Edit: Folks I am very sorry, but I made a mistake in the original post. I did not factor in the strength bonus to damage! The numbers have now been updated with the new info.
Continuing on my recent math tear, I asked the question: How effective would it be for a fighter to use the shove action before starting his barrage of death?
Lets start with my old buddy Cuthgar, 20th level Fighter. I'm giving him a longsword with dueling style, 20 strength. vs AC 16
Single Attack DPR: 10.625
Single Attack (w/Advantage): 13.67625
Now lets assume my first attack was the shove action, so we compare the lower DPR x4 vs the higher DPR x3.
42.5 vs 41.02875
Conclusion: With a regular attack routine, the shove action would never help me out, it lowers my overall DPR.
But wait there's more! With action surge, I could get 8 attacks...or 7 with the shove. Lets see if that changes the game:
85 vs 95.73375
Ok, so now a shove IN THEORY is actually better than the regular attack. However, I actually have to succeed at the shove, so lets see how that affects things.
Fighters Athletics: +5 str + 6 prof = +11
Wizard's Acrobatics (assuming 14 dex): +2 + 0 = +2
Poor Wizard
Now important to remember that contest ties in 5e keep things "the same". So in our example, a tie favors the wizard.
With that in mind, the Fighter has an 83.5% chance to throw the wizard down!
So 86% of the time, I will do the bigger (95.73375) damage. The rest of the time, I would only do 74.375 (lower DPR with 7 attacks).
If I factor all of that up I get the following:
8 regular attacks DPR: 85
1 shove + 7 attacks: 92.20955625
Conclusion: When using action surge against the wizard, the Fighter has more advantage when using the shove action. And further, this is only a 1 on 1 scenario. When you factor in the fact that the rest of your party can also get advantage on their attacks (your welcome rogue)...you can see that the shove action, at least at higher levels, can be extremely useful.
On a personal note, I now want to play a fighter with a team of rogues, and literally just walk around the battlefield throwing bodies on the ground for the rogue's to tear up!
Continuing on my recent math tear, I asked the question: How effective would it be for a fighter to use the shove action before starting his barrage of death?
Lets start with my old buddy Cuthgar, 20th level Fighter. I'm giving him a longsword with dueling style, 20 strength. vs AC 16
Single Attack DPR: 10.625
Single Attack (w/Advantage): 13.67625
Now lets assume my first attack was the shove action, so we compare the lower DPR x4 vs the higher DPR x3.
42.5 vs 41.02875
Conclusion: With a regular attack routine, the shove action would never help me out, it lowers my overall DPR.
But wait there's more! With action surge, I could get 8 attacks...or 7 with the shove. Lets see if that changes the game:
85 vs 95.73375
Ok, so now a shove IN THEORY is actually better than the regular attack. However, I actually have to succeed at the shove, so lets see how that affects things.
Fighters Athletics: +5 str + 6 prof = +11
Wizard's Acrobatics (assuming 14 dex): +2 + 0 = +2
Poor Wizard

With that in mind, the Fighter has an 83.5% chance to throw the wizard down!
So 86% of the time, I will do the bigger (95.73375) damage. The rest of the time, I would only do 74.375 (lower DPR with 7 attacks).
If I factor all of that up I get the following:
8 regular attacks DPR: 85
1 shove + 7 attacks: 92.20955625
Conclusion: When using action surge against the wizard, the Fighter has more advantage when using the shove action. And further, this is only a 1 on 1 scenario. When you factor in the fact that the rest of your party can also get advantage on their attacks (your welcome rogue)...you can see that the shove action, at least at higher levels, can be extremely useful.
On a personal note, I now want to play a fighter with a team of rogues, and literally just walk around the battlefield throwing bodies on the ground for the rogue's to tear up!
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