It’s a Tri-Stat game! We’ve done a few of these already so you already know the basics. Weird combat system where the attacker and the defender have very little to do with each other? Check. A million point buy options? Check? Balance basically a fig leaf? Check. So what are we left to do but dissect the 70% of this book that isn’t RPG. Let’s learn about harem animes!
System Mastery 
Your chance of hitting is equal to the probability of succeeding on your own check, multiplied by the probability that they do not succeed on their own check. Both values are always a factor. The math is much more solid than you give it credit for.
The problem is that they’re independent, so high-level Tri-Stat combat turns into a pile of misses and whiffs until someone explodes. And unlike Warhammer Fantasy Roleplay or the old 40K RPG systems, there’s no provision for onslaught or otherwise getting worn down. Legendarily Mark McKinnon had to be sat down and shown this because he hadn’t playtested the game beyond token attempts. (He was afterwards convinced to move to a roll-over system for the saner but extraordinarily bland BESM 3E.)
Seriously, there’s a bunch of goofy GoO history out there that you can dive into if you’re interested. Ewen Cluney even compiled it for a $2.50 zine. https://www.drivethrurpg.com/product/264224/Small-Company-Big-Mess-A-History-of-Guardians-of-Order-and-Big-Eyes-Small-Mouth?src=hottest_filtered
I decided to math out the chances of hitting your target and it turns out that it’s so transparently bad that Mark McKinnon probably should have been told to sit in the corner with Hogg & Tanis or some other probability textbook. In general those chances are equal to X * (1 – Y), where X is your attack probability and Y is your target’s defense probability. If we assume that the targets are at a rough parity with X = Y, this becomes X * (1 – X) = X – X^2. Which peaks at 25% if X = 50%, and only gets worse with deviation.
https://www.wolframalpha.com/input/?i=x-x%5E2+from+0+to+1
Meanwhile most designers with a clue these days will tell you to shoot for a 50%-70% chance to hit in “baseline” encounters. After all, missing usually does nothing and missing a lot makes combat drag on way too long. So that <=25% chance to hit is just dire.
Your problem is in assuming that X and Y are roughly equal. What this system does, in much the same way that GURPS does, is to ensure that the more-skilled character will win. Given that the game ends when the party dies, this is a good thing.
Besides, even if you are fighting a Big Bad who is equally skilled, those sorts of extended duels that go on forever and are decided by the first clean hit, are extremely in-genre. D&D-style attrition combat wouldn’t make sense here.
X and Y are going to be similar in most cases. The whole point of that example is that combat rolls are going to trend around it, so while you may get better results depending on a power disparity it’s still not going to be nearly that kind of golden mean of 50%-70% baseline to keep the majority of combat interesting.
“Besides, even if you are fighting a Big Bad who is equally skilled, those sorts of extended duels that go on forever and are decided by the first clean hit, are extremely in-genre. D&D-style attrition combat wouldn’t make sense here.” Okay, when’s the last time you saw a duel where the participants kept missing each other in the same way every time? Goku fighting Vegeta on a featureless plain or whatever? Never, that’s when, because even when they’re not hitting something about the story is moving forward. Their tactics, the battlefield, internal reserves, whatever. Meanwhile here, each miss does…nothing. It’s like a Markov chain where you aren’t allowed to just skip to the end.
There’s no reason to assume that X and Y are similar. If we’re playing to genre, then the protagonists will have a very high X, and the only ones with a comparably high Y will be the Big Bads. Protagonists don’t miss, but the Big Bad can block their attacks, and the epic duel resembles something very like Errol Flynn. Eventually, someone lands a hit, and the fight is over. I could probably find some examples from the show, if I looked.
Dragonball Z is a different genre entirely. That’s clearly a world where everyone has a million HP, and each attack does hundreds or thousands of damage. Nobody goes down in one hit, unless they’re a normal human who gets caught in the fallout.
Maybe Dragonball Z makes for more exciting combat in a tabletop game, but that’s not always the type of game you want to play.
Even Errol Flynn had interesting beats in his fight scenes. Tri-Stat just has nothing beyond the binary of hit -> deal some constant amount of damage vs. miss -> sit with thumb up butt. So existing flaws in dice math (seriously, work out the actual figures if you want to claim this works at all*) just get exacerbated by how bland the combat system is.
