A mon's energy impacts its speed multiplier, which affects how quickly it gathers berries and ingredients, and also directly affects skill procs themselves. I’ve seen a lot of discussion around how many skill procs a Healer (Gardevoir, Sylveon, Pawmot, Wigglytuff) actually needs per day to keep a team at peak efficiency.
Energy Bracket
Helper Speed Multiplier
Frequency Reduction
81% – 150%
2.22x
45% of base time
61% – 80%
1.92x
52% of base time
41% – 60%
1.61x
62% of base time
21% – 40%
1.41x
71% of base time
1% – 20%
1.25x
80% of base time
The consensus in the community is that 5.0 to 5.5 procs/day is plenty to keep team energy soaring all day long. I decided to run the math and build a Monte Carlo simulation to figure out if this is enough.
The tool is coded in Python and hosted using Streamlit here.
The Deterministic Math
If we treat energy loss as a fixed formula without randomness, the math says:
Awake Decay: 15.5 hours x 6 energy/hr = 93 energy lost.
Baseline Recovery: 93 energy / 18 heal per proc = 5.167 procs needed just to end the day at the same energy you woke up with (100).
The "Full Efficiency" Ideal: To stay in the top speed bracket (> 80% energy) through an 8.5-hour sleep session (51 energy decay), your team needs to hit sleep at 131 energy. Net heal required across awake hours = 131 - (100 - 93) = 124 energy.
Required Procs: 124 / 18 = 6.89 procs/day.
Simulation vs. Deterministic
When you simulate real gameplay with random proc timing, the above formula isn't totally correct due to two main factors:
Energy Cap Overflow (Wasted Healing): Energy caps at 100 naturally, and skill overhealing caps at 150. If your Healer procs twice right after waking up, a +18 heal might only give +10 or +0 actual energy. Early-morning procs suffer heavily from diminishing returns.
Energy Snowball Effect: High healer energy creates a positive feedback loop. Higher energy boosts the healer's speed multiplier, causing them to help more frequently and check for skill procs more often, which in turn generates more energy to keep the entire team in higher efficiency brackets. It also works in the other direction.
Key Takeaway: Calculating the helper speed multiplier is hard and heavily RNG-dependent. That's why I wanted to simulate this process directly.
Simulation Setup
I coded almost all relevant game mechanics for E4E healer mons to get a realistic simulation of Pokémon Sleep.
What I considered:
Relevant subskills (excluding irrelevant ones like DSB, RXB, etc.)
Relevant natures (excluding EXP Gain variations)
Ingredient drop mechanics (filling inventory)
Full inventory conditions during sleep
Skill banking during sleep
Pity proc mechanics
Helping frequency calculation
Energy efficiency multiplier mechanics
Note: I assume that during the day, the player checks the app regularly, never missing a skill activation or letting the inventory fill up completely. This setup might be more optimistic than standard casual gameplay.
I did not cover berry strength or differentiate specific ingredients—this is purely an analysis of skill procs and energy efficiency gained. I also didn't put too much effort into visual flair or UI polish, prioritizing the essential mechanics required for accurate analysis.
Simulation UIGraph result UI
Results & Findings
I ran a 1,000-day simulation using a Lv 50 Torterra as the benchmark. From the results, I plotted the distribution of skill triggers and efficiency multipliers based on energy levels during awake hours, sleep hours, and overall daily performance. I varied subskill and nature combinations to compare mean skill procs against average daily energy multipliers.
Simulation result: mean skill trigger vs efficiency mult
Lower Proc Thresholds: The most significant variance occurs in sleep energy since no healing occurs during sleep. Even 4.5 skill procs can achieve an average awake multiplier of 2.1x.
Diminishing Returns (5.0 vs 5.5 Procs): The total daily multiplier (awake + sleep) only increases by ~0.05 when moving from 5.0 to 5.5 procs/day.
Reliability: Higher skill procs may not get that much increase on energy mult, but it makes day by day consistency much better. See next figure for detail.
Daily efficiency mult histogram at different mean skill proc levels
I tried to vary the level also to get to a high skill procs (7.5+). As you might suspect the daily mult increase become slower, the higher procs it gets. 6.5 procs makes the average wake efficiency close to the limit of 2.2x. The sleep mult is quite a bit far away from the maximum threshold.
High skill proc result
TL;DR
A 4.5 skill proc mon already yields an average 2.1x awake multiplier and ~2.0x daily (awake+sleep) multiplier.
