I don't know about other GMs, but I like to end epic campaigns with epic battles. Sure there might be a big bad that the the PCs need to take out, or a dragon, or both, but have armies fighting in the background just makes for a cool final battle. It also is a good plot point to have throughout the campaign -- building up allies for the final showdown. However, how does one GM a large final battle?
The problem is simple to understand. If you use the same mechanics that you use for normal battles, you will never reach the end. The mechanics just weren't built for this many characters in play. Instead of running the battle with a character vs character level of detail, you need to run it with a group vs group level of detail.
To do this, you group allies and enemies except for special NPCs and PCs. A typical group can be from 5 to 12, though more or less may work depending on the overall size of the encounter. Each group takes and does damage together. Allied groups are each assigned a PC that directs them, while the GM runs the enemies.
Dealing Group Damage
Groups can attack other groups or even a single character. Group damage is calculated as an expected value. For example, if a group of 6 wizards is going to cast a fireball for 6d6 versus a group of fighters, the fighter group is going to take 6 x 6d6 damage. Generally on this scale of battles, saves against area spells aren't going to work since multiple area effects on going to hit at once, so we ignore the save. (A fighter dodges one fireball to jump in the path of another one.) Roll 6d6 and multiply by the number of attackers. In this case I roll a 22 damage, so the fighter group takes 132 damage.
In the case that there is a normal attack, we use a formula for expected damage based on the crit range of the attack, the damage of the attack, the crit multiplier for the attack, the attack bonus for the attack, and the AC of the target. Damage reduction can also be applied directly to this value.
The problem is simple to understand. If you use the same mechanics that you use for normal battles, you will never reach the end. The mechanics just weren't built for this many characters in play. Instead of running the battle with a character vs character level of detail, you need to run it with a group vs group level of detail.
To do this, you group allies and enemies except for special NPCs and PCs. A typical group can be from 5 to 12, though more or less may work depending on the overall size of the encounter. Each group takes and does damage together. Allied groups are each assigned a PC that directs them, while the GM runs the enemies.
Dealing Group Damage
Groups can attack other groups or even a single character. Group damage is calculated as an expected value. For example, if a group of 6 wizards is going to cast a fireball for 6d6 versus a group of fighters, the fighter group is going to take 6 x 6d6 damage. Generally on this scale of battles, saves against area spells aren't going to work since multiple area effects on going to hit at once, so we ignore the save. (A fighter dodges one fireball to jump in the path of another one.) Roll 6d6 and multiply by the number of attackers. In this case I roll a 22 damage, so the fighter group takes 132 damage.
In the case that there is a normal attack, we use a formula for expected damage based on the crit range of the attack, the damage of the attack, the crit multiplier for the attack, the attack bonus for the attack, and the AC of the target. Damage reduction can also be applied directly to this value.
E{damage}=Phit*Mdmg+Pcrit*Phit*(CritM-1)*Mcrit,dmg
Phit = Probability of Hit = (20-(AC-Attack))/20; Min of 1/20, Max of 19/20
Mdmg = Mean Damage =(Max Damage + Min Damage)/2
Mdmg, crit = Mean damage that is multiplied by a crit
Pcrit = Probability of a crit = Crit Rolls / 20
Crit Rolls = the number of sides on the d20 that result in a crit (so 17-20 would be a crit roll of 4)
CritM = crit multiplier
The expected damage is the damage that one character does against another character per round on average, so multiply this by the number of attackers, and you have damage from an attack per round for the group. This may seem slightly complex, but it is easy to set up in a spreadsheet, and because pairings don't get changed often in a group, it will get used over and over. Keep the expected damage and multiplier for number in the group separate, since some of the group may be killed.
There may be cases where it isn't really straightforward how to calculate expected damage. In these cases calculate maximum and minimum damage and take the average. Then estimate the probability that this damage will hit taking into account whatever complex mechanics there are. Get player agreement. Multiply the two and you have an estimate of expected damage. This will be good enough, even though every detail may not be properly expressed in you estimate.
WARNING: Generally armies don't worry about individuals, so you normally shouldn't have groups attacking PCs. The condition when this changes is when there is something big and bad that warrants a group response, like a dragon. Remind your PC of this before he or she polymorphs into a dragon in the middle of battle, or the player may be very surprised by what happens.
Groups Getting Damaged
A group that is getting damaged loses members based on total hitpoints. So for example, if we have a group of gnome alchemists getting hit by 147 points of cannon fire, we need to look at the HP of the alchemists. In this case our wimpy gnome alchemists have only 33 HP each. As a result, 147/33 number of gnomes are killed, which is 4 dead gnomes with 15 damage remaining against one gnome. This 15 damage can either be tracker or can be dropped, depending on the GM and player's wishes.
As a result of this mechanic, the groups will dwindle in number as they are hit.
