Thursday, July 17, 2014

The 1 Hit Point Jump

I cannot express how good it feels to write new theoretical content.  Advice is fine and all, but I wrote tens of thousands of words of that.  A change = a rest and all that.

So, continuing on with the stun rules described in this post.  The purpose of this post would be to determine what peculiar effects this has on the subject of creatures in the world and their behaviour.

Let's group the number of hit points creatures have according to our ability to stun them.  Thus, creatures with 1-4 hit points would be a group, since they can all be stunned (or killed) by 1 damage.  Creatures with 5 to 8 hit points would be stunned by 2 damage, creatures with 9 to 12 hit points would be stunned by 3 damage and so on.

From the outset, I'd like to point out that by giving player characters more hit points to start, as described here, vastly increases their chances of surviving the first few rounds of combat, as will become evident with the rest of this post.

Let's take a set of creatures that have already been struck with a weapon.  In this case, we will assume that all the creatures described below were hit by the first attack; the chances of that first chance succeeding doesn't matter.  We'll assume these are creatures that have already been hit with a spear (1d6 damage); all we want is to determine the effects of that spear.

Starting with the first group, those having 1-4 hit points.  We already know that all those with 1 hit point are dead, and that the attacks will kill 5/6ths of those with 2hp, 2/3rds of those with 3hp and half those with 4hp. More importantly, for our purposes, no matter how much the spear will do in damage, all of the first group will be stunned.  It only takes 1hp of damage to stun up to 4hp, so those who aren't killed won't be able to attack the next round.

This means that - using the same 35% chance of hitting that I have used all this time - a good chunk of the creatures that survived the first attack are still going to be killed before they get another swing.  Assuming we start with 100 creatures of each hit point, the results will be as follows:

'Success of 2nd Attack' refers to the creatures being 'double-tapped.'  They've been hit, and now they can be attacked again, at once, without a chance to defend themselves.

In an effort to show my work, I'll explain the above table.  The initial hit points on the left most column are those total hit points left of survivors after they've been hit once; of 100 with 1hp, there are none; 16.7 survive of the original 2 hp creatures and these all are left with 1 hp.  33.3 survive of the original 3 hit point creatures and these are evenly divided between 1 and 2 hp after being hit.  50 survive of the original 4 hit point creatures and these are evenly left with 1, 2 and 3 hit points.  The numbers are then compiled, all those with 1 hp, all those with 2 hp and all those with 3 hp.

The number hit and missed reflect the 35% chance of hitting the creature.  Those with 1 hp that are hit all die, leaving only those that weren't hit.  5/6ths of those with 2 hp die, leaving the remainder with 1 hp and those that weren't hit with 2 hp.  Finally, 2/3rds of those with 3 hp die, splitting those who were hit between 1 and 2 hp, and finally those with 3 hp that weren't hit.

The total number left of those who were hit by the second attack is a total of 3.9 out of 35.  That's a devastating kill rate.  That 3.9 that survive are of course stunned again.  But of course this only applies to those creatures that were hit.  Unhit creatures can now attack back and do some damage.

The point here is to indicate the comparative effect of the double tap.  Naturally, we've only covered weak, low hp creatures, so we don't expect them to survive anyway.  Let's move on to something stronger.

Because stunning only occurs if we do one quarter of the hit points needed, we must recognize that while 1 damage will stun anything with less than 4 hp, it won't stun something with 5 hit points.

Let's look at the table above again, only this time let's add 5 hit point creatures and let's make each line of the table specific to creatures with that number of hit points to start..  Remember that the 'Success of 2nd Attack' column can only apply to 83.3 of the 5 hp creatures - since the remainder aren't stunned and therefore can't be double-tapped:

The jump is meaningful, but not excessive.  It does mean that 16.7 1HD/5hp creatures can swing back immediately whereas their 4hp cousins cannot.  This means that, using the stun system, a 5 hp creature is considerably more dangerous simply because there's at least a chance that, if it gets hit, it will still be able to swing back.

That is significant.  It means that a single kobald leader with 5 hp has more of an advantage over his peers than merely 1 hp.  Given the same chance to hit, the same AC and so on, he is still markedly more competitive than his underlings.

None of that is noticed by a party with 12 through 17 hp, but look at the numbers above and make a reasonable guess at the difference between 8 hp and 9 hp.  The 8 hp orc, top of his untrained breed, is definitely improved upon by the 1+1 HD/9 hp elf, nyet?  The 2 hit dice creature with an average of 9 hp has more than hit points where it comes to the 1 HD creature - simply because that creature is going to be harder to stun.

Most readers, I know, don't employ stun rules, but you should really consider how a simple rule addition can alter the dynamic of combat in more ways than might be initially understood.