[Guide]Stat Growth rates

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Omnigamer
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Re: [Guide]Stat Growth rates

Postby Omnigamer » Fri Oct 21, 2016 9:57 am

Your mean is incorrect. Should be about 56.4175. Std is close; I got 1.898. At level 16, you should have ~52.29% probability of getting 57 or better.

Note that any such calculator is only an approximation, since this distribution is not a true normal distribution. It will "lean" one way or another based on the probability.

The first calculator is problematic since it is calculating on continuous values, rather than discrete. This means that it gives you probabilities for values like 57.5, which is impossible for our purposes. The second is better, but a bit tedious; if you wanted to the probability of it being 57 or better, for example, you'd have to calculate it at 57, 58, 59, 60, and so on until it hits 0 probability.

Your method of calculating for successive tiers will also not yield correct results. You have to add the distributions, meaning the full coverage of bins. If you just take the average value of earlier distributions, you will simply shift the center for your current distribution; you would not get the probabilities for, say, the worst possible luck included in the new distribution. For normal distributions, you could combine them via the method here http://pballew.net/combdis.htm .
Last edited by Omnigamer on Fri Oct 21, 2016 10:49 am, edited 1 time in total.

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ninjaluc79
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Re: [Guide]Stat Growth rates

Postby ninjaluc79 » Fri Oct 21, 2016 10:27 am

Omnigamer wrote:Your mean is incorrect. Should be about 56.4175. Std is close; I got 1.898. At level 16, you should have ~52.29% probability of getting 57 or better.

The first calculator is problematic since it is calculating on continuous values, rather than discrete. This means that it gives you probabilities for values like 57.5, which is impossible for our purposes. The second is better, but a bit tedious; if you wanted to the probability of it being 57 or better, for example, you'd have to calculate it at 57, 58, 59, 60, and so on until it hits 0 probability.

Your method of calculating for successive tiers will also not yield correct results. You have to add the distributions, meaning the full coverage of bins. If you just take the mean, you will simply shift the center for your current distribution; you would not get the probabilities for, say, the worst possible luck included in the new distribution.


I see. No wonder the probability is too low.

I know that, I just formulated that method to make things a bit easier, but I guess a lot of accuracy is sacrificed with that method.

Thanks for the tips!~
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Omnigamer
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Re: [Guide]Stat Growth rates

Postby Omnigamer » Fri Oct 21, 2016 1:35 pm

So a little more on everything:

What we calculate for any given tier is a binomial distribution, ie flipping a coin a given number of times with a specific probability of it showing up heads or tails. In this case, heads would be the higher value, and tails the lower (or vice versa). The magnitude of how it affects the final variable (stat) doesn't play a part in this initial calculation of distribution.

For a single distribution, we are interested in the probability of having us flip "heads" a given number of times, and then translating that into a stat via magnitude. Take your level 16 example. The overall range of the distribution is 15 (found from 16-1), starting at 42 (bare minimum, found from base + 15*lowval) and stretching to 57 (minimum + 15).The probability of hitting the minimum, ie winning 0 proverbial coin flips, is given by binomial_pdf(0,15,high_prob). Probability of winning 1 is binomial_pdf(1,15,high_prob), and so on up to your level. In this specific case, 0 translates directly to a stat of 42, 1 to 43, and so on.

It gets trickier when it involves multiple binomial distributions with different probabilities (one for each tier used). I'm pretty sure this would involve convolving the two distributions, however I am still looking to see if there are any shortcuts to that for binomial distributions. Right now it doesn't seem like there's a quick way though.

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Re: [Guide]Stat Growth rates

Postby Omnigamer » Mon Oct 24, 2016 1:49 am

I made a standalone program that shows character stats and distribution of specific stats by level. I just need to wrap up a few loose ends before I put it on git; likely will go up tomorrow. Runs on Windows, but will need a fair amount of porting to make it compatible with OSX/Linux.

EDIT: Program and source available here:

https://github.com/OmnigamerSDA/Sui2StatsChecker

Let me know if you have any issues getting it to work.

