Leveling math.

[Dazer]

Ever wanted to maximize your XP gains? or to raise faster in ranking sites?
Easy: always use pets that are two levels lower than half the target level. Obviously, you'll eventually need to use more unefficient pets, if you want to reach to 25 with any pet, but I imagine it's good to know these things anyway.

While battling tamers, I always noticed how I would gain wildly different gains in XP. At first I thought lower level pets would get more experience, but a carried lvl1 would get about as much as a carried lvl20. Something was off and I wanted to figure what it was.

I batled several arcane eyes and came to several conclusions:
-rarity of either the player's pet or the target is not taken in consideration for XP gains.
-the 'difficulty bonus' is just possitive feedback for the player: it does not effect XP gains.
-the only factors are the levels of both player's pets and target.

With that, I was able to come up with [XP=45+5*lvl] (for same level battles); and a modifier for different levels. This modifier ranges from 0.2 (for targets 4 levels below the player) and increases by 0.2 per level: same level battles would have a modifier of [1], targets 1 level higher than the player have a modifier of [1.2], etc. All this can be expressed as:
(45 + 5 * plvl) * (1 + 0.2 * diff)
where 'plvl' is the player level and 'diff' is the level difference. For diff<=-5, XP gais are null.

This is the base XP gain; it gest multiplied by several factors:
Safari Hat: 1.1
Target amount of pets: 1 for 1 pet, 2 for 2 pets, and 2.5 for 3 pets.
Tamer bonus: 5 for pandaria tamers, 3 for tamers like Lydia and Trixxie, 2.5 for the lowest ones like Julia Stevens or Zunta. I didn't check the Outland/Northrend ones.

For instance, a carried lvl10 pet against Aki and using the hat would get:
plvl = 10
diff = 25 - 10 = 15
hat_bonus = 1.1
number_of_pets_bonus = 2.5
tamer_bonus = 5
XP = (45 + 5 * plvl) * (1 + 0.2 * diff) * hat_bonus * number_of_pets_bonus * tamer_bonus = 5225 points.

To figure how to optimize XP gains, we can take the derivative of that function to figure the maxima; or, rather the derivative of the siginificant bit: the base xp gain:
f(plvl) = (45 + 5 * plvl) * (1 + 0.2 * (tlvl - plvl)) || plvl and tlvl being the player and the target levels.
f'(plvl) = 2*plvl - tlvl +4
maxima --> 2plvl - tlvl + 4 = 0

Max xp gain occurs at player level [tlvl/2 - 2] for any given target level.
For instance, pandaria tamers are all lvl25, so maximum gain will be at [25/2-2 = 10.5] which is levels 10 and 11.
Lydia and Trixxy both have lvl 19 pets, so the maximum gain happens at [19/2-2=7.5] or levels 7 and 8: with a hat and a lvl7 carried pet, much like the example above, pets against Lydia would get (45+5*7)(1+0.2*12)*1.1*2.5*3 = 2244 xp

[Knotrandall]

Great work! I was curious about this myself since I noticed that my level 1s were getting less xp than my ones that were a bit higher.

[Ryazan]

Thanks for the info! I've been looking for the exact formula for XP to optimize pet leveling. Time to put Excel into good use once again. :p

[Gendou]

Good stuff. /bookmark'd

[Ryazan]

Ok, I did some number crunching and calculated how many Pandaria tamers (11 in total at the moment) a lowbie pet needs in order to reach lvl 25 from any given level when using Safari Hat.
If pet reached lvl 24, I've included the remaining xp needed to get to lvl 25 instead of wasting one tamer for the remaining xp which can be easily obtained from fighting some random wild pets. Table goes as follows:

