FE7 Reliable Stats Efficiency with Expected Turncount metric - LHM in 46.5~ Turn (Guide to Expected Turncount Included)

[Irysa]

https://www.youtube.com/playlist?list=PLzHc9vjq1MicDyt1rGpaLhdyIfmMGpxHQ

This project is intended to serve as an introduction and demonstration of the application of both the Expected Turncount metric and "Reliable Stats" / "10% Quantille" / "90% binomial" / "Pessimistic Mode". Both of these are attributes that when utilised can help to make strategic comparisons between units more grounded in hard evidence rather than rhetoric.

Most existing well documented playthroughs are extremely rig heavy Low Turn Count playthroughs, where player stats are massively inflated and strategies are very unreliable, or 0% runs where many otherwise useful growth units are nearly useless. Whilst these runs are valuable and interesting in their own right, they aren't very representative of more "normal" play, making it difficult to cite them comprehensively as evidence in debates about how good characters are for more standard play.

Expected Turncount helps to account for the "wasted" turns lost to resetting in unreliable strategies, and there is a video to explain exactly how it works at the start of the playlist. 10% Quantile allows you to reward the increased reliability of high growth units without inflating the relevance of mediocre ones, whilst maintaining the importance of good base stats.

Whilst the community has often used average stats as a guideline before, I believe that these are not a good way to look at units in practical application, as a units average in any given stat is typically only about 60%~ likely to be at least that number, and when you start combining averages for multiple stats such as Strength and Speed, these values start to get less and less likely. A 90% threshold allows you to say with confidence that a unit can most almost certainly kill certain enemies or survive certain attacks when trained, which matters more than the 20 to 30%~ of the time they were on their stacked offensive averages.

Most of the descriptions on each video get more into the individual strategies and the calculations involved for the expected turncount on each map. In the future I plan to show how Kent is definitively and provably less efficient than Sain as a result of his worse base stat distribution and more middling, less reliable growths, and exactly how many turns you could expect him to cost on average.

If you find this sort of thing interesting, I run a discord dedicated to LTC and Efficiency strategies in Fire Emblem. If you would like to join, feel free to send me a PM and I'll send you an invite.

As a final note, there should be at least one small surprise in this run even if you're familiar with FE7, so I hope you take the time to watch it. Thanks.

Edited March 1, 2020 by Irysa

[XeKr]

Some potentially interesting trivia for FE7 LHM efficiency, beyond the baseline in the videos.

The specific improvement in fe7prologue is to risk the 3 turn if Lyn is not hit ep2, attacking Batta if Lyn is at full health pp3 (even though she’ll take 3 total attacks by the time she can heal). The improved 5 turn chance seems to barely outweigh the increased reset chance on turn 3, on average.

Just for the record these are the numbers
bossmisspp3ANDbothhitep3 =  0.067481
bosshitpp3ANDatleast1hitep3 =  0.17246
ep3codGIVENep2nodamage =  0.23994
ep2nodamage =  0.69190
***ep2nodamageANDep3cod =  0.16601
***ep2nodamageANDpp5cos =  0.52589
ep2damage =  0.30810
***ep2damageANDep3cod =  0.030756
ep2damageANDep3nodamage =  0.14411
ep2damageANDep3somedamage =  0.13324
***ep2damageANDep3nodamageANDep4cod =  0.015128
***ep2damageANDep3nodamageANDpp5cos =  0.12898
***ep2damageANDep3somedamageANDpp6cos =  0.13324
*** = important numbers

For a strategy with
65.5% (52.6% and 12.9%) chance of clearing on turn 5
13.3% chance of clearing on turn 6
19.7% (16.6% and 3.1%) chance of resetting on turn 3
1.5% chance of resetting on turn 4

The Expected Turncount is ~6.0

The Conditional Mean Clear Turn is ~5.2
The Conditional Mean Reset Turn is ~3.1
The Reset Penalty is ~0.8

#justdosims (>_> doing stuff by hand gets exponentially complicated even for very simple chapters)
 
