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Fates RN Regression Project

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No no no lol. I meant, add on to those data points to send to you. I think a new spreadsheet would be easier for you to add to your data vs me updating my data and resending that file. Sorry for the confusion.

Edited by Vascela

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Oh yeah, go for it. The only problem with spreadsheets is that you can't attach them to posts or messages, so you'll have to save it into another text file.

Because of the way I have my analysis algorithm set up, it's best if it's just a string of values and outcomes I can import.

[Hit Chance], [Outcome]
[Hit Chance], [Outcome]

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Good news! The data is nearing parabolic convergence for the upper range -- the current R^2 value is sitting at 0.969. I'm basically waiting for something I can adjust to better fit a floor of 50 - 50.5 and a ceiling of 99.99.

The best fit polynomial as of now is

P = -0.0168*Z^2 + 3.5614*Z - 87.635

dP/dZ = -0.0336*Z + 3.5614

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Not sure if Google Sheets is missing any features you need in your analysis, but at least for sharing the data (since you can't upload csv/xlsx) I made a sheet of the text dump you have in the OP:

https://docs.google.com/spreadsheets/d/1u4bfhaPCI2Ztl8soJk4NAmBZ_WCBDhgry5d7fY_kQL8/edit

and a data gathering template sheet that might be useful (you can copy it and share it when you're done):

https://docs.google.com/spreadsheets/d/1nOMqLVtGrUHotpfU21pdOwViRgUk4hFTgxWfHqpjPEM/edit

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I'm guessing we just don't want to deal with dual guards that report a crit?

I mean, if it displays the crit, it hits, yes? And they show that on successful dual guards as well.

Edited by shadowofchaos

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I'm guessing we just don't want to deal with dual guards that report a crit?

I mean, if it displays the crit, it hits, yes? And they show that on successful dual guards as well.

that'd be biased information towards hits. you're only adding extra hits but you'd never add extra misses, so data would be skewed

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that'd be biased information towards hits. you're only adding extra hits but you'd never add extra misses, so data would be skewed

Yeah, this is the primary reason Dual Guards aren't being counted. But we can at least say that in the limit, Dual Guard affects both hits and misses equally, so the exclusion shouldn't matter.

Not sure if Google Sheets is missing any features you need in your analysis, but at least for sharing the data (since you can't upload csv/xlsx) I made a sheet of the text dump you have in the OP:

https://docs.google.com/spreadsheets/d/1u4bfhaPCI2Ztl8soJk4NAmBZ_WCBDhgry5d7fY_kQL8/edit

and a data gathering template sheet that might be useful (you can copy it and share it when you're done):

https://docs.google.com/spreadsheets/d/1nOMqLVtGrUHotpfU21pdOwViRgUk4hFTgxWfHqpjPEM/edit

I'm doing a test import of my equations right now, and it looks like it will work. Does anyone besides me want to see confidence interval data, odds ratios, etc.?

I also consolidated the data collection and output stages into a single document on two sheets so that everything will change in real-time instead of needing new imports with each contributor's data. I've also separated data collection into columns so that there are no rush conditions in filling data points.

All told, the version I just finished will be able to manage 3 persons recording data simultaneously, with plenty of room for more. I also went ahead and imported a full all of my collected points so far, which includes everyone that sent anything to me or posted here.

https://docs.google.com/spreadsheets/d/1UaKECEGX7Dyb_JhduG6j_SPDkphsKELdVZvr2mAv5aU/edit?usp=sharing

(I had to work from a copy because view-only privilege)

So yeah anyways that's up and running, and I (or anyone else) can add whatever additional information they think may be necessary, just don't break the data-reading functions in columns B and C on the Results sheet. Edit privilege is active for anyone with the link, so just add stuff. I'm going to continue to store data locally in addition to on Google because I'm pretty sure Excel's statistics package is more rigorous. I'll also put the link in the front post.

Edited by BlenD

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Just a general update: we've hit 23000 points, the (3A+B)/4 model has resolved all of its boundary issues except for one, which is acceptable, and continues to be the best predictor for hit rate. I still haven't found an acceptable model that is linear on the low end and parabolic on the high end.

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Hey guys,

My computer is currently fried, possibly out of commission, so progress is going to halt on my end until I can get that taken care of. However, I did send the results through 23000 points to VincentASM, so from here on out it's just affirming that there isn't any better alternative model (you know, what we've been doing the whole time) and reaching a definitive degree of certainty.

