"1000 prestige/battle is most time- and potion-efficient"

#PokemonGO: When training/prestiging a gym, it is more efficient to use attackers that are 50% or less the CP of the defender so you can get 1000 prestige per battle, than to use larger attackers that get less prestige per battle, both in terms of time and potions.Using /u/celandro's Pokebattler, I built a spreadsheet (view only or make a copy).Venusaur attacking VaporeonI chose this pair since Vaporeon is very common in gyms and is a pretty tough defender. Not as tough as Snorlax, but not as easy as Arcanine. Venusaur maxes out at level 30 around 2200 CP, so I made Vaporeon also 2200 CP.DefenderAttackerAttackerAttackerVaporeonVenusaurVenusaurVenusaurBasicWater GunVine WhipVine WhipVine WhipChargeWater PulseSolar BeamSolar BeamSolar BeamCP2200220016501100HP36212610890StrategyDodge SpecialsDodge SpecialsDodge SpecialsDamage received303652Att HP remain967238Time (seconds)29.429.439.3Prestige5006661000Prestige/s17.0122.6525.45Prestige/damage16.6718.5019.23Battles30006.004.503.00Time176.40132.43117.90Damage received180.00162.16156.00For just one battle, the 1100 CP Venusaur gains more prestige per second and more prestige per damage received. Potion usage would be based on damage received, so it is both more potion-efficient and time-efficient.Another way to look at it is that in order to gain 3000 prestige, using 1100 CP attackers would only take 3 battles, while 2200 CP attackers would require 6 battles, which would ultimately take more time and more damage/potions.This assumes the same number of attacking "sessions", e.g. 3 battles then flee vs 6 battles then flee. If using 2200 CP attackers, you can only do 3 battles, then flee, then do another 3 battles, then that takes 2 sessions. There is a substantial amount of "prep time" (60 seconds?) in between sessions for healing attackers and selecting your team of six, so that would make the 2200 CP attackers even less time-efficient.Further, this also assumes that all the defenders are equally difficult. In the real world, each subsequent defender will be higher CP and usually more difficult and will take more time and more potions to defeat. So attacking 6 defenders in one session will be much less efficient than attacking 3 defenders.Hypno attacking SnorlaxAs we discovered in my thread Training against Snorlax, CP efficiency, Hypno is the best attacker against Snorlax with Zen Headbutt/Body Slam. Hypno's max CP at level 30 is only 1755, so I was not able to simulate a 2400 CP attacker, and settled on a 1621 CP one.DefenderAttackerAttackerSnorlaxHypnoHypnoBasicZen HeadbuttZen HeadbuttZen HeadbuttChargeHyper BeamPsychicPsychicCP240016211200HP434130112StrategyDodge SpecialsDodge SpecialsWinYesNoDamage dealt336Def HP remain98Damage received123112Att HP remain70Time (seconds)64.559.1Prestige7401000Attackers needed1.001.29Multiple battle time64.5076.34Multiple battle damage received123.00144.67Prestige/s11.4713.10Prestige/damage6.026.91Battles30004.053.00Time261.49229.01Damage received498.65434.00Attackers used3.843.88Attacker HP safety margin10120102Attackers used4.164.25Even in the case where the 1621 CP attacker is able to defeat the Snorlax but a 1200 CP attacker cannot, it is both more time- and potion-efficient to use multiple 1200 CP attackers to get 1000 prestige per battle.In order to gain 3000 prestige, using 1200 CP attackers would only require 3 battles while 1621 CP attackers would require 4.05 battles, which would ultimately take more time and more damage/potions.The last two rows in this table consider if you're low on revives, but well stocked on potions, then you wouldn't want to let your attackers faint, so you would probably switch out attackers when they have 10 HP left. In this case, you would use a roughly equal number of attackers to get 3000 prestige, though your 1200 CP attackers are cheaper to heal than 1621 CP attackers.ConclusionThe only significant exception is that if you don't have good attackers at 50% CP but have a good team at 60% CP, then it's probably more efficient to use better attackers for less prestige/battle.More details in my spreadsheet (view only or make a copy).I look forward to feedback. There may be scenarios I haven't tried in Pokebattler that may produce different results.This is inspired by a discussion in my thread Training against Snorlax, CP efficiency.Bonus researchWhen you have an easy defender such as the Vaporeon above, followed by a harder one such as the Snorlax above, is it more efficient to battle both in one session, or only battle Vaporeon, flee, and then battle Vaporeon again?Vaporeon*2Vaporeon+SnorlaxBattle time78.6129.15Prep time600Battle+prep138.60129.15Damage received104233.40Certainly, the amount of damage you receive for fighting the Snorlax will be much higher, so it is more potion-efficient to only fight the easiest defender.But the amount of total time is similar, assuming 60 seconds of "prep time", for healing your attackers and re-selecting your team of six. 60 seconds is just a wild guess. For some players, it may be much higher, especially if there are glitches.For me, the massive difference in damage received/potions consumed would cause me to choose battling Vaporeon twice, even if it takes a few minutes longer.Edit 1: Added Bonus research section via /r/TheSilphRoad http://ift.tt/2jjaigM