I know it's not really what D&D is designed for, and it wasn't what I planned, but one of my PCs decided to jump into the middle of a major battle with hundreds of combatants on each side. So between sessions I invented some mechanics for it.
For each unit on its turn, I roll an attack roll. But rather than hit or miss, the damage is calculated proportionally. To calculate the proportion, add the attackers' attack bonus, and subtract the defenders' AC minus 10.
Now multiply this number times the number of attackers divided by 20. Roll damage and multiply by that. Then divide by the defenders' max hp. Round up. This is the number of defenders killed.
In summary, the calculation is
(d20 + to hit - (AC - 10)) / 20 x number x damage roll / max hp
We also have to deal with saving throws. Here the calculation is
(d20 - save bonus + (DC - 10)) / 20 x number x damage roll / max hp x hits per attack
where hits per attack is an estimate of how many targets each attack can hit. Use your judgment. For example, if using a fireball with a 20' radius (40' diameter) against an enemy battle line with 5' spacing, you might expect to hit 8 targets. If they leave gaps, maybe only 4.
There is one more exceptional case. If an ability has a saving throw on a hit, then I use
(d20 + to hit - (AC - 10)) / 20 x number
to determine the number of targets affected. Subtract the number killed outright by the attack.
If the effect does additional damage, roll this damage times the number affected divided by their max hp. This determines the number of additional target creatures killed.
If the effect is a status, I just roll a saving throw as normal, and either all or none of the hit creatures are affected. You might need to start tracking affected creatures separately from unaffected creatures. For example, if targets are poisoned, you need to roll a number of these creatures at disadvantage, and the rest normally.
I would say it went okay. In this case, my player was outnumbered and the battle was essentially an inevitable loss. But the degree of devastation made it clear how bad their situation was. In this case, the player was able to use a powerful one-time use item to make a safe retreat. Seeing the dire outcome of the dice rolls helped convince him of the necessity of this action, rather than just saying, "You're losing."
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I know it's not really what D&D is designed for, and it wasn't what I planned, but one of my PCs decided to jump into the middle of a major battle with hundreds of combatants on each side. So between sessions I invented some mechanics for it.
For each unit on its turn, I roll an attack roll. But rather than hit or miss, the damage is calculated proportionally. To calculate the proportion, add the attackers' attack bonus, and subtract the defenders' AC minus 10.
Now multiply this number times the number of attackers divided by 20. Roll damage and multiply by that. Then divide by the defenders' max hp. Round up. This is the number of defenders killed.
In summary, the calculation is
(d20 + to hit - (AC - 10)) / 20 x number x damage roll / max hp
We also have to deal with saving throws. Here the calculation is
(d20 - save bonus + (DC - 10)) / 20 x number x damage roll / max hp x hits per attack
where hits per attack is an estimate of how many targets each attack can hit. Use your judgment. For example, if using a fireball with a 20' radius (40' diameter) against an enemy battle line with 5' spacing, you might expect to hit 8 targets. If they leave gaps, maybe only 4.
There is one more exceptional case. If an ability has a saving throw on a hit, then I use
(d20 + to hit - (AC - 10)) / 20 x number
to determine the number of targets affected. Subtract the number killed outright by the attack.
If the effect does additional damage, roll this damage times the number affected divided by their max hp. This determines the number of additional target creatures killed.
If the effect is a status, I just roll a saving throw as normal, and either all or none of the hit creatures are affected. You might need to start tracking affected creatures separately from unaffected creatures. For example, if targets are poisoned, you need to roll a number of these creatures at disadvantage, and the rest normally.
I would say it went okay. In this case, my player was outnumbered and the battle was essentially an inevitable loss. But the degree of devastation made it clear how bad their situation was. In this case, the player was able to use a powerful one-time use item to make a safe retreat. Seeing the dire outcome of the dice rolls helped convince him of the necessity of this action, rather than just saying, "You're losing."