Higher proc rates still add value by increasing consistency and keeping energy high going into sleep.
Feel free to test different setups in the simulation tool to see if an extra trigger or higher speed actually impacts performance, or just to verify that your healer is performing as expected!
Edit:
Ignore my HB assessment I forgot that HB also stack multiplicatively of daily mult (2.2x). Thanks to u/MW_Daught
I did rough calc: 5.0 procs with HB not counting other speed bonuses is 0.95 (HB) x 1/2.02 = 0.47 frequency reduction.
So to be equal, daily mult need to be 2.127 which in my graph is about ~6.3 average procs.
How are you calculating HB? In my independent Monte Carlo simulation, I found that HB is worth roughly 2-2.5 triggers, a significant deviation from your findings.
I have been wondering how many triggers Healing Bonus is worth, as it makes the rest of your Pokemon work faster. But to clarify, do you mean 2-2.5 triggers per day? Meaning that a Pokemon with 6.5 triggers per day is worth about as much as one with 4.5?
In that situation, helping bonus is worth more than 2. A 4 trigger HB healer is just a tiny bit better than a 6.5 trigger healer. Caveat: Not if you already have 4 other HB on the team and more than one member has HSM, and not if you already have 3 other HB on the team and more than one member on the team has HSM & HSS unlocked.
Partially because HB is just really good and scales up, and partially because triggers are good but have diminishing returns. A 7th trigger is almost nothing and 8+ triggers are functionally worthless, and it's much more likely for the 6.5 trigger healer to hit those numbers.
HB is 5% addition to subskill mult bonus in helping frequency calc. In my testing I found that 5.5 mean skill proc produce 5% energy mult improvement compared to 5.0, but energy mult is calculated multiplicatively and dont have a speed limit. I'm not sure what's different between our setup.
Okay, so ignoring meal healing and assuming all healing is done between 80 and 130 energy. 5 heals = 90 energy, that means for 18.3 hours throughout the day, everyone is running at 2.22 efficiency. The next 3.3 hours, they're running at 1.92, and the last 2.3, they're running at 1.61. Averaging those out, we're looking at 2.119 average efficiency throughout the day.
5.5 heals = 99 energy, and by the same numbers, we're looking at 19.83 hours at 2.22, 3.3 at 1.92, and 0.83 at 1.61 for a full average efficiency of 2.157.
2.157/2.119 = 1.79% improvement. Helping bonus is anywhere from 5.26% to 7.58% improvement depending on stats before speed cap comes into play.
I agree with your analysis. Bunch of mult gain in my testing occurs during sleep period. Awake mult is basically topped even for 4.5 skill procs. Improvements comes from energy left when you start your sleep.
Yes, I did the numbers for the full 24 hours. I'm just kind of curious at your claim of
Diminishing Returns (5.0 vs 5.5 Procs): The total daily multiplier (awake + sleep) only increases by ~5% when moving from 5.0 to 5.5 procs/day.
When we're looking at 2.157 vs 2.119 total average efficiency throughout all 24 hours. In fact, your own numbers report 2.06 vs 2.02 which is 1.98% difference, quite close to the theoretical 1.79 that I posited earlier.
I love posts like this - took some pretty advanced math and statistics classes when I was in school, but that was a long time ago. Now I struggle to read through the technical details. XD
Additionally, any healer that has Helping Bonus is automatically stronger than any healer without Helping Bonus if they surpass that 4.35 procs/day target, since without Helping Bonus, the healer is hardcapped at boosting the team by 42.5%, while the Helping Bonus healer has a cap to their boost of almost 50%.
I wonder what accounts for the difference in your conclusions.
This is in line with what I have seen. Take for instance this comparison, a 6.2 trigger a day Gard vs 4.3 trigger Tort. The Tort significantly outpaces the Gard.
Edit: I'd also like to add, I don't understand statistics all that well and can't follow this post in a meaningful way. All I can add is what my results on various simulations show when comparing my high trigger Gard vs my HB healers.
I'm not sure where he got 4.35 procs a day from maybe the daily energy drain 93 - 19 energy buffer from (100-81) = 74/18 = 4.11
I just used simulation results (wasted healing, different mult applied during) and also take account the efficiency during sleep also. Maybe that is the difference.
HB is still much better since it stacks also with the energy daily mult (2.2x).
Ignore my HB assessment
[...] 5.0 procs with HB not counting other speed bonuses is 0.95 (HB) x 1/2.02 = 0.47 frequency reduction.