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ninjaluc79
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Re: [Guide]Stat Growth rates

Postby ninjaluc79 » Tue Oct 25, 2016 4:15 am

That's odd. I made something similar to this in Excel, but I simply took the average probability per level once I cross tiers. I compared it to this simulator, and my calculations are off by only 1 stat point and up to 0.01% for each stat!

Let's have an example of using this simulator by determining at what levels Nanami will have the best chance of getting 121 PROT, as required to save her for the Golden Ending. Nanami has 04 PROT, meaning she will average at least 121 PROT at level 57, which is actually within the level range of 55-58 by the end of the Rockaxe Liberation Arc. In almost all my playthroughs, both Riou and Nanami always reach level 58 by the time we get to Gorudo. Thus, I never really encountered any problems saving Nanami for the Golden Ending and I got to have really shitty luck to NOT reach 121 PROT at level 57-58.

So, by levels, here are the probabilities of Nanami getting at least 121 PROT (unless you REALLY hate her guts and are willing to cheat using Stat Stones to pump up Nanami's PROT to 121 without ever using her):

Level 48 - 0.0001%
Level 49 - 0.0032%
Level 50 - 0.0436%
Level 51 - 0.3342%
Level 52 - 1.6532%
Level 53 - 5.7203%
Level 54 - 14.7024%
Level 55 - 29.4822%
Level 56 - 48.1607%
Level 57 - 66.7344%
Level 58 - 81.5548%

Level 59 - 91.1992%
Level 60+ - >93%

Therefore, Nanami has a good chance of getting 121 PROT at levels 56-58. Level 55 may be a long shot but still possible.
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Omnigamer
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Re: [Guide]Stat Growth rates

Postby Omnigamer » Tue Oct 25, 2016 8:25 am

Don't forget that it is DEF and not PROT that needs to be 121. It is pretty trivial to get her to survive at level 50 or below with just basic armor from early game.

Depending on what you did, it could be very close. For Nanami's PROT, she is growth rank 4, so her probability of gaining extra is fairly close on each levelup regardless of the tier. Other ranks with far more heavy/light probabilities might be off by a fair bit more. Check a rank 1, 3 or 5 stat.

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Re: [Guide]Stat Growth rates

Postby ninjaluc79 » Tue Oct 25, 2016 10:08 am

The 01 stat is closer to the 1st quartile at levels 2-19, grows very quickly at levels 20-59, and slightly stabilizes at levels 60-99. I really never had any experience with this stat rank because I don't get to use 01 MAG characters as magicians because they have pretty bad affinities across the board, though I think the stat stones could be of use to pump up the squirrels and the krakens' TECH to a more viable value so they could hit more, considering as animals they cannot equip any armor.

I actually see the 03 stat to be pretty wild. At level 2-19, the value is always close to the minimum; but at level 20-59 where the chance of getting an extra point is close to but less than 50%, the mean value (106.35) got shifted to ~3rd decile, but the effective value range was ripped wide open at 97-117. Due to the fact that the 03 stat gets used in A LOT of character stats, this leads to some characters not getting 100 in their 03 stat at 60 due to getting shafted by the RNG a lot, and others getting 100 in their 03 stats as early as level 55. In one playthrough, Chaco got a really nasty case of getting shafted by the RNG by only having 97 MAG at level 60, while Nanami already had 100+ MAG before she "died" at level 58. At level 60-99, however, as the chance of getting an extra point increased to close but greater than 50%, the mean (128.29) got shifted closer to the middle, and the effective value range was now at 115-142. As a result, the RNG became more forgiving overall, but not enough to cover those levels from 20-59 where a character's stat got shafted by the RNG. Only the stat stone trick can correct such cases, like Chaco's 97 MAG at 60 from earlier. Fortunately, it's so easy to fix that in some cases the stat stone trick is no longer needed.

The 04 stat is always closer to ~6th decile all throughout the game, and the only reason I soil myself over it 99 is so I could get 04 MAG mages like Millie and Eilie to 160 MAG at 99 for the 2nd lv4 MP charge so they can do Unite Magic by themselves. As I mentioned above, I found it easy to get Nanami to 121 PROT at 56+.