Edited by BlenD

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Okay, for all intents and purposes, this project is officially closed. I'm going to be continuing up to 25000 points for sake of completeness, but the system is at the very least approximated well enough by the model that barring a breakthrough from the hacking community, provides the most accurate and easily understandable breakdown of the system.

I have two write-ups available on my tumblr, one on the model (which, if you're here, you already know about), and one on how I came to the decision to declare the project complete.

Thanks again to everyone who contributed their time, efforts, and data. It's been a fun ride.

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For the single-RN part, probably to nerf Avoid tanking, because it could get rather ridiculous rather quickly in previous titles. For the rest of the formula, I'd guess to make it more likely to penalize players who see high hits and say "good enough" without exploring other options (which then keeps Bronze/Brass relevant throughout the game).

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The new formula for the high end seems to be a good happy medium between '1 RN' and the '2 RN' systems. It increases the consistency of strategies that rely on high-but-not-perfect hit rates (compared to '1 RN'), without making everything above 80% or so nigh-guaranteed to hit.

Edited by Radiant Dragon

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It's kind of funny how (compared to the 2 RN system), the new system makes the previously reliable strategies (such as dodgetanking, high hit rates, etc.) and makes them less certain, but makes RNG abuse (on a grand scale) much easier because dodging several 85% hits/making a few 20% hits is no longer quite as bad as it used to be.

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It's funny, but it also seems completely pointless to go halfsies on single RNG. Just make it 1RNG and make the numbers actually mean what they say instead of absurd outcomes like Certain Blow actually becoming increasingly more +Hit% the more Acc you start with (9% displayed without CB gains +40% like you'd figure, but 45% displayed gains +49%).

I don't understand what possible design benefit this has over a simpler system where numbers you see actually mean things. But good riddance to "True" Hit at least.

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I think it's an attempt to balance the randomness of the hit system with the planning of the dual system. Because Dual Guards now have consistent behavior and aren't RN-based, the player has the ability to choose, within limits, which enemy attacks get completely negated. This would trivialize many groups of enemies under the old system, as a cluster with sub-30 hit chances would perhaps be able to hit one time, which can be taken away via Dual Guard. Making the lower range 1-RN keeps those enemies relevant. Dropping the hit rates in the upper region by a small amount further shifts the balance so that those enemies get more opportunities to hit. It's still a fairly simple system, and as Dark Holy Elf said towards the beginning of this thread, other formulas have gone to something similar recently.

As for full 1-RN, old, Japan-only FEs have it, and it makes for a lot of inconsistency and emergency planning. Requires more skill to reach consistency, sure, but also holds much more potential for rage-inducing RN strings. XCOM also uses a 1-RN system, and it's one of the most polarizing (and I would argue more often than not, disliked) features in the game, especially for Ironman mode.

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The one counterpoint I'd note is that enemy AI seems to pretend Dual Guard doesn't exist except when it needs to negate one, so it's not always an issue where the player can decide which attack gets negated unless the AI can be manipulated (which I'm sure it can, but it's not always so easy as to decide which of 3-4 enemies will hit the guard). I can definitely count plenty of times where a 0 damage attack led off to burn my Dual Guard, as if the AI knew it might as well use its worst attack to get negated.

I understand the argument about player frustration, but I don't think the solution is to lie to the player, even if in Fates it's mostly a gentle lie in their favor most of the time. 90% might as well mean 100%. Why not just make average hitrates for the things you want to have 100% hit 10% higher? And people rage about the RNG regardless, and arguably will rage harder about things like "those enemies have 75% hit but they don't ever miss" which, under the Fates RNG, is actually expected behavior. XCOM is designed around 100% being largely unachievable, but FE makes it reasonably possible to reach 100% hitrate except in some relatively predictable and controllable circumstances. There are ways to play FE without having to gamble as much. I never had issues with the RNG in earlier FEs, I just planned around the possibilities.

It bothers me on a fundamental level when FE is a game with extremely simple mechanics that are all graspable from stat screens and combat windows, and then one mechanic is a blatant lie. If damage occasionally underreported for no apparent reason I think people would flip but for some reason we tolerate false RNG reporting and I'm not sure why, other than that most players just don't know that accuracy is not what the mechanics suggest it is.

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If you go by strict statistical analysis, 90% means that you're going to miss one out of ten times, and 25% means that you'll be hit one out of four times. I like it better than straight 1 RN, which can get pretty weird.

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