Is Point Buy Balanced? I'm not asking if Point Buy is more balanced?, but rather, is it totally balanced?
It is reasonably balanced. The pursuit of absolute perfection is rarely worth the price paid--but pushing toward better is often still worthwhile.
One of those combinations is the Standard Array of 15, 14, 13, 12, 10, 8. Another is 13, 13, 13, 12, 12, 12. Are these two combinations balanced against each other? Would two characters created with these combinations be equally effective? Would two characters of identical Race, Background, and Class built with each of these combinations be equally effective?
In order: Yes. Usually no. Usually no.
"Balance" does not mean removing the possibility of bad/incorrect/worse/less-effective choices. Rather, it means that applying basic reasoning is likely to lead to choices that are generally pretty good. Being +1 or +2 at everything generally isn't as good as being +3 at one or two things, +2 at a couple others, and being lower at anything else. Or, more simply: What things power the stuff you do a lot? Make those numbers bigger first.
They may be very few score combinations that are as stark as the ones above. It may be true that 90% of combinations are balanced against each other. But, then again, maybe it's more like 50%.
Food for thought: What high score is considered the minimum for an effective build? 16? 15? 13? I once was told characters need at least a 14 in constitution alone to be effective.
These two statements can be addressed together. Do you have at least one stat you can increase to 16? Do you have at least one other stat of 14 or better? Have you avoided odd scores as much as possible?
If the answer to all of these questions is "yes", then you have a fairly good set. If the answer to any single one of them is "no", then it's okay, but you're accepting some slight reduction in power. If the answer is "no" to more than one question, you might want to re-evaluate. The last question is pretty loose, because it has to be; with 27 point-buy, it is possible to have all even-numbered stats and 1 point left over, meaning you may need to accept one odd stat.
If you care enough for an actual numerical evaluation of how many PB options conform to this setup, I can do so. Generating the total number of valid PB slates will be a slight pain, but not too difficult.
Anyway what do you think? Is Point Buy totally balanced?°°°
° If I recall correctly.
°° As opposed to permutations, of which there are billions.
°°° Remember, any comparison to rolling is irrelevant because this thread is about the balance of the Point Buy method compared to itself.
Combinations with repetition would be (16+6-1) choose 6 = 21 choose 6 = 54624, so yes, your number is correct. And yes, the number of permutations is 16^6 = 16777216. Combos-with-rep, where you have n options and pick r from them, is always (n+r-1) choose r, and permutations is always n^r.