Best Offensive movesets may be different than we think..

Okay, so this took me quite a little while but I have developed something very interesting.

I realized about 2 days ago, that I kept looking at the highest DPS moves to determine the best offensive moveset, I have also noticed this is how most lists seem to determine the best moveset, but then I realized, technically speaking, highest DPS is not really what we care about. What we truly care about is which Pokemon can do more damage at the end of "x" number of seconds, and I noticed something very worthy of note. (This study focuses primarily on the charge move because the fast move is significantly more straightforward to deduce).

So, I used Dragonite as my case study. I compared two Dragonites, both with Dragonbreath, but one with Dragonclaw (DC) and the other with Dragonpulse (DP). (I use non-STAB values since they are easier to work with and it does not matter as STAB is simply a scaling factor on both fast and charge moves equivalently.)

Now, most people think, "yea, higher DPS, this move is better!!", but that "higher DPS" has a built in assumption - that you get to continually use the move over and over, but as we all know, that is sadly not the case. So then let me ask you, if you only get to use a charge move once which is better, one that takes 2 seconds and does 40 damage, or one that take 4 seconds, and does 70 damage? As we see, the former move has a higher DPS (20, versus 17.5), but remember you only get to use the move once. So would you rather do 40 damage or 70? The answer actually comes down to how many times you would be able to use your fast move while the longer charge move is still finishing up. So in this case, if we used Dragonite, he can do 12 DPS with his fast move. So, a Dragonite with DC (let's call him Blue) does 40 damage, then executes a total of four fast moves to do a total damage of 24 damage in fast moves and a total damage in the 4 seconds of 40+12+12=64, great!! but.... let's look at the Dragonite that used DP (let's call him Orange), sure, it took him all day to finish up, but! at the end of those 4 seconds, he did 70 damage. A lower DPS but higher damage. And at the end of the day, total damage is all we really care about, DPS is just an indicator but that indicator can be misleading. I have included a graph below that illustrates this principle. (The x-axis is time in seconds. The y-axis is total damage. The blue line is a Dragonite with DC. The Orange line is a Dragonite with DP). Now, Blue does indeed spend some time above Orange, but the crucial part is not who is higher, but who spends more time being higher. Since we cannot guarantee ahead of time without a lot of math how long a battle will last, we care about which move has more opportunities to do more damage.

Now, there are some more crucial factors to include here. The graph I have included is based off an EPS of 7. This is the EPS of Dragonbreath - the fast move. BUT EPS actually comes from two places - one, your fast move, and two, taking damage. So, really, we can guarantee that the true EPS is higher than 7, but how much higher depends on who you are battling. And here is the crucial part as EPS gets higher, the charge move matters more.

Let's take this example. Imagine an EPS of 100, well, then you get to continually use your charge move over and over, and the DPS listed for the charge move is exact. You don't just get to use it once, but constantly. So, the higher the EPS the more we get to use are charge move, the closer we get to that true value of the DPS seen for the charge move. But, as we know, EPS is never going to be 100, in fact it is drastically lower than that, and it matters on the battle. So unless you are going to pre-calculate the EPS of every battle before you click "go" the best plan of attack is to take the average, and see which moveset is more applicable (something that sounds exhausting), you want to average over a range of different EPSs, something which I have gone ahead and done for you.

Also, as stated above, battle duration matters, so I also calculated over all possible battle lengths 1 to 99. Here are the results. (I have discluded any times at which the two Dragonite would do equal damage, like when they are charging up initially).

Overall, DC is much better, for EPS ranging from 7-16, and battle times ranging from 1-99, 61.5% of the time DC does more damage. BUT we know most battles don't last for 99 seconds, and most probably aren't an EPS of 16. So, I split this data into quandrants.

For battles lasting less than 50 seconds and EPS 7-11:
DC does more damage 56% of the time.
DP does more damage 44% of the time.

For battles lasting less than 50 seconds and EPS 11-16:
DC does more damage 68% of the time.
DP does more damage 32% of the time.

For battles lasting greater than 50 seconds and EPS 7-11:
DC does more damage 36% of the time.
DP does more damage 64% of the time.

For battles lasting greater than 50 seconds and EPS 11-16:
DC does more damage 76% of the time.
DP does more damage 24% of the time.

As, we can see, DC is much better overall. Only in the case in which that you are in a long drawn out battle in a low EPS situation, so many a Chansey or maybe a Snorlax which you can dodge or possible has earthquake (I am just speculating here, I do not know the actual EPS of any given fight, but would really love to if anyone knows of a resource) would DP be better. BUT BUT BUT BUT BUT

Here is the HUGE "BUT"! These are again NOT MOST BATTLES. Think about it, most battles last under 30 seconds, and have a varying range of EPS. SO, here's the numbers I calculated on those.

For battles under 30 seconds and an EPS of 7:
DC does more damage 46% of the time.
DP does more damage 54% of the time.

For battles under 30 seconds and an EPS of 8:
DC does more damage 40% of the time.
DP does more damage 60% of the time.

For battles under 30 seconds and an EPS of 9:
DC does more damage 44% of the time.
DP does more damage 56% of the time.

For battles under 30 seconds and an EPS of 10:
DC does more damage 53% of the time.
DP does more damage 47% of the time.

For battles under 30 seconds and an EPS of 11:
DC does more damage 61% of the time.
DP does more damage 39% of the time.

For battles under 30 seconds and an EPS of 12:
DC does more damage 68% of the time.
DP does more damage 32% of the time.

As we can see, as EPS goes up, DC gets better, but remember an EPS of 12 would equate to having both charge bars full every 8 seconds, that seems a little too frequent to me, but again I am just speculating. The point is this. The fact of the matter is most battles last under 30 seconds, and do not have incredibly high EPS, and this is when DP is most useful. In other words, DP is significantly less useful in most situations, but in the most situations, it may actually be the better move. Since an EPS on 10 would mean it takes 10 seconds to fill your 2 charge bars fully, you can basically boil it down to one simple principle for Dragonite:

In battles that take less than 30 seconds -
If it takes greater than 10 seconds to fully fill your 2 charge bars, Dragonpulse is the superior move.
If it takes less than 10 seconds to fully fill your 2 charge bars, Dragonclaw is the superior move.

Do not get me wrong, I still think DC is generally the better move, and I am super happy that I have a Dragonite with it and DB but (again) my point is, do not get too upset if you get a Dragonite with Dragonbreath and Dragonpulse, because in many relevant scenarios, he's actually the better Pokemon (offensively).

I also think it might be a good idea to extend this analysis, or rather this technique to all Pokemon and movesets. But really to be able to do that, I need a breakdown of the average battle length and EPS and their respective distributions. Then I can make a true map of which move is best, in the situations that matter. If anyone has this or knows where to find it, I would be greater appreciative.

Best,