Most people would reasonably agree with slight variation that football boils down to 40% offense, 40% defense, and 20% special teams. Now we can also agree that of these 40% for offense and defense that 80% of the value is starters, 20% second string. This is assuming that all positions are equal in value.
We can use these numbers to calculate how many games Coach Dodge should have to win based on the total value lost of his team.
So on offense we have lost:
6 First String: JJ Johnson, Nathan Tune, Conor Gilmartin-Donahue, Micah Mosley, Chris Bynes, Tyler Stradford
7 Second String: Derek Thompson, Nick Leppo, Greg Brown, James Hamilton, Breece Johnson, Riley Dodge, Benny Jones
On defense we have lost:
2 First String: Dewaylon Cook, Steven Ford
3 Second String: Jesse Desoto, Chris Neal, Konockus Sashington
Special Teams: Many of these players played special teams, but we can not determine accurately which of these players played. So worse case scenario none of them were of any value and we will keep the value at 20%.
On to some hardcore math.
So we can break down that the value of each unit(offense, defense, special teams) to be, a(.2) + b(.4) + c(.4) = 1, where 1 is a complete whole team and a = special teams, b = offense and c = defense.
Now we must break up a,b and c into their respective parts. A is 1, because we ass(u)me no loss to special teams. B is broken up into .8 for starters and .2 for second string. Therefore the equation for the total amount of players lost is ((.8*(6/11) + (.2*(7/11))). This comes out to be (.44 + .13) = .57. . x = .57, the number of players lost so 1-.57, or .43 is the value of offense we have left.
b = .43 players left out of 1
C is broken up into .8 for starters and .2 for second string. Therefore the equation for the total amount of players lost is ((.8*(2/11) + (.2*(3/11))). This comes out to be (.15 + .05) = .2. . x = .2, the number of players lost so 1-.2, or .8 is the value of defense we have left.
c = .8 players left out of 1
So now we must apply these numbers to our master equation for the total value of the team. ( a(.2) + b(.4) + c(.4) = 1). So the new equation is, (1*.2) + (.43*.4) + (.8*.4) = Z.
Z = .2 + .172 + .32 = .69
Therefore, assuming none of these players participated in special teams, and that none of the positions are valued different from each other and that the generous numbers given to second team, Coach Dodge should be responsible for winning 69% of the original 7 games expected from him which means 4.83 games, which you round down since you can't win .83 of a game.
My conclusion is that 4 wins would absolutely guarantee Coach Dodge should keep his job considering the circumstances that have arisen.