RotMG Pet Leveling Mathematical Analysis by OtherBill

Abstract

This thread attempts to determine the most effective routes to typical “final” pet levels (70/70 maxed Rare, 90/90/90 maxed Legendary, 100/100/100 maxed Divine). This is done through a mathematical analysis of the pet feeding system.

Introduction

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From my playing of RotMG, I have found that the better loot drops from the stronger enemies so defeat stronger enemies and take their loot. Many of the enemies yielding the best loot can really only be defeated with a larger group of mostly level 20s with better equipment and therein lies a large part of the problem as the best regular loot is often if not always ninja'd.

RotMG pet abilities can be improved by feeding items to the pet; the feed power (FP) of the items are then applied towards the pet’s abilities, improving them through “level-ups”. Once suitabily improved, two pets of the same tier can be fused together to create a pet of the next-higher tier (Common to Uncommon to Rare to Legendary to Divine).

However, the potential “max level” of these new pets directly depends on how much the original pets had been improved. To ensure that a post-fuse pet can be improved to its theoretical max level, it is critical that the pre-fuse pets first abilities have been completely improved. While it is not mandatory to improve the pre-fuse pets second/third abilities to their max level as well, it is often considered desirable to do so since the per-feed costs (in fame or gold) roughly triple from one tier to the next.

This leads to a number of interesting compromises. Intuitively, it would make sense that players with a lot of excess feed items but not a lot of excess fame will be best served by completely maxing their pets before fusing, and players with a lot of excess fame but not a lot of excess feed items will be best served by fusing as soon as possible (and thereby spending as little on the pre-fuse pets as possible).

The two most interesting questions here are cheapest route to a Maxed Rare pet (both in terms of fp and fame/gold) and cheapest route to a Maxed Legendary pet. (Maxed Divine is addressed here as well, although it is not as interesting since these players typically rely on realm gold and purchased pet food instead of fame and looted items).

Key Assumptions Codeigniter paypal library download windows 10.

The analysis and results discussed here are only valid if the following holds true:

Only the routes that lead to fully maxed pets are discussed here. While pets can be fused before their first abilities are maxed, the end result is a post-fuse pet that cannot be improved to its theoretical max. There’s a whole continuum of suboptimally maxed pets, but the routes capable of leading a maxed pet are more interesting.
Fame is used to cover all per-feeding costs. Fame-per-feed costs consistently triple (roughly) from one tier to the next. On the other hand, gold-per-feed costs have different ratios (which vary from tier to tier) and are not addressed here.
The FP required to improve a pet’s abilities from one level to the next can be calculated in advance. The best reference here is a Google Docs spreadsheet that was originally created by The Oppai Stars and privately shared with the author. There might occasionally be minor random variations in these values from pet to pet (which may depend on ability, but a solid link has not been established there). The key data here are that improving the pet’s first ability from lvl1 to lvl2 requires 20fp, the second ability from lvl1 to lvl2 requires 31fp, the third ability from lvl1 to lvl2 requires 67fp, and everything from that point on increases by 8% from one level to the next. This has largely been verified to be accurate for most key values, but some anecdotal experiences may vary slightly from this.
When fed, an item’s FP value is applied in whole to all abilities. If the FP is at all divided (either evenly or unevenly) between abilities, then the analysis below would be incorrect. However, this has been verified to be true in this RotMG Forum thread.
Fame costs associated with Pet Fusion are not addressed here. Regardless of what path(s) you take, these remain constant.
Fame costs associated with Pet Yard upgrades are not addressed here. Regardless of what paths(s) you take, these remain constant as well (77500 fame to fully upgrade to a Divine-level Pet Yard, or 27500 fame to stop at Legendary).
All pets are hatched from Common eggs and fused upwards. Uncommon/Rare/Legendary eggs begin with their first abilities at a known starting level, but the abilities for the second/third abilities begin at a random level. As such, they won’t sit on the graphs that will be presented later. (However, adiscussion in this thread points out that for the pets that will be consumed in fusion, it is always better to hatch an Uncommon egg (if you have one) since it might be better (and will never be worse) than a freshly-fused 30/1 Uncommon pet. Still, that alone is not a compelling reason to buy Uncommon eggs; use them if you have them, but don’t spend Realm Gold get them if you don’t.)

Getting Started: Maxed Common and Maxed Uncommon Pets

The route to a maxed Common or Uncommon pet is very straightforward. However, it’s the first step along some paths that are considerably more interesting, so let’s go ahead and get these cases out of the way.

Lvl1 Common pets (1/0/0) begin with 0fp consumed. The first 20fp raise it to Lvl2 (2/0/0), 22fp more raise it to Lvl3, and so on. All in all, it takes 2080fp to raise a freshly-hatched Common pet to 30/0/0:

Once you have two maxed Common pets, they can be fused to create a 30/1/0 Uncommon pet. From that point, an additional 8527fp is enough to max the pet’s first stat; this raises the second stat to lvl41, for a 50/41/0 Uncommon pet. Finally, once you reach this point, an additional 7791fp is required to max the pet’s second stat:

On a mathematical note, one intermediate goal in this work was the development of a weighted directed acyclic graph depicting every possible route to a maxed pet of any tier. Note that there’s only one path to a maxed Uncommon pet (not very interesting so far), and the weights on these edges don’t account for the fact that a second Common pet has to be maxed for fusion. So, let’s go ahead and track total FP investment for the points on this graph; this will allow us to make reasonable FP-fame decisions when we have multiple options:

In this case, 2*2080 (for two maxed Common pets) + 8527 (for maxing the first ability) = 12687fp is the total FP required to build a 50/41 Uncommon pet.

Analysis

If your goal is a maxed Uncommon Pet, you really have no options: max two Common pets, fuse them, and keep on feeding it until it’s done. 50/41/0, meanwhile, is where the first ability is first maxed; this will be important when dealing with “feed or fuse?” decisions in later tiers.

Fuse First or Feed First? Maxed Rare Pets

Now we’re getting to our first interesting decision. Should you fully max your Uncommon pets to 50/50 first, or should you fuse your Uncommon pets as soon as you possibly can (to hit 70/70, this would be at 50/41)?

Assuming that those are the only two fusing points of interest, this presents two different routes to 70/70:

Path #1: If you fully max your Uncommon pets to 50/50, it will take 39746fp to max the Rare pet’s first ability to lvl70. This is enough fp to bring the pet up to 70/65. From there, it takes an additional 21403fp to max the pet’s second ability to 70/70.

Path #2: If you fuse your Uncommon pets at 50/41…well, the first abilities were maxed, at least, so it will still take 39746fp to max the Rare pet’s first ability to lvl70, but this only brings the pet up to 70/63 instead. From there, it takes another 7791fp to “catch up” to the pet on Path #1…and from there, the same 21403fp is required to bring the pet up to 70/70.

Comparing the two path

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