# How do I calculate DPR under my DM's crit house rule?

In 1st edition AD&D, my DM uses a system where on crit you do max damage and roll an additional die, i.e., if you crit with long sword you do 8 points of damage plus another d8 and whatever bonus you get; if you crit with a two handed sword against something large you do 18 points of damage plus another 3d6.

How do I calculate DPR for multiple attacks per round, factoring in potential crits, with this house rule? For example, when I have 3 attacks every 2 rounds and want criticals factored in, or if I want to compare dual-wielding short swords vs. a bastard sword with crits.

• Typically, DPS is damage per second. In this case, does that translate to damage per round? Also, other than this critical hit house rule, does the DM adhere strictly to the AD&D rules-as-written combat round (i.e. speed factors, weapon types versus armor adjustment, intent declaration, etc.)? – Hey I Can Chan Feb 1 '18 at 18:00
• The only other house rules DM uses if you a d10 for initiative and what you roll is what segment your attacks go off and she only uses armor class adjustments for a duel. everything else she tends to strictly follows – huginn Feb 1 '18 at 19:06
• Do you mean damage per segment? In 1e AD&D, segments were a thing at a lot of tables, since a lot of casting times were in segments ... and are you using the Unearthed Arcana rules for AD&D 1e? – KorvinStarmast Feb 1 '18 at 19:06
• No Unearthed Arcana rules. There are 10 segments to a round she is using a d10 to determine which segment in a round an melee attacks go off. My question has nothing to do with spells. I am more interested in comparing 3 attacks every 2 rounds with 1 weapon or 1 attack a round with 1 weapon vs duel wielding – huginn Feb 1 '18 at 19:20
• For those of us who don't play AD&D but like calculating dice statistics, could you add the factor that go into determining DPR? What determines how many attacks you get? What determines if the attack hits? How do you determine if you get a crit? I assume there is a lot of overlap with later editions, but I know there are differences too. – Barker Mar 21 '18 at 22:11

All you really need to do is to calculate what the expected damage per attack is, then if you know the number of attacks you can calculate the expected average per round.

The expected damage per attack is (% chance to hit without crit * average damage for the weapon) + (% chance to crit * (max damage for the weapon + average damage))

So assuming you hit on a 10+ and crit on 20: a single attack with a 3d6 weapon yields (0.45 * 10.5) + (0.05 * (18 + 10.5))

if you have two such attacks in a round your expected damage for that round would be double the answer.

For the smaller weapon it would be (0.45 * 4.5) + (0.05 * (8 + 4.5)) but if you have four such attacks then you would multiply the result by 4.

Using this formula you can also adjust for the hit number so if you have a plus 1 sword (1d8+1) vs a +2 (1d6+2) you can run the numbers through the fomula adjusting both the to hit chance and the damage numbers.

• While the question does specifically ask about average DPR, it might be worth at least briefly noting that other factors matter, too. In particular, especially against large numbers of weak enemies, weapons that consistently deal moderate damage tend to have an advantage over "bursty" weapons that occasionally deal high damage. This is both because bursty damage makes battles less predictable and harder to plan, and also because the extra damage from occasional massive crits is simply wasted if the enemy doesn't have that many HP to begin with. – Ilmari Karonen Feb 6 '18 at 6:01
• Technically this calc is for hitting on 11+ - if you want to hit on 10+, you should replace the 0.45 factor with 0.5 – DM_with_secrets May 19 '20 at 6:26

So, Im just going to make an assumption that there are also crit fails where you hit nothing for the round. We will assume 3d6.

• Average of 3d6 = 3×3 = 9
• Average crit success value = 18+9 = 27
• Average crit fail value = -9
• Average of success/fail values= (27-9)/2 = 9

So it seems, calculating with the assumptions above, that the effect of the crit system in place has no variance from the average dpr and actually maintains a consistent dpr.

• Rolling a 1 in AD&D doesn't nullify all your attacks in a round, so that early assumption doesn't hold and the math and conclusion therefore don't describe the game being asked about. (In fact, rolling a 1 in AD&D isn't treated specially at all.) – SevenSidedDie Feb 2 '18 at 1:24
• The average of 3d6 is not actually 9 -- it's $10.5$. This is because the average roll of a single d6 is $3.5$, not $3$. (Forgetting about that half-a-point is not an uncommon mistake.) Rolls of $10$ or $11$ are tied for the most common. – doppelgreener Feb 2 '18 at 12:07