The 05 stat is always pretty close to the maximum all the way to 99, which makes it very difficult for Riou to reach 175 MAG naturally; the most he can get in a normal playthrough is 170, you really need to be very lucky to get 175 naturally on him. I had to use like FIVE stat stones to get Riou's MAG that high.

The 06 stat rank is quite a disaster as well, I had to use SIX stat stones on Viki to get her MAG to 200 at 99 for that 3rd level 4 MP charge. Suffice to say, getting Flik, Rina, Sierra, and Tengaar to 200 MAG is going to be really painful.

The 07 stat rank is quite odd. Sure, it's close to the maximum at levels 2-19, but it starts getting crazy at levels 20-59, as it also had the same "close to but less than 50%" problem that 03 had. As a result, the mean veered closer to the median so quickly; however, the 07 MAG mages in all of my playthroughs always got to 175 MAG at level 60. The crazy thing about the 07 stat usually happens when getting Jowy and Tir to 99 instantly. Some playthroughs had King Jowy with 220 MAG at 99 via the "Recruit at Level 99" bug, but when I try grinding Tir to 99, he rarely ever gets to 220 MAG at 99. Maybe the RNG likes to pump 07 stats to 220 at 99 but does not like it when you try it yourself?

I could only say that the 08 stat rank is actually quite fun to play with, solely because of how close it is to the maximum of 255. I was really excited to get Luc to 250 MAG for him to get the highest MP count in the game at 9/9/7/5, so I did not mind using up to SEVEN stat stones just to get him to 250 MAG. Luc can pretty much spam spells all day with MP that high.

I would like to remind you that Stat 10 (Viktor's STR) is quite off. It's supposed to be 6-7 only up to level 14, not level 19. So it should be 1-2 at levels 15-59, not 20-59. Many thanks.
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Omnigamer
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Re: [Guide]Stat Growth rates

Postby Omnigamer » Tue Oct 25, 2016 10:58 am

What I meant above is to compare my program output with your approximation calculations. You should find that it is similar for distributions closer to "center," but may be less so as the cumulative distribution approaches the edges.

I did not notice that it worked differently. A lot of the logic is somewhat hardcoded, but I think I can probably adapt it easily to account for growths 9 and 10. Chuchara, however, will always remain incorrect because it would involve a significant change for just him, and he's frankly not worth it. I will try to update it tonight, as well as provide portraits in the UI.

I built the program specifically for my purposes, as it simplifies a lot of other calculations necessary for determining stat ranges at given levels for speedrun purposes. For example, Bolgan's speed (rank 1) is important to know for planning optimal Mist Monster strategies. Eilie's MAG stat range at level 19 is extremely important for fast strategies on Star Dragon Sword and Abomination. Combinations of Luc's and Nanami's stats at levels ~37 are important for Luca setups. Hopefully other people find it useful for their various purposes, but at the end of the day I'm satisfied when it meets my purposes.

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Re: [Guide]Stat Growth rates

Postby ninjaluc79 » Tue Oct 25, 2016 12:39 pm

I also noticed that LC Chan and Wakaba did not have their level 1 HP modified (it's 10x the usual for both, so that they have 240 and 200 HP respectively at level 1), while the animals and Gadget did not use their stat multipliers. The first can easily be fixed by creating a different HP rank for LC Chan and Wakaba that uses their respective HP rank but with a different base HP. The second one, maybe we can apply the multipliers to the final stats (Average, Maximum, and Minimum) while keeping the probability tables untouched? Or we can just leave it to the users to actually apply the multipliers?

The squirrels, Shiro, Gadget, and Chuchara have STR and PROT multipliers of 2.2.
The large size beasts (Feather, Abizboah, and Rulodia) have STR and PROT multipliers of 3.1 and 1.5, respectively.

You can probably use this modified stat growth chart for Chuchara's STR so you can use it alongside stats 9, 10, and 11.

As always, numbers in parentheses after X-Y of each level tier indicate chance in 256 to obtain the higher number, and the number in parentheses in the final stat indicate the mean stat value at level 99 rounded off to the nearest multiple of 5.

