Do we know how the game deals with would-be zero stat levels?

[Tables]

In other words, how does the game avoid giving you a zero-stat level up? Do we know exactly what method it uses? It's not hugely interesting or important I know, but I find it intriguing to know.

Anyway, in case we don't, I did a little research with Sothe in 3-6. He's capped everything except SPD and LUK, so I trial ran 100 levelups and saw if the distribution of levels gave away what the game was doing. Unfortunately it didn't, but here's the results:

[spoiler=data and some hypotheses]For reference, Sothe's speed growth is 45% and luck growth is 65%.

SPD only: 19

LUK only: 59

Both: 22

LUK total: 81

SPD total: 41

There were two likely possibilities I thought of: 1) Zero stat levels are rerolled by the game some number of times until another method is used (to stop infinite recursion) and 2) If a level would give a zero stat gains, the highest growth rises, defaulting to the first in the stat order in a tie (e.g. HP always goes up if all growths are 0%).

In case 1, I can essentially consider only the probabilities of gaining stats given a stat rises which gives the following:

LUK growth: 80.5%

SPD growth: 55.7%

LUK only: 44.3%

SPD only: 19.5%

Both: 36.2%

These fit the data... moderately well, but there are too many luck only levels and not enough speed levels.

In case 2, it's even easier to calculate the expectation: In the 19.25% chance of no growth, then LUK goes up instead. In that case we'd get the following:

LUK growth: 84.75%

SPD growth: 45%

LUK only: 55%

SPD only: 15.75%

Both: 29.25%

As you can see, the data fits this much better. I'd do some proper statistics with a null hypothesis and stuff, but that would require remembering how to do so. Either way, I can't be certain of anything, but this looks the more likely answer. Unfortunately I really need more data to work with, which I don't have and can't be bothered to gather.

TL;DR version: I think that when you would gain a zero stat level, you instead gain a level in your highest growth.

[Anouleth]

dondon saw when he did 0% growths that when a character had 0% in every growth, it was their HP that invariably rose.

EDIT: oh, you knew that already.

Well, I think that what the game does is roll each stat (from highest to lowest) until one of them procs, and if it goes on too long it just returns the highest growth (but that would happen so rarely as to be negligible).

Edited September 16, 2011 by Anouleth

[Narga_Rocks]

I know what way I would have done it if programming it. Closest to rising, so if a stat rolled 46 and the growth is 45, and nothing else came within 2 of going up, that would be the one. I am pretty sure the game doesn't do that, though, based on dondon saying hp went up always. Doesn't dondon's experience suggest that the game does not care about any of that? The first case is probably my second choice for what I'd do, but it seems like the second case is the answer. Sothe's speed growth is 45, and you got 19+22=41, which is in the range I'd expect (40 to 50) based on a 45% growth. He has a 65% luck growth, and you got 59 + 22 = 81. The chance of neither happening is .55 * .35 = .1925, so I'd assume 60 to 70 + 14 to 24, a range of 74 to 94 (too big to mean much). Yours landed in that range. Basically, it seems likely that they simply take your highest growth if nothing goes up, and if there is a tie then go with hp then whatever whatever depending on which growths are tied, which is stupid.

And Anouleth, by invariably, do you mean it always rose, or it rose most of the time? Invariably should mean always, but your next statement about what you think happens would seem to indicate that you didn't mean that.

Edited September 16, 2011 by Narga_Rocks

[Tables]

IIRC, HP always went up when Dondon set all the growths to 0%. So it can't be the closest growth method, as that wouldn't work.

Also your calculation there is a little off, and your ranges seem quite abstract. If no growths (19.25%) becomes luck, then we can simply consider the luck growth to be 65+19.25=84.25%.

[Anouleth]

And Anouleth, by invariably, do you mean it always rose, or it rose most of the time? Invariably should mean always, but your next statement about what you think happens would seem to indicate that you didn't mean that.

I mean always. When all growths are zero, you'd never get a proc so the game would default to the highest stat; when all stats are tied, it probably tiebreaks in the order HP->STR->MAG->etc.

[nflchamp]

I'd like to add that, under the highest growth increases idea, it's likely the game would simply start with HP growth and ask if there is a growth that is larger. If yes, it'd continue to STR growth and ask again. So on and so forth until it returned 'no', at which point that stat would auto-increase. This would cause the phenomenon of the highest growth increasing with the order stated.

[Narga_Rocks]

IIRC, HP always went up when Dondon set all the growths to 0%. So it can't be the closest growth method, as that wouldn't work.

Also your calculation there is a little off, and your ranges seem quite abstract. If no growths (19.25%) becomes luck, then we can simply consider the luck growth to be 65+19.25=84.25%.

Where did I say differently? I was giving ranges of -5 to +5 and rounded down because it was simpler. 65 becomes 60 to 70, and 19.25 becomes 14 to 24. The reason for the abstract is because in 100 trials I can almost guarantee you aren't getting 84 or 85 on the dot. Far far more likely to get something in the ranges I listed. If I remembered how from my stat courses, I'd be happy to give you the proper formulas for prediction intervals and then give you the 95% prediction interval. But I neither remember nor care to go figure it out. Point is, my ranges are better than saying 84.25%. 3 years ago I could've even calculated the probability that you'd get the results you got assuming we are correct about how this all works.

Edited September 20, 2011 by Narga_Rocks

[Tables]

The difference is in how you estimated your range. You went for the no growth scenario being ± 5 AND the luck only scenario being ±5, then added those uncertainties up, when since we're assuming no growth would become luck, what you'd want is just to add the growths THEN apply some uncertainty.

And calculating the results I got isn't that difficult :P. Binomial distribution function in excel works wonders for it. I'm in the same boat for the exact confidence intevals as well, can't remember how to do it, but I can tell you the standard deviations and things.

For:

Luck: 84.25 ± 3.64

Speed: 45 ± 4.97

Both: 29.25 ± 4.55

Luck only: 55 ± 4.97

Speed only: 15.75 ± 3.64

So my results are this many S.D.s from the means:

Luck: -0.89

Speed: -0.80

Both: -1.59

Luck only: +0.80

Speed only: +0.89

I'd say that's certainly reasonable for all of them, although they all seem perhaps a little further away than I'd be happy with.

[Narga_Rocks]

I'd say that's certainly reasonable for all of them, although they all seem perhaps a little further away than I'd be happy with.

Can't do anything about that. I think you'd need more than 100 to be sure of anything. Really I'd recommend (if you really wanted) trying this with more than just one unit, though of course you are limited by the number of units you've got that only have two stats remaining in low enough percentages that the testing will show something (eg, not an 80+ growth).

If you could test with 5 or more units and see if the numbers are close enough then that's at least somewhat convincing. Anything further and you'd need to hack and test with multiple scenarios where some things are 0 and the stats you want to test are like 30 to 50.

As for whether or not I should have doubled my intervals, maybe you are right. I wasn't putting too much thought into it, so I'm not married to my intervals.

Edited September 20, 2011 by Narga_Rocks

[Tables]

Typical moderator. Any excuse to get out of sloppy statistics .

Hm, yeah, I think you're right. Unfortunately I can't really be bothered to do more testing. Not least because I've only got a little while left with my Wii until I head back to uni.