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I have tested this a little bit and I'm not quite sure I understand the exact numbers or what impacts them.

I took a gym, put in a 25cp Magikarp, and trained against it.

521cp Vaporeon: 10xp and 100 prestige

10cp Magnemite: 100xp and 1000 prestige

I didn't record other numbers, but I know I would only get around 800ish prestige with pokemon around the 25cp-35cp range.

Purpose to this (feel no need to answer these): What if there were 2+ low cp defenders? Would I gain 100xp per defeat as long as my cp is equal to or lower than theirs? Could I gain more xp if the defender was 500cp and I won with a 200cp? Is this a strat to take down more prestige at an opposing gym (low cp, type advantage)?

For all I know, getting less than 100xp per defeat is based on HP difference, attack power difference, or even how many attacks it took to win.

Does anyone know the math for how much xp you gain or prestige you gain when training, and how much they lose at opposing gyms?

Thanks!

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The xp is 10% of the prestige that you get.

When training at a gym you will get 500 prestige per pokemon you defeat with equivalent CP value. ie. If you beat a 100cp pokemon with a 100cp pokemon, you will get 500 prestige.

You will get more than that if your Pokemon is lower than the one in the gym and less if it is higher.

How much less/more I am not exactly sure but as pointed out by Sobrique the formula may be P * D / A if the defending pokemon is of a higher CP. Where P is a multiplier of 500, D is the defender's CP and A is the attackers CP.

If the attacking Pokemon is higher then P is reduced to somewhere between 250 and 350.

The maximum you will get is 1000 prestige if your Pokemon is at least half the CP of the one in the gym. The minimum is 100 prestige which is when your Pokemon is double or more of the CP of the Gym's pokemon.

You cannot lose prestige by training at a friendly gym.

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  • The minimum you get from training and defeating a Pokemon is 100 prestige.
    – Ekmod
    Commented Jul 20, 2016 at 15:03
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    I was hoping for exact numbers, but this is still extremely helpful. Any chance you could address opposing gyms too? My testing was only with training, but hoping for the other as well.
    – Mythics Winter
    Commented Jul 20, 2016 at 15:06
  • @MythicsWinter I've added a bit of additional information.
    – Aequitas
    Commented Jul 22, 2016 at 4:40
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    I am at least fairly sure it's: 500 * (defender CP / attacker CP) capped at 1000 - I got 823 - a 512 a defender, vs 311 attacker. I think on the flip side if attacker CP > defender, then it's 250 * the ratio.
    – Sobrique
    Commented Jul 29, 2016 at 12:48
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According to heavy.com, it is:

  • When your attacker has a lower [or same] CP than the defender:
    500 x (Defender CP / Attacker CP)
  • When your attacker has a higher CP than the defender:
    310 x (Defender CP / Attacker CP) – 55

and the max is 1000 per defender you beat.

Also note that the attacker's CP is the highest CP of your 6 Pokemons, even if you didn't use it. For example, if you beat a CP 1000 Arcanine using a CP 500 Vaporeon, but one of your other 5 Pokemons that was chosen for battling have CP of 1100, then the CP 1100 is used to calculate the prestige increased, instead of using CP 500. As a result, if you intend to beat only that Arcanine, then choose your other 5 Pokemons to have CP at or lower than 500 CP if you want a prestige increase of 1000.

The XP is 10% of the prestige increased.

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    I have purged all comments because the conversation was not heading in a constructive direction, let's end it here before someone says things they will regret. To everyone that was involved: Pure duplication of an answer is problematic, so when someone copies an answer verbatim i.e. word-for-word, we have a problem. That is not the case here. It's still up to the votes to determine what is good/bad from a content perspective. Don't sweat over downvotes - they happen, every user has differing stances on what constitutes a 'good' answer and it is up to them to decide how they want to vote.
    – Robotnik ♦
    Commented Dec 6, 2016 at 0:22

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