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The Problem with Extending Critical Hits

by Mike on 23 December 2013

Extending critical hits may not seem like a big deal but the results can unbalance an entire game system. Extending critical hits turns a random bit of fun into a character-building strategy that ends up trivializing high-level combat encounters. We saw the damage of extending critical hits in high-level 4th Edition games. Now we're seeing extended critical hits in the final public D&D Next playtest. We can only hope extended critical hit ranges don't make it into the final published rules.

Why are critical hits so potentially destructive? Let's take a look.

A Look at the Math

Before we dig in, let's take a look at some of the math behind critical hits. As most can figure out, the odds of rolling a normal critical hit on a single attack are 1 in 20, or 5%. That's not bad. You'll see it happen, but not all that often. It's low enough that few people would bother to build a character around it.

If you get two attack rolls, the math gets a little more complicated. Instead of using the chance to crit, you use the chance not to crit in the following formula:

crit % chance = (1 - failure chance ^ number of rolls) * 100

If we fill in this equation with two rolls we get the following:

(1 - .95 ^ 2) * 100 = 9.75% chance to crit.

When you start looking at multiple attacks, the number continues to increase.

If we have three attacks, we have (1-.95^3) * 100 or 14%.

If we have advantage on those attacks, we get six total rolls: (1-.95^6) * 100 or 26.4%.

Now let's look at the insidiousness of extending critical hits. This is where the math starts to take a curve greater than a linear path. Let's extend the crit range to 19 and 20 and do the math again.

A crit on 19 or 20 is 10% for a single attack. On two attacks we use our formula (1-.90^2) * 100 or 19%. On three attacks it's (1-.90^3) * 100 or 27%. If we have advantage on those attacks? (1-.90^6) * 100 = 47%. Nearly half the time you will get at least one crit and potentially more.

At 11th level, a D&D Next fighter choosing Path of the Warrior has three attacks and crits on 18 to 20. Assuming they have advantage on their turn they get six total rolls. Here's the math: (1-.85^6) * 100 = a 62% chance to crit on each turn.

The statistician and friend of Sly Flourish, Benjamin Reinhart helped verify this math and also helped clarify the issue:

"When something happens 1 in 20 times, and can only increment by 5%, then any increase is multiplicative."

Ok, Nerdy McNerdonton but Why Should I Give A Shit?

So why should you care about whether or not some PCs get some extra damage once in a while? Extra damage doesn't break a game.

That's true, extended crits alone doesn't break a game. Stacking additional effects onto extended crits breaks games.

Let's say we stack a stun onto a critical hit. Now those odds aren't just about extra damage, they're about totally incapacitating a monster. And not just boring mooks but big monsters like ancient red dragons, beholders, the Tarrasque, Orcus, Lolth, or Asmodious. Whoever your supervillain of choice is will get stunned before they can even begin their bold James Bond villain speech.

Adding effects onto non-extended critical hits isn't quite so bad. Again, a fighter with three attacks and advantage can trigger at least one crit 26% of the time but that's still not too bad. If you start extending crits, that 26% quickly turns into 47% or even 73% if you have a level 20 fighter with four attacks, a crit on 18-20, and advantage. We all love 20th level fighters but no PC should be able to stun-lock Orcus.

Ruining the Fun of the 20 Roll

When you start figuring out all this math and stacking on all these effects, powergamers will start to see the advantage (no pun intended). Instead of choosing linear increases to their character power, anything they can do to increase the percentage chance of critically hitting can pay big dividends. Rolling a 20 and shouting about a crit is no longer some fun rare occurrence. Instead, increasing critical hit ranges becomes a strategy. Players begin to count on getting those crits and, as we've seen in the math, they'll be right to count on it.

We don't have to hypothesize about this. We've seen it in action for the past five years with high-level 4e play. The rogue's Daggermaster paragon path increased critical hits to 18 through 20 and quickly became a strategy. Get the most attacks you can and stack on the most effects to debilitate whatever monster you're fighting. We saw twin-strike rangers extending crit ranges and getting ranged critical hits all the time. We saw warlords granting an entire party a free attack when anyone in the party scored a critical hit, which was at least once a round.

This tiny little mechanic, increasing critical threat ranges, seems like a nice easy way to make someone feel powerful. The problem is, it quickly escalates into global thermonuclear war and has the potential to ruin every challenge in a high level game.

What's The Alternative?

The best alternative is to keep critical hits on a die roll of 20. It's easy, it's fun, and it isn't overpowered. As PCs gain more attacks and find themselves in positions where they have advantage, they will naturally score crits more often. Stacking on additional powers on a crit isn't so bad when that chance is low. Even a true vorpal sword attack that beheads creatures on a crit can be a lot of fun if it doesn't happen all the time.

Removing any effect on a crit is another option but it's less fun. It still turns crit-fishing into a strategy instead of a random bit of fun and some designer somewhere is going to screw up and add in a crit effect that will end up breaking things. Extending crits is easy but it's also boring. Coming up with new and interesting effects on a crit is a better choice.

Offering both extended crit ranges and effects in crits escalates the entire power curve of the game well above the intention. It trivializes monsters and it fuels powergamers who choose multiplying math advantages instead of interesting character options.

Getting An Expert's Opinion

I'm going to end with a quote from a lead D&D developer you may have heard of before, Mike Mearls, who had this to say back before D&D 4e Essentials came out. You'll note that Essentials had very few, if any, ways to extend critical hit ranges. Let's look at what Mike had to say about critical hits in an interview with myself and Quinn Murphy at Gencon 2010:

Mike Mearls: There are definitely things where as we moved along with the game and looked at feedback where we know that here's this type of mechanic we're not going to use anymore because we know it leads to trouble.

Quinn Murphy: Do you have any specific examples of this?

Mike Mearls: Critical hits. Critical hits started out design-wise as it only happens 1 in 20, it's random, players can't control it, let's throw a lot of effects there. But then if you have things like "hey, you crit more often". It's the example of two design ideals that come into collision. It's really tricky in D&D because with the compendium and everything it only takes one feat that goes rogue and it messes up a lot of characters.