Playing with the Averages - A simplistic approach

[DND_Reborn]

Actually, an easy way to do this is using the average to replace any re-rolled number, and then re-average with those numbers.

Example:

d6 average is 3.5. So if I want to re-roll 1's and 2's, I replace those with the average 3.5

1 2 3 4 5 6 => average 3.5

becomes (replacing 1 and 2 both with 3.5)

3.5 3.5 3 4 5 6 => average 4.167

So, the average of 2d6 would be 7 (3.5 + 3.5), while the average of 2d6, reroll 1's and 2's, would be 8.33.

So, the increase is 1.33 overall.

I was thinking for something like Great Weapon Fighting Style, I would probably just add 1 or 2.

 

[DND_Reborn]

Since I'm not math-oriented, I'll show you the long version.

Definitely not math-oriented LOL. It is a nice reasoning, but you have to understand the re-rolled 1 results in an average of 2.5, so replace that 1 with 2.5 and re-average

2.5 2 3 4 => 2.875

So, only an increase of 0.375 points.

The reason is your version would be better shown like this

(1 2 3 4) 2 3 4

The re-rolled 1 can be (1 2 3 4).

Each of these has an equal 25% chance of occurring, so you get

0.25*(1+2+3+4)/4 + 0.25*2 + 0.25*3 + 0.25*4 = 0.625 + 0.50 + 0.75 + 1.00 = 2.875.

Hope that helps, but it probably just confuses people LOL!

 

[CubicsRube]

I have the players roll damage against their PCs. It frees me up to focus on other things and speeds play up as well. I haven't found problems with players being the one that kills their PC if it comes to that.

I started doing that with Dungeon World and I will carry that across to all games wherever I can.

The players feel like they have that extra bit of control over if their character goes down or not, it frees me up for other things, and it really signals how dangerous a foe is. The players recognise even if they roll well for that hit, they got lucky. I find it ramps up the tension.

 

[Brashnir2]

Since I'm not math-oriented, I'll show you the long version. Average damage is the sum of all possible outcomes, divided by the number of outcomes.

No re-roll d4:
Roll 1 2 3 4
Sum 10
Avg 2.5

If you re-roll 1s on a d4, you have these outcomes:

1st roll	1	1	1	1	2	3	4
Re-roll	1	2	3	4
Result	1	2	3	4	2	3	4

Sum 19
Avg 2.7

Teach a man to fish (by using lengthy tables)...

I prefer to think of it like:

re-roll ones and twos:

no re-roll:

2.5

Re-roll 1s and 2s

2.5+2.5+3+4 = 12 / 4 = 3

So it's + 0.5

D6 = 3.5 average.

D6 roll 1 and 2 is 3.5+3.5+3+4+5+6 = 25 / 6 = 4.166~ So +0.66~

D8 roll is 4.5 average

D8 reroll 1s and 2s = 4.5+4.5+3+4+5+6+7+8 = 42/8 = 5.25 average, or +0.75

D10 = 5.5 average

D10 reroll 1 and 2 is 5.5+5.5+3+4+5+6+7+8+9+10 = 63 / 10 = 6.3 average or +0.8

D12 is 6.5 average.

D12 reroll 1 and 2 = 6.5+6.5+3+4+5+6+7+8+9+10+11+12 = 88 /12 = 7.33~ or +0.833~

2D6 reroll 1s and 2s is just the D6 calculation twice, which comes out to +1.33~. Mauls are awesome.


As for turning that into an average damage, it all depends on how much of a nerd you want to be.

 

[FrogReaver]

I like the idea that @FrogReaver put forth. What your DM is considering would require that he knows how many hit points the player has left, or would result in the player saying "oh, that takes down" and the DM responding "no, wait; let me roll the dice," then gathering up the dice, etc.

I think that it would be more straightforward when a player is dropped to 0, he flips a coin. Heads, he's still up at 1 hp. Tails, he's on his butt at 0. A character with only 1 hit point when he takes damage doesn't get to make the coin flip.

Yea, rolling damage die at that point would be blah. I think tying it into a con save would work well and be more thematic than a coin flip. Maybe follow the concentration save rules for the DC?

