User blog:TenkouKuugen/Akashi's Improvements - Sliders & Expectations

This is a short article on when to apply Akashi Slider during Improvements. This is for my personal references rather than a guide, therefore some concepts may not be explained in detail and may contain my subjective views on the matter. Feedbacks are welcomed as usual though :)

Intro
Equipments can be improved via Akashi's Improvement Arsenal by spending Improvement Material (aka Screws), Development Materials (DevMats) and fodders. Notably, there is a chance of failure depending on the level of improvement.

Success can be guaranteed by investing more screws/devmats via the Slider function. This article explores the sweet-spot/threshold for applying the Slider while avoiding excessive spending.

Success Rates
Improvement Success rates can be found on wikia and various other sources. The exact % varies from test to test, however they all follow a common trend: the higher the improvement level, the more risky it gets.

It would be nice if it doesn't cost anything extra to guarantee a success (via Slider). Alas, this "investment" varies from one equipment to another. We will thus need a measure to guide our decision making.

Expectation Values
Expectation value, in short, is a probability-weighted average of all possible values.

Personally I enjoy utilising Expectation Values (in a broader sense) when it comes to investments and returns, basically anything that has more than 1 outcome. It helps establish whether an investment return is "fair" and whether it's "good business" or a "scam."

For Akashi Improvements, obviously the outcome is either Success or Failure, weighted by a % (probability).

Expectation Tables (Akashi Kai)
Without further ado, here are the tables I refer to when I have a decision to make:



Red represents expected Loss, while Green represents expected Gain. More explanations later.

How to use: check the equipment's screw consumption with and without sliders, then read the corresponding lines vs Improvement levels.

For example, improving a Type 0 Fighter Model 21 (Skilled) from 6★ to 7★ costs 2 screws (3 screws with slider). The expectation is -0.8, ie one can expect, in the long run, to lose 0.8 screw per try if Slider is used.

Or you may be improving Type 1 Fighter Hayabusa Model III A from 8★ to 9★ (6/7 screws). In this case the expectation is +0.37, ie one can expect to slide and gain (save) 0.37 screw per try in the long run.

TL/DR: if a cell is Green, you can Slide without 2nd thought; if a cell is Red, there're more to think about before Sliding. This will be discussed later.

If the screw combinations are not listed on the table, try following the line that gives the same fractional number, eg: F6F-5 costs 8/12 screws past 6★. The 2/3 (or 4/6, 6/9) line can be read in substitution. The threshold should be the same, however the expectation value will not be accurate.

How Are The Values Derived
Those who are not interested in calculations can skip this and go straight to the next section.

The values in the tables were calculated by comparing screws wasted in failed improvements vs additional investments (Slider), ie:

Expected Screw Savings = [ Expected Screw Loss due to Failure ] - [ Extra Screws required by the Slider ] = [ (Chance of Failure) x (Default Screw Count) ] - [ Extra Screws required by the Slider ]

Example 1: Consider an equipment that costs 5 screws (6 with slider) to improve to 4★.
 * Chance of Failure is 0% for Akashi Kai
 * Default Screw Count = 5
 * Extra Screws required by the Slider = ( 6 - 5 ) = 1
 * Expected Screw Savings = [ 0 x 5 ] - [ 1 ] = -1

ie it's a waste to use slider in this case. This one's easy, let's see another one...

Example 2: Consider an equipment that costs 6 screws (7 with slider) to improve to 9★.
 * Chance of Failure is (100% - 77%) = 23% for Akashi Kai
 * Default Screw Count = 6
 * Extra Screws required by the Slider = ( 7 - 6 ) = 1
 * Expected Screw Savings = [ 0.23 x 6 ] - [ 1 ] = 0.38

ie one is expected to save 0.38 screws per try in the long run via Slider. Note that the value here is slightly different from the tables due to rounding.

What Else to Consider
The Expectation value is only a guide. It gives a sense of "what to expect" in the long run, but it's up to the TTK to take everything else into consideration. Here are a few things I'd consider personally:

Fodders
Are the fodders easy to obtain? I'd go by the expectation alone if it only eats common, craftable fodders eg Type 0 Fighter Model 21. If the fodders are not craftable, or a pain in the rear to craft (eg Shiden Kai 2), I'd generally use slider from 6★ onwards.

If the fodders are not craftable, but readily farmable, I'd weigh the screw savings vs the effort then make my decision.

Savings
Is the expected saving worth the trouble of re-obtaining the fodder? You may have noticed that some expected losses are quite small (<0.1). Is it worth the trouble to craft the fodders again, just to save so little?

Urgency
Personally I do only 1 improvement per day, so every failed improvement is a day of delay for other equips. Do I need this equipment bad? Can it wait, or do I prefer to have peace of mind right here, right now?

Well that's enough for today I guess...