Troop Leveling Analysis [Math, Stats]

I begin this thread with an acknowledgement to Prajna and his detailed analysis of reduced ham costs for troop leveling , since that post is what inspired me to dig into this further. Also a shout out to folks like Gryphonknight and Guvnor, who lead us all to think critically, use data, and do the hard work of publishing their ideas and open themselves up to the “public editorial process”. I admit that I was not optimistic about finding some hidden technique to reduce the ridiculously high costs of leveling troops, but based on that previous work I was curious.

My analysis does find a couple of interesting new insights, and offers up a conclusions that I definitely would like others to examine and validate.

The hypothesis is that “fattening up” feeder troops before feeding them to our “keeper troops” will result in some overall cost savings (food). There may be some break-even point where the savings peaks or begins to turn negative.

Two important findings (again, I encourage and welcome review of the math here and these conclusions):

  • The mechanics of leveling troops (we are limited in feeding a maximum of 10 feeder troops at a time) is crucial in improving overall efficiency. We should ALWAYS USE 10 FEEDER TROOPS AT A TIME when we level our keeper troops. This is true regardless of the level of feeders being used. We lose a ton of efficiency when doing “partial leveling”.
  • “Fattening up” feeder troops provides cost savings for nearly all rarities and levels of keeper troops.

Details / Analysis:

In order to perform the calculations necessary for this analysis, I first needed 3 base tables of data:

  • the XP requirements to move keeper troops to the next level
  • the ham costs of feeding keeper troops at each level
  • the XP yields of feeder troops at each level

Pictures of tables are below and online here: Troop Leveling Analysis

As you can see looking at the base tables, the data is all static and linear. That is, this data for all rarities of troops progresses by level in set increments using a static base value. If we predict leveling costs by just looking at the base tables, and not taking the “10 feeders per round” mechanics into account, our analysis will be significantly flawed. Once I had generated the base data, I could then start working on an algorithm to model the actual troop leveling process in the game.

While I was experimenting to obtain the base table data, I had the insight that the cost to level our troops is set at the beginning of each “round” based on the current level of the troop. If we can level our “keeper troops” across several levels each round, we skip over the cost increases of leveling at those levels we skipped. A picture is worth a thousand words here:

Look at the first round of leveling up these 3* troops as an example. Here we’re feeding 1* troops (at level 1) which yield 40 XP / feed. We only needed 7 feeds to get the keeper troops to level 2, but by continuing to add 3 more feeds in that round, we gained 120 more XPs into level 2 at the 9,000 hams/feed cost rate. We saved 13,500 hams! This may not seem like much, but when you scale this stacking across all the levels we need for 3* or 4* troops, the savings really adds up.

Once I had this model built in a spreadsheet, I could then start working out the pseudo code I’d need to write a program to calculate all this and simulate leveling any troops with any feeders. I used Python3 to code it up. It didn’t really take long and the core logic of the program is pretty short.

Once I had the program working properly, I can now easily calculate the costs of “fattening up” feeder troops, and then in turn using that data for further analysis. Here’s a table of the costs of “fattening up” feeder troops:

Here’s what most of you are probably wanting to see at this point - - - the cost comparison of using leveled feeder troops to level up 4* keeper troops. I just ran the numbers for using 1* feeders that have been leveled up to Levels 1-4.

These “net costs” are calculated as follows:
For fattened-up troops (at level 2, 3, & 4), the cost of the feeders themselves is derived from the above table (10K each for level-2, 25k each for level-3, and 45k each for level-4) and then multiplied by the number of feeds required at each level. The python code spits out the number of feeds at each level.

Summary:
My hope is that this framework is useful for generating cost efficiency when leveling troops. I think there’s some reasonable steps we can all take based on this to save hams. At higher levels, there are obvious constraints of availability of feeder troops, hams, and the trade-offs associated with those constraints. But the key thing to remember is fully using all 10 feeds per round, especially on the boundaries when we level up. Using higher yield feeders helps to maximize this efficiency and so generally speaking, the fatter the feeders, the more you save!

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That is an interesting take on the troop leveling process.

I‘m always lacking food, but I‘m also lacking troops. Wouldn‘t you gain less XP from fattened up feeders than from simply feeding all of the involved troops? Just like it is with 1* and 2* feeder heroes?

I can easily get more food, but troops are rather limited for me.

Yes, and that’s why this isn’t a great strategy for most.

I can think of one use, which is if you only have one 4 troop of a color to work on you’ll get to the point where using 1 or 2 troops isn’t worth it. At that point using them to fatten a troop is likely worth it, although it’s pretty marginal.

But unless it’s your last 4 troop of that color, you’re better off saving them for another 4. Or even a 3 or 2 (for tournaments). At least in my opinion.

Hmmmm, I now went for the details myself and checked the XP gain for my leveled 2* and 3* and 4* and could derive the XP gain also for leveled 1*:
grafik

If I would level a 1* feeder with 1*, I would get considerably less XP out from the troops:
grafik

A level 2 1* would give a total 48 XP, while using 3x 1* (=120 XP), and so on.

This looks similar for 2* and 3* troops that are fed with 1*:
grafik grafik

Although I have 831 feeder troops right now, I’m quite sure that I’ll burn through them in the next weeks since my last remaining HA research will be finished tomorrow. So my bottleneck is troops

edit: corrected the XP from leveled 1* to +8 per level

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It looks like your XP yields for leveled troops are off. Take a look at the table I published out in g-drive. For 1* troops, the base XP yield is 40 at level 1, and increases by 8 each level. So a level-2 1* gives a total of 48 XP.

That said, yes, I agree that my analysis is based on the hypothesis of saving food, not optimizing on XP yields. And the leveling assumes a theoretical huge supply of feeder troops. Now, if only we could take all that saved ham and buy more 1* troops… :joy:

As far as your 831 feeders, make sure you use them all ten at a time!!

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I’ll even recommend to feed troops as you like right before as level up, and then use 10 troops to get the lower food costs for all of them :slight_smile:

Now after Atlantis I have 796 troops, so the number actually decreases when you kind of focus on leveling troops :smiley:

Just a note on the 10 at a time, my understanding is the food usage per “feed” only goes up when the troop being levelled goes up a level, therefore it is actually better to feed up to the point where 1 more feed will increase the level and THEN feed 10 at a time. The feeding in the patch between levels can be done in any increments

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Agreed and I do this as well.

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