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Method for Unit Analysis and Comparison 1.x

 
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syntaxerror111
dragonmount



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PostPosted: Fri Jul 01, 2016 1:08 pm GMT    Post subject: Method for Unit Analysis and Comparison 1.x Reply with quote

Part 1: Introduction and Assumptions

Disclaimer: This is a work in progress. It is provided simply as a guide and is subject to critique and modifications over time.

What I am presenting is the method I use for comparing and determining the power level of units in Dragon Dice™. I hope that others might benefit from this and that I can get some feedback on ways it can be improved.

Here some assumptions you should know about:
1. All normal die results are of equal worth (1 melee == 1 missile == 1 magic == 1 maneuver == 1 save).
2. A unit’s damage mitigation or vulnerability based on die size is not considered.
3. The ability for units to be taken as a casualty has some unknown value and is not considered. This is relevant when comparing with magic items.

I will be using the term normal result equivalent. This is used for SAIs when estimating how “good” they are. This will be explained in more detail in a later section.

I am not including standard deviation or an analysis of high/low variance. An example of this would be (melee x5 + melee x1) vs (melee x3 + melee x3) vs (melee x2 + melee x2 + melee x2). That type of analysis is best done on units with a similar average output.

This method says nothing about total army composition, only about the number of results a single unit can generate in comparison to the cost. Less powerful units do not mean bad and can still be incredibly useful when considering other factors such as consistency. However this method can effectively show why some units are generally better or worse than others and presents a common framework for comparison.
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syntaxerror111
dragonmount



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PostPosted: Fri Jul 01, 2016 1:08 pm GMT    Post subject: Reply with quote

Part 2: Method and Baseline

The first metric that I use are the individual sums of a unit’s possible normal results (plus normal result equivalents from SAIs) for each of the 5 basic types: melee, missile, magic, maneuver, and save. This allows for a quick comparison between units to see how much they contribute to a given action type.

The second metric that I use is the average normal result equivalent output (this needs a better name). This is used to compare the raw output power level of a unit. A normalization factor of 2 is used to bring the overall power rating close to 1.0 for easy comparison.

Here is a verbose example of 2 common units:

Lava Elf Bladesman [missile, save, melee, melee, melee x2]
Melee 5: ID, melee x2, melee, melee
Missile 2: ID, missile
Magic 2(1): ID
Maneuver (1): ID
Save (2): ID, save
Total Output: 12 (11)
Rating: 12(output) / {6(sides) * 1(cost) * 2(normalization)} = 1.0 (0.92)

Lava Elf Scout [maneuver, maneuver, melee, melee x2, missile]
Melee 4: ID, melee x2, melee
Missile 2: ID, missile
Magic 2(1): ID
Maneuver 3: ID, maneuver, maneuver
Save 3(1): ID, maneuver, maneuver
Total Output: 14(12)
Rating: 14(output) / {6(sides) * 1(cost) * 2(normalization)} = 1.17(0.92)

Here is what I would normally write down:

Lava Elf Bladesman [missile, save, melee, melee, melee x2]
5 2 2(1) 1 2 1.0(0.92)

Lava Elf Scout [maneuver, maneuver, melee, melee x2, missile]
4 2 2(1) 3 3(1) 1.17(0.92)

When 2 values are given the first represents the best case scenario. The second number in parenthesis represents worst case. For example, this Bladesman can double ID results for magic when on a red terrain and/or when there are units in the DUA. The Scout can do the same, and can in addition count maneuvers as saves when on a highland terrain. When units are broken down in this way they can be easily compared. For instance, we can see that on a highland that the scout sacrifices 1 possible melee result in order to gain 2 maneuvers and 1 save (quite a deal!).

The final number at the end is basically the overall power level of the unit when considering all 5 normal results together. The Bladesman receives no benefit for being a Lava Elf and has no SAIs to help either. The Scout on the other hand has effectively 2 more ‘pips’ than the Bladesman when on a highland. We will look at racial abilities in general in a later section.

This setup can be used to compare units of different sizes. For instance, compare a Duelist with 2 Scouts:

2x Lava Elf Scout [maneuver, maneuver, melee, melee x2, missile]
8 4 4(2) 6 6(2) 1.17(0.92)

Lava Elf Duelist [maneuver x2, save x2, melee x2, melee x4, missile x2]
8 4 4(2) 4 6(4) 1.08(0.92)

We can see that the Duelist is strictly inferior to the 2 Scouts on a highland, as you trade 2 maneuver results for no benefit. It is also easy to see that there is a tradeoff between maneuvers and saves when not on a highland. Notice that the overall power rating for the scout did not change.

SAIs and racial abilities can sometimes be hard to quantify in terms of normal results. For SAIs that attack or defend I will explain how I estimated their normal result equivalent. These numbers are subjective and you may prefer a different value. In cases where the SAI or ability has absolutely no likeness to a normal result, you or I have to assign a value based on how “good” we think it is. This is arbitrary and might differ quite a bit by individual. We will look at SAIs in a later section.

Lets look at a baseline power level for the overall power level of each unit type without including racial abilities or SAIs (based only on the number of ‘pips’, and assuming the option to double magic exists)

Common: 1.0(0.92)
(ID + 6 pips) / (6*1*2)

Uncommon: 1.0(0.92)
(ID + 12 pips) / (6*2*2)

Rare: 0.94(0.86)
(ID + 16 pips) / (6*3*2)

Monster: 0.75(0.70)
(ID + 36 pips) / (10*4*2)

Rares and Monsters need SAIs to make up for the smaller number of pips. Also note that Monsters start significantly further behind because their ID is diluted over 10 sides instead of 6. Any SAIs on a monster are also similarly diluted. Many monsters are weak because their SAIs do not compensate for their initial performance gap.

Now that we have our method of comparison and a baseline established, we can proceed to the messy parts: racial abilities and SAIs.

-Note: I am having trouble with formatting multiple spaces / tabs. I will fix this once I figure out how to properly insert whitespace.[/list]

-Edited for clarity
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Last edited by syntaxerror111 on Fri Jul 01, 2016 2:49 pm GMT; edited 2 times in total
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dragonmount



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PostPosted: Fri Jul 01, 2016 1:09 pm GMT    Post subject: Reply with quote

Part 3: Racial Bonuses
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PostPosted: Fri Jul 01, 2016 1:09 pm GMT    Post subject: Reply with quote

Part 4: SAIs
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PostPosted: Fri Jul 01, 2016 1:10 pm GMT    Post subject: Reply with quote

Part 5: Applications
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PostPosted: Tue Jul 05, 2016 10:39 am GMT    Post subject: Re: Method for Unit Analysis and Comparison 1.x Reply with quote

syntaxerror111 wrote:
This is relevant when comparing with magic items.


I will wait until you are done to fully comment, but as a terminology issue we are pushing for these to just be 'ITEMS'. that avoids the confusion of 'Melee Magic Items' and 'Magic Magic Items'. Smile
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PostPosted: Thu Jul 07, 2016 10:26 am GMT    Post subject: Reply with quote

Between hosting family in town for the US holiday and a delivery due at work, I haven't had time to finish the article. Please be patient. Thanks!
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