Rp Game Design Crits And Hit Chance

Balancing critical hits with mere extra damage is not that difficult after all, your average damage can be calculated as
Code:
                      normal_dmg * (1 + crit_chance) * (1 + extra_crit_multiplier)                    

Just to correct your formula, it is not

Code:

                  normal_dmg * (1 + crit_chance) * (1 + extra_crit_multiplier)

but rather

Code:

                  normal_dmg * (1 + (crit_chance * extra_crit_multiplier))

You can plug in 100 Normal Damage, 100% Crit Chance, and a mere 5% Extra Crit Multiplier to see how big the difference is between the two equations (210 average damage in the first equation, a correct 105 average damage in the second equation).

EDIT : Turns out we were looking for two different things.

As long as the formula itself is balanced you should not worry too much about critical hits being broken at all, the average damage will not be affected. You can land 3 critical hits in a row in a single fight and then land 0 critical hits in another fight. As every random distribution it creates problems if the number of trials is not high enough, when the number of trials is sufficiently high it tends toward the average value - thus balancing luck its own. Usually in a game you have to make a lot of attacks so this falls perfectly in that category.

There are probably combat designs where this holds true, but in general I'd call it a dangerous way to approach balance. Games with failure conditions (such as getting killed/KO'ed) don't usually play well with "averages". Take for example a boss enemy whose "normal" damage is 60% of a character's HP, in a setup where the party's healer can heal 80% of a character's HP each turn. Now assume that boss has a 25% crit rate and that crits deal double damage. If you average it out, the boss is dealing an average of 75% of a character's HP each turn - the healer can barely manage to outheal that damage. Looks like pretty good balance (especially if the healer's MP will eventually run out).

But when we actually play it out, what happens? Each time the boss crits a character, they deal 120% of the character's HP in damage - meaning that they outright knock them out. Woops! It doesn't matter that the healer can outheal the average damage; as soon as a character is knocked out the healer can't help them anymore. The boss is badly balanced because they can spike a character from full health to zero without any chance to react. (This is when good design would dictate adding in skills that can buff the party's defense, etc.)

Bothering about adding something like critical hits is worth the effort in my opinion. Having critical hits in your game increases the level of customization in your game without influencing the overall game balance. Players might decide to go for a critical-based build instead of a flat-damage based one and have the same average damage with two different builds.

I always think this is a really fun way to add some diversity into character management.

Not only is this a free and safe way to add customization, it even helps you widening the audience. Just think of tabletop games: Eurogames and Amerigames are two completely different categories. The former (category) has little or no luck at all involved while the latter has more of it. This alone should be enough to explain how luck can widen your audience.

If a whole category of games involving luck exists then people who like taking their chances exist as well. At the same time people who dislike a luck-based system exist as well. If your overall game balance is not affected why should you limit your audience to only one of those groups? Why not taking that chance to include them both?

Luck can be good in a lot of games, but the one big difference between video game RPGs versus most other types of games (including Eurogames, "Ameritrash", Pen & Paper RPGs, and some video game genres like Strategy games) is that in RPG success in combat is a gate to Progression (and usually Progression is required in RPGs to enjoy its main Aesthetics of Play, such as Narrative and Discovery).

In Settlers of Catan or Sorry!, rolling an unlucky number or drawing an unlucky card doesn't stop the game from playing out in interesting ways.
In Dungeons & Dragons, getting an unlucky roll is more of a roleplaying opportunity than anything else (and even character deaths can create interesting stories - you still get to have fun if you're doing it right).
In Civilization, if you get an unlucky (hidden) roll that causes an enemy Spearman to defeat your Tank, it feels kind of bad but you just continue without your Tank, and perhaps it even creates an interesting board position. The game continues on and can continue to be just as fun and interesting even though you're a unit down.
In Final Fantasy or Persona, if you get hit with a powerful Critical Hit or screwed by the RNG on an Instant Death skill, well... Game Over. Go back to your last save point and do it again. You can't see the cool new stuff until you beat it (and by the way you're at the mercy of the RNG for that). That doesn't allow for interesting gameplay. The penalty might not be as bad for something like a Missed Attack during a random encounter, but in that case it's just a complete waste of 10 seconds of your time.

I feel that's the reason why low variance and low RNG influence tends to make for better games in the RPG genre. That's a topic we've recently discussed here, and as a community of JRPG players and designers, it seemed that there was a strong consensus for very small (but nonzero) amounts of RNG influence in combat.

I like my Ameritrash, but it's because I can still play through a board game after a bad series of rolls.