What it Looks Like in Practice
Here's what a stat block for each group looks like as you are keeping track. Of course, behind each group there should be a full character sheet to grab AC, attacks, equipment, spells, and etc from.
Group A Elf Rangers
Attacking Group G
Number: 8
Expected Damage vs G (Longbow): 12
HP Each: 34
Remainder Damage: 6
Group B Tengu Sorcerers
Attacking Group 3
Number: 5
Expected Damage vs E (fireball): 14
Expected Damage vs E (magic missile): 12
HP: 14
Remainder Damage: 3
In terms of logistics, the GM is keeping track of this for the enemies (usually fits on a notebook page or two). The GM is probably running the expected damage spreadsheet as needed. The PCs are keeping track of their characters and the groups they are directing.
Calculating the initial expected damages and changing them does take a moment, but in return for this small expenditure you can easily have hundreds of characters "on the board".
Miniatures
When playing with miniatures, there are a couple of simplifications you can introduce. First, you use only 1 mini per group. Second you can add both a group letter and a number left to each group mini, so someone looking at the board can tell what is going on. A small post-it note works fine for this.
Endgame
The most important thing to keep in mind is that you don't need to play the battle out to the last man. Once your NPC BBEGs have been killed (or alternately, all of the PCs. Oops!) and the army has killed over half of the opposing army, there is a good chance they will start into retreat. Let the winners hunt down the retreating army if they wish. You can even make this a plot point that leads to another battle when their backup troops arrive.
Experiences
I have used this method several times. Here is an example where a high level party got attacked by 72 goblins. We ran the encounter easily in one 3 hour session despite the number of characters involved.
"Friday Night Pathfinder: Goblins" Link
The expected damage is the damage that one character does against another character per round on average, so multiply this by the number of attackers, and you have damage from an attack per round for the group. This may seem slightly complex, but it is easy to set up in a spreadsheet, and because pairings don't get changed often in a group, it will get used over and over. Keep the expected damage and multiplier for number in the group separate, since some of the group may be killed.
There may be cases where it isn't really straightforward how to calculate expected damage. In these cases calculate maximum and minimum damage and take the average. Then estimate the probability that this damage will hit taking into account whatever complex mechanics there are. Get player agreement. Multiply the two and you have an estimate of expected damage. This will be good enough, even though every detail may not be properly expressed in you estimate.
WARNING: Generally armies don't worry about individuals, so you normally shouldn't have groups attacking PCs. The condition when this changes is when there is something big and bad that warrants a group response, like a dragon. Remind your PC of this before he or she polymorphs into a dragon in the middle of battle, or the player may be very surprised by what happens.
Groups Getting Damaged
A group that is getting damaged loses members based on total hitpoints. So for example, if we have a group of gnome alchemists getting hit by 147 points of cannon fire, we need to look at the HP of the alchemists. In this case our wimpy gnome alchemists have only 33 HP each. As a result, 147/33 number of gnomes are killed, which is 4 dead gnomes with 15 damage remaining against one gnome. This 15 damage can either be tracker or can be dropped, depending on the GM and player's wishes.
As a result of this mechanic, the groups will dwindle in number as they are hit.
What it Looks Like in Practice
Here's what a stat block for each group looks like as you are keeping track. Of course, behind each group there should be a full character sheet to grab AC, attacks, equipment, spells, and etc from.
Group A Elf Rangers
Attacking Group G
Number: 8
Expected Damage vs G (Longbow): 12
HP Each: 34
Remainder Damage: 6
Group B Tengu Sorcerers
Attacking Group 3
Number: 5
Expected Damage vs E (fireball): 14
Expected Damage vs E (magic missile): 12
HP: 14
Remainder Damage: 3
In terms of logistics, the GM is keeping track of this for the enemies (usually fits on a notebook page or two). The GM is probably running the expected damage spreadsheet as needed. The PCs are keeping track of their characters and the groups they are directing.
Calculating the initial expected damages and changing them does take a moment, but in return for this small expenditure you can easily have hundreds of characters "on the board".
Miniatures
When playing with miniatures, there are a couple of simplifications you can introduce. First, you use only 1 mini per group. Second you can add both a group letter and a number left to each group mini, so someone looking at the board can tell what is going on. A small post-it note works fine for this.
Endgame
The most important thing to keep in mind is that you don't need to play the battle out to the last man. Once your NPC BBEGs have been killed (or alternately, all of the PCs. Oops!) and the army has killed over half of the opposing army, there is a good chance they will start into retreat. Let the winners hunt down the retreating army if they wish. You can even make this a plot point that leads to another battle when their backup troops arrive.
Experiences
I have used this method several times. Here is an example where a high level party got attacked by 72 goblins. We ran the encounter easily in one 3 hour session despite the number of characters involved.
"Friday Night Pathfinder: Goblins" Link
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