DPS*DPE
The article proposes this as good metric and notes that Damage is overrepresented in the results. Of course, because it introduces a factor D^2. The correct metric should simply be:
Damage/(EnergyBuildupTime+MoveDuration).
These parameters are of 1 execution of a charge move with a long bar (100), medium bar (50) or short bar (33).
Since EnergyBuildupTime is a function of the fast move, you could rank charge moves only by assuming an average or standard EPS for all charge moves, e.g. 10 EPS. In that case, EnergyBuildupTime is simply replaced by EnergyBar/10.
So I suggest to rank by Damage/(EnergyBar/10 + MoveDuration) instead.
Answers
The advantage of battle simulations is you know all the variables. You can also rank the Pokémon as they do after millions of calculations, very useful.
But for a easy to understand ranking of moves, the above formula is simple and correct... DPS*DPE does not work. It's like in my field of meteorology: you could concoct all sorts of indices combining various parameters, but it does not replace physical models and understanding of processes.
This is a lot of work to solve a simple question. Here's the simple answer.
How many fast attacks will charge up enough energy for one charged attack. Do that many, and then add the charged attack. Calculate the total damage done, and the total time it takes to do that damage. That gives one the Cycle Damage Per Second, or CDPS. And it tells you exactly which attacks are good and bad.
The only weakness is that it doesn't incorporate the energy gain from damage taken, which means that it overemphasizes the fast attack and underemphasizes the charged attack. That can be compensated for by making assumptions about damage done vs. damage taken, and correcting the totals. In a raid, you're taking a bit more than you're giving, most likely, whereas clearing a gym, probably taking 1/2 to 1/4 of the damage you're doing.
Don't understand why this isn't the standard method of analysis. Seems to agree completely with consensus, Wild Charge, Shadow Ball, and Ice Beam rock, Stone Edge is fair at best, and Thunder and Close Combat pretty much suck.
I would not take it so far to assume parameters for energy gained for damage received. You would assume a dodging style and the wildly varying range of Defense stats across the board. It is best to keep things understandable and accept errors in factors that matter less - if you wanted higher DPS in exchange of a loss of total damage potential, tank some charge move.
Stone Edge and Thunder are not quite as bad on defense, if we factor in the chance that they are succesfully dodged (only 25%?), compared to stronger, frequent moves which you can see coming every time and dodge (e.g. Shadow Ball or Solar Beam). For defender purposes the charge move execution time also totally does not matter, only the damage window and damage.
First off, we know what cycle DPS is and how to calculate it, given the fast move.
Here what we are trying to do is: evaluate a Charged move stand-alone; i.e., independent of the fast move. For example, when you claim "Dynamic Punch is better than Close Combat", what's your proof? How do you show that, for every fast move, Dynamic Punch yields higher cycle DPS than Close Combat does? The article suggests comparing D^2PES. It's not perfect but much better than DPS or DPE alone.
Close Combat 1 bar 100 Damage 2.30 sec
Dynamic Punch 2 bars 90 Damage 2.7 sec
Focus Blast 1 bar 140 Damage 3.50 sec
Contribution of the charge moves to cycle DPS according to
Damage/(EnergyBar/10 + MoveDuration):
CC: 100/(100/10+2.3) = 8.13 DPS
DP: 90/(50/10+2.7) = 11.69 DPS
FB: 140(100/10+3.5) = 7.41 DPS
Gamepress calculated DPS*DPE: 43.48, 59.99, 56.00
That figure suggested Focus Blast to be very close to Dynamic Punch (93%) but its DPS is really only 63% of Dynamic Punch!
Close Combat would scale 72% to Dynamic Punch by Gamepress DPS*DPE, but real contribution to cycle DPS shows it 69.5%.
So DPS*DPE is not the metric you would want to accurately compare charge moves.
edited: Removed nr of bars - we consider only 1 bar and 1 execution of charge move. Corrected DP move power 100 to 90.
bioweapon,
First off, big respect for the work you all, and you specifically, do here. You've made a lot of PoGO duffers much better players. That said, you still have this one a little wrong.
Easiest way to prove that Dynamic Punch (DP) is better than Close Combat (CC) is to calculate the CDPS for Counter/DP and Counter/CC, and compare them. Then compare Bullet Punch/DP and Bullet Punch/CC. Comparing Close Combat and Dynamic Punch in a vacuum is, well, at best an academic exercise because they are never used in a vacuum (unless you just sit there taking damage until you get enough energy to use the charged move, which, unless you're fighting with Slaking, is stupid, and even then it's still stupid).
What you're looking for, if you want a standalone measure, is damage per second per energy. Your measure of DPS * DPE effectively squares the damage and divides it by time and energy. Damage squared isn't an effective measure, because we don't multiply damage by itself, and it overcompensates for big damage (like SolarBeam, Overheat, etc., which are pushed to the top of your list. They are good attacks, but damage squared makes them seem better relative to smaller, faster, more energy efficient attacks that don't do as much damage all at once.)
However, when you calculate some of those out, you find that Seed Bomb is stronger than Solar Beam (0.786 vs. 0.367, so more than twice the DpTE), but CDPS shows Seed Bomb to be about 15% weaker than Solar Beam, when paired with every fast move possible for Exeggutor. Similar examples abound.
