Cost-benefit analysis of attack potions

Attack pots. Are they worth it? Or do we just cider forever? Let's find out, using napkin math because I have no idea how to make cool tables and calculators on Google Sheets.

For the most part the answer is "no" though, and I haven't even done any of the math yet. I am confident enough in that answer though that you can just close out of this tab, dear reader. Essentially attack pots are only efficient when they are a requirement to finish within a certain time, or are capable of making absurd amounts of money quickly.

You can calculate the effectiveness of attack pots based solely on how much attack you currently have, but that differs from class to class. The lower your current attack, the more effective the increase of DPS is. So if you have 170 attack on cider, then on apple you'll have 250 attack. This means your DPS will increase by 250/170 = 1.4706 times, as pure increases to attack are proportional regardless of base stats due to the formula. On the other hand, if you have 220 attack on cider(pog) then on apple you'll have 300 attack, increasing DPS by 300/220 = 1.3636 times. You can read about damage calculations more in Nise's formula compilation here:

https://forum.maplelegends.com/index.php?threads/nises-formula-compilation.36234/

So, what's next is to list a general range of attack between all classes using all unique sources, but for the sake of simplicity Marksmen will be left out(Snipe makes things complicated) and will be listed mostly via dragon weapons and close meta alternatives, along with 10 attack MoN in some cases or HTP, and 20 att shield on warrior and 33 dkhan for shadowers.

Buccaneer - 83 (HTP)
Night Lord - 86 (Sleeve - HTP - Magic Throwing Knives)
Buccaneer - 93 (MoN)
Night Lord - 96 (Sleeve - MoN - Magic Throwing Knives)
Corsair - 105 (Armor-Piercing Bullets - HTP)
Dark Knight - 109 (MoN - Skis)
Corsair - 115 (Armor-Piercing Bullets - MoN)
Bowmaster - 120 (Bow Expert - Diamond Arrow - HTP)
Hero/Paladin - 120 (Claymore - MoN)
Dark Knight - 122 (Faltizan - MoN)
Bowmaster - 130 (Bow Expert - Diamond Arrow - MoN)
Shadower - 138 (Kanzir - 33-att-Dkhan - HTP)
Hero/Paladin - 138 (Carabella - 20-att-Shield - MoN)
Paladin - 150 (Crushed Skull - 20-att-Shield - MoN

This creates a fairly vast range of potential when comparing the effectiveness of apple. Depending on class and build, there can be up to a 67 point difference in how the effectiveness of attack pots are calculated. So for an avoid focused Buccaneer the effect of an apple is significantly higher than for a 1h bw Paladin, with everyone else falling somewhere in between.

Now we add in the universal attack potential, attack that can be added regardless of class or general build:
35 (weapon)
17 (cape)
23 (gloves)
20 (cider)
10 (other - Stompers, event rings, event face)

Total - 105, added to the top and bottom range of classes. More is possible, but this makes for a decent guideline for end-game. So in the case we're looking at avoid Bucc to skull Paladin, the attack range we're looking at is between 188 and 255 before apple. Alternatively we can look at MoN NL compared to Shadower, as within that range we can find most players without large outliers skewing the data. For that group the attack range is 201 to 243.

Now we look at the DPS increase expected from using an apple - replacing cider for 80 more attack:

HTP Bucc vs. Skull Paladin:
(bucc) 268/188 = 1.4255, or 42.55% more DPS
(paladin) 335/255 = 1.3137, or 31.37% more DPS

MoN NL vs. Shadower:
(NL) 281/201 = 1.3980, or 39.8% more DPS
(Shad) 323/243 = 1.3292, or 32.92% more DPS

So using an apple in the end-game will increase your DPS somewhere in the neighborhood of 30-43%, with the majority of cases increasing by around 33-40%. As gear gets worse, the effectiveness of the apple increases, while as it gets better the effectiveness decreases.

That's the benefit of using an apple, but now we need to review the cost. It's 2mil per apple. Done.

Now on to the cost-benefit analysis. There's probably a simple way to do this but I am not very smart so I'll do it by the meso cost per 1% damage increase over 1 hour.

Given a cost of 12mil/hr in apples, the theoretical HTP Bucc with 188 attack spends 282,021 mesos per 1% damage increase over 1 hour.

The Skull Paladin on the other had, with 255 attack, spends 382,531 mesos per 1% damage increase over 1 hour.

In most cases, you will be spending between 280k and 380k per 1% damage for 1 hour by continuously appling. It's not very good value.

Night Lords on the other hand get much better value via alchemist, along with already being on the more efficient side of the spectrum.

Given a cost of 9.6mil/hr in apples, the MoN NL with 201 attack, spends 241,206 mesos per 1% damage increase over 1 hour. It's better than anyone else by a good margin, but still a rather expensive habit to make.

More words later, for now I'm tired of writing, and I didn't even get to the abysmal value of using Cheese on a mage. If you want to let me know how to express the math better or want to do it yourself then go ahead, I already see that it's confusing and hard to understand as I am a dingus. I'm thinking if you multiply the last numbers(240k, 280-380k) by 100 that's the amount of money you need to make in an hour to benefit from apple time save, but that's a random guess and I have no idea how numbers work.