Do PCs get enough improvement rolls... and more?

[PhilHibbs]

Thanks for the maths. Anyone care to explain the calculation a little better for the daft?

Average increase if you roll over your skill is 3.5.

If you calculate the chance of getting this, and express it as a fraction between 0 an 1 (where a 50-50 chance is 0.5, a 1-in-10 chance is 0.1) then you multiply this chance by 3.5. Then, you take the inverse chance, i.e. 0.5 and 0.9 in these examples, and multuply that by what you get - i.e. multiuply it by 1 because you get +1 if you didn't roll over your skill.

So, your skill is 50 and your INT is 10, you have a 40% chance of getting +1 and a 60% chance of getting 3.5, so the average is 0.4*1 + 0.6*3.5, i.e. 2.5.

So, that gets your skill up to 52.5 on average. Then, your average improvement is 0.425*1 + 0.575*3.5, i.e. 2.4375

That gets your skill up to 54.9375, etc.

Repeat until you get over 100%.

The problem here is, you can't have a skill of 54.9375%. If my simulation is correct, then clearly performing the calculation based on these fractional average skill levels does not reflect reality.

The simulation calculates it properly - it rolls a random number between 1 and 100, adds the INT value, compares it to the current skill or 100, adds 2-5 if it's over or adds 1 if it's not over. Then it repeats until the skill is 100 or more, and then it repeats again as many times as you specify and takes the average resulting number of improvements.

 

[Mixster]

My calculation does fractional skill values as well. I just hid them in the document.

My calculation does have a domain though. If you go below a skill value of 10, you get increases that are larger than 3.5 where you should only have 3.5 and if you go over a skill value of 110 you get increases that are less than 1.

Basically when you look at a graph of this, what you should get would be two lines, one with a tilt of 3.5 skill value/improvement roll stopping at 10 and the other with a tilt of 1 skill value/improvement roll begins at 110, and in between the one gradually becomes the other.

 

[PhilHibbs]

I just fixed my spreadsheet, it had a major bug in the "chance of 3.5" calculation. It now says 28 rolls to get to 100%.