C will be defined as the scenarios if the Packers decide to go for it on 4th and 8 and X, Y will be the probs if they kick the FG**.A = A1 + A2 + A3 + A4 where

**A is converting the 4th down TD and the 2 pointer**, and 1 is probability of GB winning in regulation, 2 is GB winning in OT, 3 is losing in regulation, 4 is losing in OTB = B1 +

**B is converting the 4th down TD but not the 2 pointer**, and 1-4 are the same arrangement as in A1-A4, but OT isn't really possible here so B2 and B4 are goneC = C1 + C2 + C3 + C4 where

**C is failing to score the TD on 4th down**, and 1-4 are the same arrangement as in A1-A4X = X1 + X2 + X3 + X4 & Z1 + Z2 + Z3 + Z4 are the same idea as A, B, C but

**X is making the FG and Y is missing it**With me so far?

Since I have Rodgers at 40% to score the TD and another 67% to convert the 2 pointer, then it follows that:

**A = 26.7% B = 13.3% C = 60% these are the proportional pies within the ABC decision**A1 = 40% FORCE PUNT WITH ~1 MIN x (40% GET FG TO WIN IN REGULATION + 3% TD TO WIN IN REG) =

**17.2%**A2 = (40% FORCE PUNT WITH ~1 MIN x 57% GOES TO OT x 50% WIN IN OT) + (60% NO FORCE PUNT x 10% CLOCK TO OT x 50% WIN IN OT) ----note that I am saying if they don't force a punt, and the game is tied, that Brady will go down and win the game in regulation 90% of the time in this scenario, but 10% it goes to OT =

**14.4%**A3 = 60% NO FORCE PUNT x (70% GIVE UP FG + 20% GIVE UP TD) =

**54%**A4 = (40% FORCE PUNT WITH ~1 MIN x 57% GOES TO OT x 50% LOSE IN OT)+(60% NO FORCED PUNT x 10% GOES TO OT x 50% LOSE IN OT) =

**14.4%****A1+A2+A3+A4 = 17.2 + 14.4 + 54 + 14.4 = 100%**(of the 26.7% slice of ABC pie)**A1+A2 =**17.2 + 14.4 =**31.6% to win**(of the 26.7%)B1 = THIS CALCULATION HASN'T CHANGED = STILL 40% x 43% TO WIN IN REG =

**17.2%**B3 = WITHOUT POSSIBILITY OF OT, THIS IS JUST 100% - B1 =

**82.8%**note that there are non-zero paths to OT still, but come on now**B1 = 17.2% to win**(of the 13.3% slice of ABC pie)C1 = NEVER SAY NEVER BUT THE ODDS OF WINNING IN REGULATION IF THEY DON'T GET THE TD ARE PRETTY CRAPPY, GONNA SAY (2% CHANCE OF PICK 6 OR FUMBLE 6 x 10% CHANCE GETTING BALL BACK x 10% SCORING AGAIN) ALSO KNOWN AS 1:5000 =

**0.02%**C2 = 40% FORCE PUNT ~1 MIN x 30% RODGERS LEADS TD DRIVE x 67% 2PT x 50% WIN IN OT =

**4.0%**C3 = 60% NO FORCE PUNT + (40% FORCED PUNT x 70% NO TD) + (40% FORCED PUNT x 30% TD x 33% 2PT NO GOOD) =

**92.0%**C4 = 40% FORCE PUNT ~1 MIN x 30% RODGERS LEADS TD DRIVE x 67% 2PT x 50% LOSE IN OT =

**4.0%****C1+C2+C3+C4 = 0.02 + 4 + 92 + 4 = 100%**(I am leaving out the 0.02, there are other small factors missing in all of this as well)**C1+C2 = 4.0% to win**(of the 60% slice of ABC pie)Ok now let's add up the winning probabilities by weighted pie sections:

Chances of winning under

**A is 31.6% x 26.7% = 8.4%**Chances of winning under

**B is 17.2% x 13.3% = 2.3%**Chances of winning under

**C is 4.0% x 60.0% = 2.4%**

*****************************************************************************************************

Chances of winning if going for the TD on 4th is 8.4 + 2.3 + 2.4 = 13.1%

**********************************************************************************************************************************************************************************************************

Chances of winning if going for the TD on 4th is 8.4 + 2.3 + 2.4 = 13.1%

*****************************************************************************************************

**Now for the FG decision tree and XY pie:****X = 90% Y = 10%**- based on Crosby making the FG 90% of the timeX1 = 40% FORCE PUNT ~1 MIN x 30% RODGERS LEADS TD DRIVE TO WIN IN REG =

**12.0%**X2 =

**60% NO FORCE PUNT x 20% BUCS SCORE FG TO GO UP 8 x 10% ENOUGH TIME FOR GB TD x 67% 2PT x 50% WIN IN OT =****0.4%**X3 = 60% NO FORCE PUNT + (40% FORCED PUNT x 70% GB FAILS TO SCORE TD DRIVE) - (X2+X4) =

**87.2%**X4 = X2 = I'm tired and I am pretty sure that the odds of winning in OT vs losing in OT need to be the same now matter how this is mapped out = 0.4%

**X1+X2+X3+X4 = 12.0 + 0.4 + 87.2 + 0.4 = 100%**(of the 90% slice of XY pie)**X1+X2 = 12.4% to win**(of the 90% slice of XY pie)Y1 = without diving fully, I'm going to say these odds are the same as C1, since they are down 8 still =

**0.02%**Y2 = C2 due to same logic as Y1 =

**4.0%**Y3 = 100 - (Y1 + Y2 + Y4) =

**92%**Y4 = Y2 If it goes to OT the odds should be the same to win/lose =

**4.0%**

Y1+Y2+Y3+Y4 = 0.02 + 4.0 + 92.0 + 4.0 = 100%(of the 10% slice of XY pie)Y1+Y2+Y3+Y4 = 0.02 + 4.0 + 92.0 + 4.0 = 100%

**Y1+Y2 = 4.0% to win**(of the 10% slice of XY pie)Ok now let's add up the winning probabilities by weighted pie sections:

Chances of winning under

**X is 12.4% x 90.0% = 11.2%**Chances of winning under

**Y is 4.0% x 10.0% = 0.4%***********************************************************************************************************

Chances of winning if attempting the FG on 4th is = 11.6%

*****************************************************************************************************Chances of winning if attempting the FG on 4th is = 11.6%

*****************************************************************************************************

**Final numbers are that going for the TD gets you a 13.1% chance to win vs 11.6% going for the FG**I'll tell you right now, though, that those numbers are pliable and you can find plenty of wiggle room based on many of the assumptions I made. But perhaps more fundamentally than any of this, the difference is very marginal. That is the ultimate conclusion.

Another spin on this. If we did a little exercise where we said "what if the NFL changed the rules and said if you elect to go for a FG, that it is just an automatic 3 points and run like 4 seconds off the clock?" So Crosby's factor jumps to 100%. That changes the 11.6% number to 12.4%, still less than the TD side, according to my parameters.

**But here is the thing. Why would you willingly sign up to be a 12.4% underdog?**

If you get the FG, you're 12.4% to win. If you get the TD and 2 pointer, you jump to 31.6% to win.This is actually the right way to think of it. Even if the NFL would *give* you the 3 points, why would you take it?If you get the FG, you're 12.4% to win. If you get the TD and 2 pointer, you jump to 31.6% to win.

Interesting and dorky thing about numbers here. 31.6% to win is a factor of

**2.56**times greater than 12.4%. Getting 8 points on the NFL scoreboard is worth**2.67**times more than getting 3. That shouldn't be too surprising that those numbers are so close.Ok well I'm going into hibernation now. @Joe Bryant let me know if you're hiring. JK but seriously.

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