 

[Larrin]

The best use for using average dice rolls is when I'm DMing and I end up fighting myself, either with an NPC in the party or when the city watch shows up to help or when enemies attack enemies for whatever reason. I've sat through DMs who end up in a situation where they have 10 guards attack 14 goblins and 400 dice rolls and 15 minutes later there are 9 guards and 12 goblins and then the players get to go and its the most bored I ever get at a table. I don't want that for my players. I switched to using average damage anytime I attack myself as a DM and it is the best decision one can make in that situation. I like the swing of random dice as much as anyone, but I find it more respectful of the players time to get the NPC on NPC violence out of the spotlight and over as quickly as possible. Heck sometimes I just abstract attacks rolls, roughly estimate probabilities and just roll a d6 (guards hit on a 4 and deal 6 damage, goblins hit on a 5 and deal 4 damage). The players hear dice rolling, and it looks the same to them as rolling mittfuls of dice they never really get to experience would.

 

[S'mon]

Heck sometimes I just abstract attacks rolls, roughly estimate probabilities and just roll a d6 (guards hit on a 4 and deal 6 damage, goblins hit on a 5 and deal 4 damage). The players hear dice rolling, and it looks the same to them as rolling mittfuls of dice they never really get to experience would.

I've been known to roll d6s for NPC vs NPC, but if so it's more "kill on a 6" - if you are still going to the effort of deducting NPC hit points you might as well invest in a pile of d20s, decide how many attacks each side gets, and just roll them en masse. You can add up damage and deduct that many enemies whose hp are exceeded, but it's more realistic to assume around 50% of damage is 'wasted' on non lethal wounds and overkill - you can just increase NPC hp by 50% for purposes of resolution.

So eg 10 Guards ATT +3 AC 16 hp 11 (16) dam 4 attack 12 Goblins ATT +4 AC 15 hp 7 (10) dam 5:

1. Roll 10 d20 for the 10 guards, they hit on a 15-3 = 12+. Every 10/4 = 2.5 > 3 hits removes a Goblin.
2. Roll d20s for the surviving Goblins, they hit on a 16-4 = 12+. Every 16/5 = 3.2 > 4 hits removes a Guard.

At the end of the battle the survivors will have taken hits up to 50% of the total damage inflicted on their side, but will still have at least 1 hp each. So eg the 11 hp guards will have taken 0, 1 or 2 5-hp hits each. You probably don't need to worry about this though.

You can pre-calculate and factor in average critical hit damage if you like, eg guards do 2d6+1 = 8 on a crit, goblins do 2d6+2 = 9 on a crit. This is effectively identical to a crit being 2 normal hits.

We can easily abstract this down to:

Guards ATT +3 AC 16 hits 4 damage 1 (crit 2)
Goblins ATT +4 AC 15 hits 3 damage 1 (crit 2)

Or don't use the +50% hp if you want it faster & bloodier:

Guards ATT +3 AC 16 hits 3 damage 1 (crit 2)
Goblins ATT +4 AC 15 hits 2 damage 1 (crit 2)

After all that work we see that the result is effectively the same as "Guard kills goblin on a d4 roll of 4" and "Goblin kills guard on a d6 roll of 6" 5e goblins are unusually high damage & squishy; in most caes you can get a perfectly decent result by going straight to "NPC mook kills NPC mook on a d6 roll of 6".

 

[GMMichael]

Definitely not math-oriented LOL.

Yeah, I didn't pay enough attention during the permutations part of math class. If only my teacher had put it in terms of "damaging orcs," I might have perked up.

Since I'm not math-oriented, I'll show you the long version. Average damage is the weighted-average sum of all possible outcomes.

Fixed it. But I think my earlier version still works with rounding.

 

[DND_Reborn]

Yeah, I didn't pay enough attention during the permutations part of math class. If only my teacher had put it in terms of "damaging orcs," I might have perked up.

Fixed it. But I think my earlier version still works with rounding.

You might have paid more attention then, but when I taught math if I had done it most of my students would have looked at me like I was crazy!

Luckily the numbers are generally small enough that even in a round-about way you still get about the same results.