Wednesday, July 9, 2014

Dex vs. Con

As long as we're talking about hit points.

Having watched as many people as I have making up characters, I have certainly noticed there is a tendency to ignore the constitution bonus in favour of dexterity.  I thought it might be interesting to investigate that.

A high dexterity improves your armor class, making it harder to hit you.  Presumably, this will cause you to live longer.  It also provides a bonus to initiative and hitting with a missile weapon.  I do not dismiss these; they're good reasons to pick dexterity over constitution.

The first table on the right shows the percentage chance of being hit either twice or three times in two or three rounds of combat, respectively.  Comparing one dexterity against another, the improvement is not that great.  A 15 dexterity is only a 20% improvement over a dexterity without bonuses (dexterities with penalties have been left out).  An 18 dexterity, however, is a 250% improvement - which is rather startling.  An unarmored character with a 14 dexterity could expect to go only 3 or 4 attacks before being hit twice, more likely 3 than 4.  A similar character with an 18 dexterity could expect to go eight attacks before getting that second hit.

If we presume the same spear used in this post, and we are presuming an attack against a player character, that second hit is important.  A character with 7 or more hit points can easily take one hit, but that 2nd hit could put a character with 12 hit points or less into the negatives.  Avoiding that second hit is critical.

Things get even better where it comes to being hit three times.  The spear does an average of 10.5 damage over three rounds, which will put a thief or a cleric into serious trouble.  Take note that the table above also demonstrates the improvement of armor over the unarmored - but that was always obvious.  The point here is to compare dexterity with constitution.

Bringing us to this table on the left.  Here are the chances of two or three successful spear hits dropping a defending number of hit points to zero.  The list includes up to a fighter rolling maximum on a d10, with an 18 constitution.

Take special note of the difference in two sword thrusts 'killing' (I use negatives, so it doesn't quite) a 10 hp defender vs and 11 hp defender.  The addition of a single hit point drops the likelihood of death to less than half!  In the short term at least, putting that 15 under your constitution can double your survival rate.  A 16 can multiply it by better than 500%.

This is short term, however.  The next column shows how quickly this improvement evaporates.  The reason for the difference has to do with the bell curve on 2d6 dropping sharply above 8 damage, while the bell curve on 3d6 doesn't begin to drop sharply until above 11.

That's why a 15 constitution isn't much use to a thief or a mage (2 hits will probably kill anyway), but middling help to a cleric and tremendous help to a fighter.  It isn't just the size of the bonus, it is the size of the dice under the bonus.

Therefore, if you are running a low hit-point character, put that stat under dexterity.  If you're running a fighter or a cleric, put it under constitution.  The armor will handle the attack chance against you - that hit point benefit will be better for you, since you're not likely to get hit more than three times in 10 rounds of combat anyway (presuming you're not fighting something bigger).

Ah well.  Just thinking aloud.


Maxwell Joslyn said...

I like reading this kind of thing. A little bit of connective tissue and pure math (given certain assumptions, such as those of your game world) that prove one thing or another about the game world - all thanks to rigid application of the rules.

Is it any wonder I can't stomach the 'rules-lite' crowd who crow proudly about their stories and their fantasies? They did not have to work against the odds for the story they boast about. They picked and chose at will, like rich children in a chocolate shop.

I can have their indulgence, or I can have the reality of percentages.

Robert Masengale said...

It's very understandable that this works in the short term. I would like to know how this ratio expands in the long term of a character as the amount of hit points they have gained for the con modifier have increased by another factor every time?

Of course, that's harder to calculate, since damage goes up hit points go up, and defenses go up over time.