LVL 1 - 6 tamers
LVL 2 - 5 tamers + 1932 xp left to lvl 25
LVL 3 - 5 tamers + 1602 xp left to lvl 25
LVL 4 - 5 tamers + 1563 xp left to lvl 25
LVL 5 - 5 tamers + 1368 xp left to lvl 25
LVL 6 - 5 tamers + 1006 xp left to lvl 25
LVL 7 - 5 tamers + 776 xp left to lvl 25
LVL 8 - 5 tamers + 684 xp left to lvl 25
LVL 9 - 5 tamers + 34 xp left to lvl 25
LVL 10 - 5 tamers
LVL 11 - 5 tamers
LVL 12 - 4 tamers + 1751 xp left to lvl 25
LVL 13 - 4 tamers + 1028 xp left to lvl 25
LVL 14 - 4 tamers + 642 xp left to lvl 25
LVL 15 - 4 tamers
LVL 16 - 4 tamers
LVL 17 - 3 tamers + 1579 xp left to lvl 25
LVL 18 - 3 tamers + 672 xp left to lvl 25
LVL 19 - 3 tamers
LVL 20 - 2 tamers + 1757 xp left to lvl 25
LVL 21 - 2 tamers + 767 xp left to lvl 25
LVL 22 - 2 tamers
LVL 23 - 1 tamer + 820 xp left to lvl 25
LVL 24 - 1 tamer

So basically for example, if you are leveling pets up a bit for tamers, it doesn't matter whether your pet is level 10, 11 or 12 since it will always require 5 tamers to ding the pet level 25. So you might as well stop the leveling to level 10 in this example.

[Stonewallred]

I have to say thanks for this post.
Using the EZ mode (lvl/2-2), has allowed me to level most of my pets to at least lvl 5 and allowed me to use the trainers more efficiently at all levels.

[Ryazan]

I wanted to refresh my mad PHP-skillz (*cough*) so I pushed Dazer's post into a calculator on a simple website (with an extra feature):

[url=http://cryados.net/wow/pet_xp/]Pet XP calculator[/url]

It basically has two features:

"Single battle" is basically the basic calculator where you input all the stuff mentioned by Dazer. The tamers are categorized as:

• Pandaria tamer - Pandaria tamers and spirit tamers (multiplier 5)
• Master tamer - Cataclysm and Northrend tamers added with Stone Cold Trixxy and Lydia Accoste (multiplier 3)
• Basic tamer - Rest Azeroth tamers (multiplier 2.5)
• Wild pet - Wild pets and elite pets (multiplier 1)

"To max level" does roughly what my post lists above. It calculates how many tamers is needed to beat in order to reach max level with the pet's starting level and XP. There is one caveat tho, calculator assumes you don't want to waste a tamer when you have reached level 24. So if level 24 is reached, calculator tells the leftover XP at level 24 so player can do few wild pets to cap the pet. The "Opponent type:"-dropdown offers following options:

• Pandaria tamers - Basically my post above, tells how many Pandaria tamers is required to win for the pet to reach level 25.
• Supply bag tamers - This is bit trickier but basically this options tells you how many Pandaria tamers is needed cap a pet after you have done all the pre-Pandaria tamers which give you a Pet Supply Bag reward. The assumed kill order is Trixxy&Lydia > Antari > Payne > Obalis. This option is meant to simulate your daily pet bag tour.
• Level 25 wild pets - Not much of real use but this options tells you how many level 25 wild pets is needed to cap your pet.

Single battle works as it should and based on my testing, To max level too but it's coding was more difficult and complex so some bugs may appear. I know calculator ain't perfect but it's a start, so please report bugs if you encounter some. Enjoy planning your leveling. :)

[Ryazan]

Pandaria tamer - Pandaria tamers, spirit tamers and elite battle pets (multiplier 5)

Scratch that underlined part, apparently the elite pet XP is either bugged or just seriously soaked down. Gonna keep following what's going to be as I can't log for another 9h or so.

[Dazer]

Scratch that underlined part, apparently the elite pet XP is either bugged or just seriously soaked down. Gonna keep following what's going to be as I can't log for another 9h or so.

They count as normal wild pets in sigle teams; using my notation:
number_of_pets_bonus = 1
tamer_bonus = 1

[Ryazan]

Scratch that underlined part, apparently the elite pet XP is either bugged or just seriously soaked down. Gonna keep following what's going to be as I can't log for another 9h or so.

They count as normal wild pets in sigle teams; using my notation:
number_of_pets_bonus = 1
tamer_bonus = 1

Ok, I was suspecting that but I was so dribbling over my keyboard last night while grinding raptors that I forgot to test it. :P