**Q: What's the distribution of stat bonuses?**

The stats have a bell curve distribution:

Note there is quite a high probability of getting +3 or -3 (3%).

The RMS is 1.36, which is 50% more than B/X 3d6 bonuses.

Although the stat bonuses always add up to zero, they are not all equal. Higher rolls are usually more desirable results, though some character conceptions would prefer lower results. The aim is to give you a choice of a couple of reasonable options, without being able to hand pick your ideal set, as that would encourage "cookie-cutter" characters.

Each +1 amounts to being approx 25% better. Specifically +3 makes you twice as good. For example, with +3 STR you could lift four times as much as someone with -3 STR.

This is a bit complicated...

My initial system is easier to understand - I started with a rolling sets of stats using 3d6 and throwing away any sets whose bonuses didn't add up to zero. This gives a skewed distribution of bonuses - you become very unlikely to get any +3 or -3 bonuses.

(3) These pairs can be summed to get a distribution of sums of pairs -6 to +6. Then all you need is a way of generating three numbers -6 to 6 which sum to zero and whose distribution matches this and this can be reversed.

The RMS is 1.36, which is 50% more than B/X 3d6 bonuses.

**Q: Is the aim of the stats to make everyone the same?**Although the stat bonuses always add up to zero, they are not all equal. Higher rolls are usually more desirable results, though some character conceptions would prefer lower results. The aim is to give you a choice of a couple of reasonable options, without being able to hand pick your ideal set, as that would encourage "cookie-cutter" characters.

**Q: What does a +1 bonus mean?**Each +1 amounts to being approx 25% better. Specifically +3 makes you twice as good. For example, with +3 STR you could lift four times as much as someone with -3 STR.

**Q: How is the stats table calculated?**This is a bit complicated...

The system therefore is:

(1) I selected the distribution above for bonuses -3 to +3. This was chosen to be so wide to reduce the possibility of boring characters with few or no bonuses.

(2) Then I chose a distribution for pairs of values which would give that distribution whilst only allowing differences of 2 or less.

(3) These pairs can be summed to get a distribution of sums of pairs -6 to +6. Then all you need is a way of generating three numbers -6 to 6 which sum to zero and whose distribution matches this and this can be reversed.

(4) Given a bell curve distribution for sums of pairs -6 to +6 you pick three random results, but throw away the result unless it gives a sum of 0, This gives you a distribution of three pairs of bonuses -6 to +6.

The bell curve is chosen so that it matches the distribution (3).

The bell curve is chosen so that it matches the distribution (3).

This gives you a fair distribution, but at step (2) you have a big choice as to how you arrange the values. To make it fair I selected a skewed symmetrical distribution so that it also gives a bell curve for sums and differences of pairs, which as a side effect makes the Height and Weight formula into bell curves.

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