Privateer

2011-01-29, 11:03 PM

Now, I'm sure I'm not the first person who thought of this, so I'd like to hear other people's take.

I figured I'd make a little thought exercise to figure out how many NPCs should there be of what level. To do that, I calculated the chances of a 'newborn' level 1 NPC making it to a particular level.

So, let's do some math. We'll take an army, and we'll keep throwing it against an equivalent army until there is only one soldier left - the one who survived all fights and progressed to the highest level. At each iteration, any soldier will have a 1 in 2 chance of survival, since he is facing his equal and the outcome is truly random.

So, suppose we had 2 soldiers of level 1 in our army and they each fought an enemy until either our soldier or the enemy one was dead. After the dust settles, 1 of our 2 soldiers won and survived, and 1 of the enemy soldiers won and survived. How much experience did he gain?

http://www.penpaperpixel.org/tools/d20encountercalculator.htm

The calculator above says 300. In other words, a soldier would need to survive three such fights (and a bit, but I'm rounding down) in order to earn enough experience to become level 2. In fact, plugging in different levels into the calculator we will get the same result regardless of level - winning an encounter with an enemy of the same level as yourself will give you 30% of experience needed to progress to the next level. So in total you need to win 3 battles at every level to advance.

Meaning that a soldier's chances to advance a level are 1 in 8. That is, for every single level 2 NPC in your world, there are seven who died trying.

Chances to advance two levels and make it to level 3 are 1 in 64.

The general formula is: Padv(X) = 1/(8^(X-1)), where Padv(X) is the probability of any given soldier advancing from level 1 to level X.

Like any exponential, this explodes VERY quickly:

Padv(5)= 1 in 32768

Padv(10)= 1 in 1 Billion

Padv(20)= 1 in 1.15*10^18 ( that is, a level 20 character would appear once in 192 MILLION Earths)

So it looks like the odds of even a single NPC surviving long enough to reach a moderately high level are miniscule.

Assumptions used:

1. All newborn NPCs start at level 1.

2. NPCs always fight enemies that are exactly their level and number.

3. Fighting encounters is the only way for NPCs to earn experience.

4. NPCs earn experience and have the same experience thresholds per level as PCs.

Number 2 is the questionable one, but seems a fair approximation. Sure, in reality fights are often unfair with one side strongly favoured, but just like an NPC would find it safer to hunt lower-level foes, so would he himself be an easy prey for those above his level.

I figured I'd make a little thought exercise to figure out how many NPCs should there be of what level. To do that, I calculated the chances of a 'newborn' level 1 NPC making it to a particular level.

So, let's do some math. We'll take an army, and we'll keep throwing it against an equivalent army until there is only one soldier left - the one who survived all fights and progressed to the highest level. At each iteration, any soldier will have a 1 in 2 chance of survival, since he is facing his equal and the outcome is truly random.

So, suppose we had 2 soldiers of level 1 in our army and they each fought an enemy until either our soldier or the enemy one was dead. After the dust settles, 1 of our 2 soldiers won and survived, and 1 of the enemy soldiers won and survived. How much experience did he gain?

http://www.penpaperpixel.org/tools/d20encountercalculator.htm

The calculator above says 300. In other words, a soldier would need to survive three such fights (and a bit, but I'm rounding down) in order to earn enough experience to become level 2. In fact, plugging in different levels into the calculator we will get the same result regardless of level - winning an encounter with an enemy of the same level as yourself will give you 30% of experience needed to progress to the next level. So in total you need to win 3 battles at every level to advance.

Meaning that a soldier's chances to advance a level are 1 in 8. That is, for every single level 2 NPC in your world, there are seven who died trying.

Chances to advance two levels and make it to level 3 are 1 in 64.

The general formula is: Padv(X) = 1/(8^(X-1)), where Padv(X) is the probability of any given soldier advancing from level 1 to level X.

Like any exponential, this explodes VERY quickly:

Padv(5)= 1 in 32768

Padv(10)= 1 in 1 Billion

Padv(20)= 1 in 1.15*10^18 ( that is, a level 20 character would appear once in 192 MILLION Earths)

So it looks like the odds of even a single NPC surviving long enough to reach a moderately high level are miniscule.

Assumptions used:

1. All newborn NPCs start at level 1.

2. NPCs always fight enemies that are exactly their level and number.

3. Fighting encounters is the only way for NPCs to earn experience.

4. NPCs earn experience and have the same experience thresholds per level as PCs.

Number 2 is the questionable one, but seems a fair approximation. Sure, in reality fights are often unfair with one side strongly favoured, but just like an NPC would find it safer to hunt lower-level foes, so would he himself be an easy prey for those above his level.