After a lot of testing in practice mode and watching a lot of matches video, I found what factors could influence the death respawn timer.
For clarity sake, I will talk about "death" when killed by a player and "execution" when killed by an NPC. A "kill" is done by the player (assists aren't relevant). I am specifying this because that means you can't abuse this mechanic by dying on purpose versus neutral Pokemons in order to reset those factors (more specifically K and P) while avoiding giving exp poins to your opponents.
So with all of this, I came up with this formula:
D = L + K + P/40 + T
where :
- D is the death respawn timer
- L is a duration depending on the Pokemon level at death time
- K is the number of kills since last death (1 kill = 1s)
- P is the sum of points scored since last death (40 points = 1s)
- T is a duration depending on the time remaining in the game (always 0 in practice mode)
L possible values:
Player level | L
---------------------
1 | 4s
2 | 4s
3 | 4s
4 | 4s
5 | 5s
6 | 6s
7 | 7s
8 | 8s
9 | 9s
10 | 10s
11 | 11s
12 | 15s
13 | 17s
14 | 19s
15 | 19s
T possible values:
Time remaining | T
--------------------------
> 2 min | 0s
> 1 min & < 2 min | 4s
< 1 min | 10s
For further details about my analysis, you can look at my reddit topic: Death respawn timer formula.
Disclaimer: Like I said, all of this is solely based on my observations and testing and is not related to any official statement about the game but you can obviously verify it yourself. Having said all that, I honestly think those results are pretty solid but if you find anything interesting or contradicting about it, I would be eager to know it! :)