Stat 14 (Chuchara's STR)
Level 1: 10

Level 2-14: 0-1 (94)
Level 15-59: 0-1 (83)
Level 60-99: 0-1 (157)
Final Stat: 10-108 (50)

It's still not exact, but it's better than just using Stat Rank 12 as a placeholder or creating a new level tier just for him.
Last edited by ninjaluc79 on Tue Oct 25, 2016 1:02 pm, edited 1 time in total.
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STARWIN
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Re: [Guide]Stat Growth rates

Postby STARWIN » Tue Oct 25, 2016 12:55 pm

You know, my code from the last page only needs minimal work to output whatever you want?

like, here is rank 10 stat reach table: http://pastebin.com/XEUbT8tA

rank 14 with your page 3 post data: http://pastebin.com/9nGD6tXG (you can see the extreme low cases rounding to zero at double precision after level 59, so my print routine can't distinguish those cases from the initial zero there)

what is with the multipliers exactly? what is multiplied at which point in level up by what?

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Re: [Guide]Stat Growth rates

Postby ninjaluc79 » Tue Oct 25, 2016 2:52 pm

The stats for each level is directly multiplied by the beasts' multiplier to get the final stat. So you need to get the stats for each level first, then apply the multipliers.

For example, Abizboah has 07 STR and 06 PROT. As a large size beast, he has multipliers of 3.1 and 1.5 respectively.

At level 99, he has an average of 212 STR and 188 PROT. Applying the multipliers, we have:

212 * 3.1 = 657 STR and 188 * 1.5 = 282 PROT.

Or the aforementioned Chuchara with 14 STR and 05 PROT. As a regular size beast, he has multipliers of 2.2 for each.

At level 60, he has an average of 30 STR and 144 PROT. Applying the multipliers yields 66 STR and 316 PROT.

So at level 99, he has a base average of 52 STR and 168 PROT and final stats of 114 STR and 370 PROT.

Another example: Gadget at 04 STR and 07 PROT. At 99, he has base averages of 168 STR and 212 PROT, yielding final stats of 370 STR and 466 PROT.
Last edited by ninjaluc79 on Tue Oct 25, 2016 3:04 pm, edited 2 times in total.
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STARWIN
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Re: [Guide]Stat Growth rates

Postby STARWIN » Tue Oct 25, 2016 3:01 pm

So the game keeps the non-multiplied stats internally, but when they are used for any other purpose, they are multiplied as stated temporarily before use?

I can whip up a similar table for those if so, but what are the ranks?

some of your numbers seem a bit off.. 168*22/10=369 and chuchara seems to have 316 PROT at level 60 with 5% probability only..?

dunno if this table format is useful for your purposes but

14 2.2: http://pastebin.com/t3GE6mAH
05 2.2: http://pastebin.com/1k4GGP2r

more?
Last edited by STARWIN on Tue Oct 25, 2016 3:38 pm, edited 1 time in total.

Omnigamer
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Re: [Guide]Stat Growth rates

Postby Omnigamer » Tue Oct 25, 2016 3:38 pm

I hesitated to implement any of the multipliers since I wasn't sure if they were truly sourced or not. As far as I can tell, they were found via observation and assuming the older stat growth tables. Were the actual values used for multiplication part of the data dump?

The missing constant bonuses and otherwise I can include for the next release.

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Re: [Guide]Stat Growth rates

Postby ninjaluc79 » Tue Oct 25, 2016 4:23 pm

We will know more about how the beasts' stats are calculated once Pyriel or whoever comes back.
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Re: [Guide]Stat Growth rates

Postby Omnigamer » Tue Oct 25, 2016 6:22 pm

Going through and doing some tests with directly modifying the values in memory, the "small beast" equations seem accurate. I don't have a save file that can check the large beasts at present, but I'll assume that the 3.1 and 1.5 modifiers are also correct for the time being.

EDIT: Updated the program. Now supports all of the oddball characters (sans Chuchara), and incorporates portraits for flavor.


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