Simulations suggest ~96% chance of the bosskill in fe7c2 if you consider kent pp, kent ep, kent pp, sain ep, but forcing it does incur a bit of Kent cod as mentioned which may not be worth it. I believe the 90% 4 turn was calculated manually, and it seems pretty complicated with all the conditionals. We could do a more involved sim but ultimately it wouldn’t affect the numbers too much (but could be an interesting exercise)
 
The 5 str Lyn (64% for at least 1 proc in 2 levels at 40% growth) 3 turn in fe7c3 (~3.4 turns) is basically just the Sain cod on ep3, plus a tiny bit of unreliability elsewhere. Lyn can die ep1 though it’s very unlikely (she faces 1 less merc and 2 more bandits than the other variant, where she has 4.9% cod). Lyn can miss the merc, and if she doesn’t crit it’s probably a 4 turn (slightly more likely but it’s just 1 more turn at low probability, not rly worth the calc).
 
Other units with the requisite stats, like Florina with at least 6 str (78.4% for at least 1 proc in 3 levels at 40%) 11 spd (57.5% for at least 2 proc in 3 levels at 55%) (overall 45.1% at lvl 4, 66% at lvl 5, 80.1% at lvl 6), can possibly combo for the fe7c7 bosskill, though the exp buffer is nice for Sain. Such a Florina can manage around a 95% 2 turn, though she may want the robe to avoid cod. We investigated other combos with Lucius, Rath, and Lyn, and such, but even with the crit chance and potentially doubling the odds aren’t really any better than Sain Iron Sword.
 
If you don’t have the armorslayer from c6 and your invested cav is Sain, in fe7c9 you probably want to use the Lyn+Sain combo on Eagler for the 3 turn. The chances are pretty good, around 93.6% that Lyn and Sain have some str combination that will enable the kill, if Lyn is lvl 7 (90.5% with lvl 6 Lyn) and Sain is lvl 11. Lyn also has to hit a spd benchmark which she’s very likely to get (95.9%/91.3%) by lvl 7 or 6. Sometimes with this variant, Lyn will crit to get the bosskill, which you just have to accept since you have to use the Mani Katti for effective damage. So uh, get the armorslayer.

[Irysa]

https://www.youtube.com/watch?v=yk2FMu8uSAs&list=PLzHc9vjq1MicDyt1rGpaLhdyIfmMGpxHQ&index=14
 

Updated with Kent % version.

The total expected turncount for Lyn Hard Mode with Kent as your primary Paladin is is 49~ (50 if you add in the extra turn the game counts on defend maps).

Kent costs about 3.5 turns compared to Sain as a result. Most of the turnloss was in Chapter 3 (can't be 3 turned with Kent as a primary EXP candidate), and Chapter 10 (can't be 3 turned by Kent unless he crits or somehow has 14 str like Sain), along with moderate "leaks" of turns here and there thanks to his bad luck and inability to finish off enemies in less attacks requiring extra hits from other characters. Kent's reduced strength actually reduces reliability the most out of anything else, and his skill increase does not make up for it. His higher speed barely mattered at all because he needed to also have better strength to 2HKO properly even whilst doubling. It seems unlikely Kent can eke back 3 turns in HHM considering that Marcus does so much of the heavy lifting, and Sain's speed is pretty sufficient on the whole.

In the future I'll be taking the Sain file to HHM and doing an ETC run of FE7 as a whole.

As a comparative note, here are the Cav's averages and 90% individual binomial stats. You can see how Sain's better growth and base distribution makes him compare much better to his average stats (lower variance) wheras Kent's middling growths with typical 5% increases to make up for lower bases hurt him quite a bit more.
 

Averages at 12/3

Sain	31.4	16.8	9.55	12.2	8.55	10.6	3.6 
Kent	33.05	12.2	13.5	13.85	4.6	10.25	5.25

90% Individual Binomials at 12/3

Sain	29	15	7	10	6	9	2
Kent	31	10	11	12	3	8	3

 

 

Edited October 7, 2020 by Irysa