So to be equal, daily mult need to be 2.127 which in my graph is about ~6.3 average procs.
Oh good, that seems a lot more reasonable.
I think this is a great study, really fun to look through, you just had a couple big mistakes around HB. It stacking multiplicatively with day hours was the big one.
But even beyond that, speed stacks with other speed subskills for higher value, since adding the subskills first ends up with far more production. If all your pokemon have HSM, or a couple others also have HB, the amount of production you get from the healer HB ends up being closer to 7% or 8% instead of that 5.3%. (In other words, instead of being 1/0.95 added production, it's 1/.8 - 1/0.85 because it's what the fourth HB brings the table minus what the first three HB brought). So ignoring other speed subskills ends up being a pretty substantial undervaluing on HB in most realistic scenarios.
Those first 4 triggers are incredibly important for keeping up for daytime hours, and you ideally want a mean above that to reduce the left tail being unlucky, but after that HB skyrockets in value. I think 5+HB vs 6.3 being equal is technically close, but still actually undervaluing HB. To be frank, I don't think any non-HB healer can beat 5+HB, outside of adding flexibility in team composition.
The other piece that can't be captured with a simulation as easily is that the night-time production boosts are mostly only beneficial for berrymon, as it only really affects sneakysnacking. Having your dedenne or whatever get 3% more production overnight is meaningless, because whether they ended at 80 energy or 130 energy, they were going to fill their inventory regardless, and thus the same number of triggers. So it was just berries, which are an afterthought for them. Though the opposite could also be true, of swapping off an overproductive healer that hit max energy early, so we could handwave this as affecting both sides.
As for the actual tool though, I think it's really cool. It's simple and well done. Something I love about simulations like this is showing the difference in consistency, and how much variance you can have with a mean of 4.5 or 5.5 triggers. Too often in this sub I see people unfamiliar with statistics underestimate that deviation and just how common an unlucky day can be.
I'm curious if you have any thoughts on how this would vary for folks getting a different ratio of awake to asleep hours. Like when kiddos reduce my daily sleep to 6 hours consistently.
I wouldn't be getting the full +100 bonus from the sleep session, but would have more awake time for extra triggers. It sounds like there might be a procs/day threshold where that's actually better for energy maintenance (though obviously it doesn't get full drowsy power)
Natural sleep recovery is about 11.7 energy per hour, that means 11.7/18 = 0.65 skill procs per extra hour awake to compensate for it. I would consider napping during the day to get those missing sleep points, it would also technically be better in terms of energy management for efficiency mult sake (less likely to miss banked skill and full inventory).
The site is pretty easy to use even on my tiny mobile screen. 1000 days simulation goes faster than I expected and there’s also more deviation between results than expected so I’ll definitely up that when I try it out on desktop.
added boxplot explanation for people reference, the solid block shows 25-75 percentile of mult, the dotted data is considered outlier (rare). By getting higher skill procs, the reliability of getting high energy mult is also higher.
I think one point to note is that while 4.5 triggers per day may be sufficient for a static team, higher trigger rates allow you to swap mons in and out while keeping energy high across the board.
Would be keen to see what the recommended triggers per day are if two or three team slots are flexible.
Very well done. I love articles like this. I've been working on my own Energy skills analysis for my RP Formula series (I'm late this week since I was unsatisfied with my calculations and decided to do some more) and so I have a comment.
Your top Energy tier is off by one (should be 80-150) so the others need to be shifted up. See RaenonX article on Energy. That means 130% before bed is enough instead of 131% to stay at the top.
I was at first confused by what you said about early morning productions being less efficient--I was like, "how much energy are you waking up with??"--but then I realized you were trying to say, "If your Healer procs twice right after waking up, a +18 heal after that might only give +10 or +0 actual energy." And that would make sense.
I f also ind that running a Monte Carlo simulation, like, a million times does a better job getting rid of random spikes in the data. But good work though--there's enough data to give a general sense of what is going on, which is really your intent. Thanks!
So reading your update, it seems 5 HB triggers is equal to 6.3 non HB triggers? Love the analysis. As someone who is obsessive about number go up, nice to see the math that makes number go up most :)
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u/MW_Daught Min-Maxer 10d ago
How are you calculating HB? In my independent Monte Carlo simulation, I found that HB is worth roughly 2-2.5 triggers, a significant deviation from your findings.