*It was shown on an old rpg.net post that with reasonable effort a 2-person duel could take 32 rounds, or with a bit more 296 rounds. Either of these probably takes hours with a full party involved.
If you’re trying to do mostly noncombat, cool! But combat is the only major subsystem that gets fleshed out in these games, and even then with not a lot of guidance on composition, so you’re mostly making stuff up without the help you should be getting from the book you purchased.
I’ve done the math. It really does work out, for high values of X and low values of Y. It doesn’t work for frequent combat with high values of Y, and you shouldn’t use this system (or GURPS) if you want to run those types of games.
Combat isn’t super granular or detailed. It’s a lot like old D&D. You can either downplay the combat aspect of the game, or you can get creative with your descriptions. If you want a system that offers more complexity in combat, then there are plenty of alternatives.
It is a bit unfortunate that they don’t spell this out in the rule book, but that’s true of most systems. If you judge a game based on your misconceptions about what it should be, rather than what it actually is, then even 4E looks like a failure.
No, you haven’t done the math. Unless you’ve got work to show here and you just haven’t written it out yet. And even then it’s for a special case that isn’t at all universal.* We’re not talking about a sandbox game here, where encounter variance is expected to be high and PCs are intended to be ruthless in either quashing easy stuff or avoiding hard stuff. Whether it’s in genre for the fiction or for most TRPGs, there’s a baseline that’s usually expected to start from where you can then deviate.
In fact the existence of BESM 3E is clear evidence that the math was found to be borked, and that parity is expected as a baseline. Keep in mind that Mark McKinnon was eventually forced to sit down and actually run a full combat with characters at similar power levels by his co-designer David Pulver, and that they actually regarded this as enough of a failure in what they considered “standard” play to change things in the newer edition. Mark McKinnon ripped out the old Tri-Stat resolution system of 2d6 + roll under fixed targets and replaced it with 2d6 + roll over variable targets, not unlike d20 or anything else that uses the terms Target Number/Difficulty Class. Even attacks, while still longer than they should be, succeed if the attacker rolls higher on offense than the defender rolls on defense. (Really there only needs to be one roll of attack vs. static defense value, but it’s a step forward.)
Really, given available evidence I figure that Mark McKinnon just didn’t use most of the rules he’d printed in the first place. The original BESM was heavily inspired by Amber Diceless, which worked on similar principles but which McKinnon neglected to actually articulate until 3E itself. (Check it out if you can for historiography – there are a lot of snippets of play advice such as how to make things more complicated or more simple.) Most new systems printed in the past decade (at least) will thankfully be more up front about expected play – cf Lasers & Feelings for one of the slimmest examples of this – but back in the 90s or earlier people were often expected to be taught by veterans rather than freshly picking up a sourcebook.
*Found the dated rpg.net post: https://forum.rpg.net/index.php?threads/besm-combat-mods.9964/#post-153806
Seriously, I worked out all of the math with a pencil, back when they reviewed BESM the first time. The game works for high values of X and low values of Y. It doesn’t work well for low values of X or high values of Y. It may very well have been unintentional, but that doesn’t make it less true.
It’s entirely believable that they changed the mechanic because they wanted to support higher values of Y, or lower values of X. Personally, I would have resolved that by changing the system to ensure X is always high and Y is always low, but it sounds like the guy didn’t really know what he was doing to begin with.
As has already been pointed out, that in the above example combat is slated to last an average of 36 (!!!!) rounds. For two characters squaring off. Two. There is no universe in which that’s good game design, especially when it’s as witless as rolling one and only one stat vs rolling one and only one stat. Not to mention every round it drags out for grossly reduces the possibility that the match will be decided by anything other than ‘I have the bigger numbers’. In other words it’s basically an MMO DPS fight. There’s also no real room for anything clever unless you go to the GM and beg them to give you a bonus for something you’re doing which will slow things down even more as you’ve got the tedious roll-off mixed with a negotiation. Unless you’re okay with players only ever picking on enemies specifically designed to be weak to them (no way that’ll ever get old) it’s pretty dire and comparing it to old-school D&D combat is not only inaccurate (as in D&D you’re at least chasing a static number which speeds things up) but not a good one as D&D combat has always been pretty lousy in its most basic form, especially those interminable high-level fights. I’d also mention ‘the goal of the game is to not die’ is, at best, a gross failure of imagination and scenario design; this isn’t an MMO.
Fruits Basket kind of sort of is the distaff version of a harem anime.