So my question remains, why try to use any bad approximation to effective damage that ignores the fast move when a very good approximation to effective damage (CDPS) exists that takes any and every possible fast move into account? And even if you get that to work, it won't show how Psycho Cut/Shadow Ball Mewtwo is more effective against Lugia than Confusion/Shadow Ball Mewtwo, or even how Charge Beam/Shadow Ball Gardevoir is very strong against psychics, stronger than Confusion/Shadow Ball. Of course, you're trying to compare the charged moves, not the quick moves, but CDPS shows them all in the right perspective.
Bullet Punch has an energy per second of 11.11 and Counter 8.89.
One could easily see the "standard" charge move DPS (using 10 EPS) gets adjusted by 0.889* or 1.111*:
EPS/10 * Damage/(EnergyBar/10 + MoveDuration)
and then add 13.33 DPS for Counter or 10.00 for Bullet Punch, as first approximation to cycle DPS (see my post below top). :
C/DP = 13.33 + 0.889 * 11.69 = 23.72
C/CC = 13.33 + 0.889 * 8.13 = 20.56
BP/DP = 10.00 + 1.111 * 11.69 = 22.99
BP/CC = 10.00 + 1.111 * 8.13 = 19.03
Of course, effectiveness is a thing when considering the final result of mixed type movesets, then you would use e.g.
C/CC = [1.4]*13.33 + 0.889 * [1.4]*8.13 = 28.78
BP/CC = [1.0]*10.00 + 1.111 * [1.4]*8.13 = 22.64
But this goes beyond the purpose of having a metric just to compare charge moves in a meaningful way - just Damage/(EnergyBar/10 + MoveDuration) would do that.
Some more examples:
Brick Break: 40*3 / (10 + 1.6*3) = 8.11
Frenzy Plant: 13.16
Grass Knot: 11.82
Leaf Blade: 12.21
Seed Bomb: 10.12
Solar Beam: 12.08
Petal Blizzard: 8.73
Solar Beam to Frenzy Plant ratio: 12.08/13.16 = 91.7%,
but in "DPS*DPE": 66.11/76.92 = 85.9%
Note that Leaf Blade to Solar Beam is 12.21/12.08 = 101%,
but in "DPS*DPE" 61.88/66.11 = 93.6% which has Leaf Blade weaker.
How can that be if we release 210 power every 17.2 sec for Leaf Blade and 180 power every 14.9 sec for Solar Beam?
But also incomplete. Get hit with the raid boss's charged attack, suddenly there's a lot more energy available, unless you had almost filled up a one bar move, in which case it gets wasted. Dodge key charged attacks, and you may get another charged attack off, but the DPS will go down, because of the lost time (dodge) and lost energy from taking less damage (dodge).
Even CDPS doesn't get that part right, so you have to do simulations. Even simulations don't get it right, because while I'll probably attack Lugia (say) with PC/SB Mewtwo, I won't be the only player in the raid attacking, so Lugia will take more damage, which will get Lugia more energy, which will mean more frequent charged attacks, which changes the balance and timing of the damage (esp. if it has, say, ES/SA, doing psychic damage on fast attacks but flying on charged attacks). I strongly suspect that 5 Mewtwos against Lugia and 7 Mewtwos against Lugia would have different DPS ratings per attacker (divide total DPS by number of attackers), so one would have to do the right kind of simulation (and never mind the people at raids who bring Aggrons and Blisseys, tanking damage and doing little).
So to predict the actual results of a raid, do the actual raid and find out. Nothing else is as accurate. For my time and effort, CDPS in a spreadsheet gives me a lot of good information for little cost. Convince me there's a better sweet spot, and I'll start using that instead.
That is only true if the charged move is used in a vacuum, and they never are. They have to be charged up with enough energy to use, and the charging comes from the fast move and from taking damage.
Ridiculous example: megamove has 10,000 base power (contrast with Solar Beam having 180). But megamove requires 1000 energy, and takes a mere 0.1 second to use. The DPS, DEPS, D^2PES, will all be off the charts for megamove, but in a real fight, one would never get it off except in extreme cases when fighting something trivial to beat. The CDPS will be fairly low, unless the base power is multiplied by 100 or more. Any simulation will show how useless megamove is. But I can't imagine a standalone measure of charged moves that would show that without having some artificial threshold or arbitrary step function to make the move seem weak. Any of those thresholds or step functions could be beaten by a move designed specifically to fool it.
Models are inherently a simplification of the real thing, and thus are inherently not perfectly predictive. Good models are simple and pretty accurate. I admit that DPS * DPE is better than either alone, but it's still far from a good model in terms of accuracy.
I think cycle DPS is a good parameter to evaluate a move set, but not good when evaluating charge moves alone. To evaluate charge moves alone, we need to ignore the contribution by fast moves in the moveset.
We can substitute a dummy fast move (0 DPS, x EPS) into the cycle DPS model. For a 1 EPS fast move we'll get:
charge move score = charge move only cycle DPS
= (charged move damage + 0)/(energy cost/1 + charge move duration)
= damage/(energy cost + duration)
That's easy to calculate and meaningful. Compared to DPES, the above shows that S and E are both time dependent and denies each other rather than amplifies each other (you either spend time earn energy, or spending energy).
To make the evaluation more accurate, just substitute x with more reasonable numbers, then we'll get
charge move score = damage/(energy cost/x + duration)
The x in equation shows how significantly does "using the charge move now" hinder "using the charge move later".
