Statistical Research

[Wataru]

Hey all. I have been compiling a statistcal database of the Suikoden characters in each game (I have no idea what I will use this for, but hey, I'm having fun playing all the games again) and have run into a snag in my data analysis. I want to see if anyone can help me. Right now I have completed my data sampling for Suikoden 1 only.

First, my process. Using a Gameshark (yeah, so sue me) I leveled up every character (including Ted and Odessa) to level 99 and copied down their stats. I have also ignored Gremio's ridiculous PWR growth above level 60 for purposes of this). What I want to do is assign each character a letter grade for each stat. Since stat growth patters are fairly consistent throughout (everyone's growth seems to slow down at the same time) the proportions of each character to each other should remain fairly static regardless of level (except for the "Gremio Problem"), so this database would give everyone a general rating of their stats at any given time. This would basically show who's better at what overall. For example, if I want a super mage, I would look for someone with an S in MAG, but I may want to go down to an A to get someone with better HP.

This is where my problem lies. I am stuck for a way to have a consistent grading scale and the stat spreads do not seem to allow for one. I want to see if any math/statistics wizards out there can give me a hand. My first attempt used 8 ranks like in Suikoden III (E, D, C, B, B+, A, A+, S). I decided that the mean score would be the border between B and B+. From there I tried to use distance from the mean to decide ranks. At first I tried each rank being 10% (A would be 110% of the mean, A+ would be 120% and so on). This worked very well throughout, with one exception: magic. Suikoden 1 is a game of magical extremes. Tjose who are good at it are REALLY good at it and those who are bad at it are REALLY bad at it. Most characters tend to be on the low side, so the mean is also low. The mean magic score at level 99 is 128. The lowest was Eikei with 54 and the highest was Luc with 265 (I don't adjust for locked stat-boosting equipment). The best mage is more than DOUBLE the mean! My problem is that using these proportions, I have almost 15 people wih an S rank in magic. Basically anyone who gets a level 4 spell by level 60 or so gets an S and that is too great a spread. This system does, however, work well with the other stats.

My next attempt was using Standard Deviation. This cut me down to 6 ranks instead of 8 (because 4 SDs above the mean is too great a number for anyone to qualify). Again, it seems to work fairy well across the board (except for a ridiculous number of B ranks, which is to be expected), but, again, magic is the problem. Excel says the SD of magic is 50, so an A would be 178 and an S would be 228. This seems OK for the high end (albeit I'll have a million people with A), but it makes an E rank a score of 28, which no one would qualify for. Even Fu Su Lame, Kanak and Eikei (the Horrible Magic Trio) would almost qualify for a C in this spread.

So here I am. As I see it, I have three options:
1- Use one of my previous strategies (probalby the % one) and suck it up that I have 800 S-rank mages.
2 - Use the % for all but magic and find some other system for magic
3 - Scrap all of that and just use my own judgment to assign ranks.

Any suggestions?
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[Scarlet Assassin]

This makes me wish I had kept my statistics textbook frmo last semester, or my notebook for that matter. I coudl say it would be better to assign them Stars instead of letters, that way you have as much room as you need. Make the average four stars and use percentages of population to judge where the class boundaries for each star should fall. That way you can get up to 7 or 8 stars if neccesary without it looking silly.
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Chief of Beat-em-up Honeys Division, Devoted Protector of Lady Tifa Lockhart

[Wataru]

Not a bad idea. That would fall along the lines of "making up my own levels."
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[Camus the Noble]

That sounds like a good idea. However, I also like proposal number two, the "find a different system for magic" proposal. Really, pure mages work under a different system than the majority of characters. They're almost all short-range, but are too frail to fight in the front row, so they almost never attack physically. Therefore, their usefulness is limited to magic and magic only, unlike physical attacks, which you have a neverending supply of. The different dynamic changes the nature of the stat, skewing the data favorably toward pure mages; hence the large number of "S" rankings.

Perhaps a solution would be to arrange the data in a box-and-whisker plot, but to expand the quartiles out to create a large middle? Not having the data right in front of me, I don't know for sure if this would work, but it should pull characters like Cleo and Rubi down toward the middle.