Introduction
The player has access to (up to) 3 Resource Bars in AdventureQuest (AQ): HP, MP, and SP. We’ve already discussed two of these in my last post about the Player Turn Formula. The first, SP, forms the SP component of the turn formula. Each turn, the Player regenerates 25% Melee in SP, which can then be used to cast Skills and sustain Misc items/Guests. The second, MP, is part of the Player Damage component for Mages, and essentially represents compressed Player damage that can be used to cast Spells and sustain Guests. MP allows Mages to frontload their damage at the start of battle. The final bar, HP, refers to player health. If your HP reaches 0, you lose the battle.
In this post, I’ll explain the formulae underpinning the HP, MP and SP resources for your player. I’ll also discuss some of the inconsistencies around how HP is used in AQ.
Visit the Content Hub for other parts of this series
Calculating your HP/MP/SP
Player HP, MP and SP vary depending on both your Character’s level and stat spread (except for SP). You don’t need to worry about most of the numbers found in the following formulae, only those I explicitly discuss. Normally, these formulae produce decimal results, which are then rounded to give the correct amount.
Player HP
Your maximum HP depends upon both your Character’s Level and investment in END. Player HP can be calculated by substituting these values into the following formula:
HP: 23.8 * ((5.25 + 0.5625 * Level + 0.00375 * Level^2) + (1 + 0.066 * Level) * END/16) * 1/1.4
Let’s assume that we have a Level 80 Character with 150 END. We can substitute these values into the formula like so:
23.8 * ((5.25 + 0.5625 * 80 + 0.00375 * 80^2) + (1 + 0.066 * 80) * 150/16) * 1/1.4 = 2263.125 HP
Rounding this down, our example character would have 2263 HP. Plug your character’s values into the formula and watch it calculate your HP!
Player MP
Calculating your MP is a little more complicated, and depends upon both your Character’s Level and investment in INT. You can substitute these into the following formula:
MP: 4.1 * (33 + (5.1 + 2.3375 * Level + 0.01125 * Level^2) * MIN(1, INT / MAX(MIN(2 * Level + 4, 250), 10)))
To deal with this equation, it’s best to break it down into smaller parts. For this calculation, we’ll assume we have a Level 100 player with 200 INT. First, we have:
MIN(2 * Level + 4, 250)
MIN() means “Take the minimum of”. In this case, we want to take the lower of either 2 * Level + 4 or 250. As our example character is level 100, our first value is 2 * 100 + 4 = 204. The formula then becomes:
MIN(204, 250) = 204
What is this doing? It's calculating the amount of INT the player is expected to have at your Level. This means, at Level 100, you’re expected to have 204 INT. We’ll use this value in the next component:
MAX(Expected INT, 10)
MAX() means “Take the maximum of”. The formula here is therefore asking us to take the higher of either the value we just calculated (204) or 10. In other words, the formula always assumes the player has at least 10 INT. This is to be expected for a mage; players that choose to be a Mage at the start of the game receive 10 INT points. There’s one last component to calculate before we can calculate your MP:
MIN(1, INT/Expected INT)
Here, we’re taking the minimum of either 1 or INT/Expected INT. This second component compares your Character’s actual INT to the Expected INT we’ve just calculated. Since our character has 200 INT and we calculated an expected value of 204, our second value is 200/204 = 0.98. Plugging this into the formula:
MIN(1, 0.98) = 0.98
This mechanism makes sure the formula never calculates your Max MP assuming you have more than the expected amount of INT for your level. We’ll call this value our Modifier. Finally, we can calculate our Max MP:
4.1 * (33 + (5.1 + 2.3375 * Level + 0.01125 * Level^2) * Modifier
Substituting in our Level of 100:
4.1 * (33 + (5.1 + 2.3375 * 100 + 0.01125 * 100^2) * 0.98 = 1547.02 MP
So, our Level 100 Character with 200 INT will have 1547 MP.
Player SP
Player SP can be calculated using:
SP: 2.25 * (38.1 + 2.3375 * MPLevel + 0.01125 * MPLevel^2)
As you’ll have noticed, SP is not affected by Player Stats. This is intentional – SP is a universal resource and independent of Player build. MPLevel can be calculated using this formula:
MPLevel: Item PowerLvl*3/4 + Item Level/4
Generally, this produces a value equal to the Player's Level + 2 except at low levels (when it's equivalent to Player Level). Assuming we have a Level 120 Player:
2.25 * (38.1 + 2.3375 * 122 + 0.01125 * 122^2) = 1104.12 SP
The amount of SP the player regenerates can be calculated in the same way:
0.15 * (38.1 + 2.3375 * MPLevel + 0.01125 * MPLevel^2)
0.15 * (38.1 + 2.3375 * 150 + 0.01125 * 150^2) = 73.608 SP
Thus, a Level 120 player will have a maximum of 1104 SP and regenerates 74 SP per turn.
Resource conversion
It is possible to convert between SP, HP and MP. Each point of SP;HP;MP is valued at a ratio of 1.125;1;1.5 respectively, meaning 1.125 SP, 1 HP, and 1.5 MP are all worth the same amount.
For example, let’s say you were a level 150 Warrior trying to use a Skill that deals 200% Melee damage. Your base damage is worth 100% Melee (see part 1 of this blog series), meaning you need an additional 100% Melee from either HP, MP, or SP. At level 150, you need 392 SP to add the 100% Melee needed to use a skill. However, you could also pay for that damage by paying either 392/1.125 = 348.45 HP or 392/1.125*1.5 = 522.67 MP.
We can also use this to work out how much a MP a Level 150 Mage needs to cast a spell. To bring up their 75% baseline damage up to Spell level, the Mage needs 125% Melee in MP. Given we know that 392 SP is worth 100% Melee:
392 * 1.25 / 1.125 * 1.5 = 653.34 MP
If you look at normal Level 150 Spells, you will see this is how much they cost!
The HP Cost problem
As we’ve just calculated above, a Level 150 Player is expected to spend 348 HP on a Melee Skill. Warriors are expected to deal 100% Melee per round, with the rest covered by SP. This means 348 HP is worth 100% Melee.
In the Player Turn Model, the monster is expected to deal 5% of Player HP per turn (this is part of why it’s known as the 20-turn formula). The formula assumes the player has no investment in END. In the past, this assumption has allowed items like Pyromancer Bloodmage to value 100% Melee at 151 HP.
How can 348 HP and 151 HP both be worth 100% Melee at the same time?!
This all comes down to how HP works. HP is used in two ways:
i). To absorb monster attacks and
ii). To spend on items that cost HP to use.
In an ideal world, both of these would value HP the same as they’re both using the same resource. However, AQ isn’t perfect and its inconsistencies give rise to this major discrepancy. This has implications; a major reason why Healing items are generally seen as weak is because you’re spending other resources to heal HP, which is hugely overvalued. At the same time, items that cost HP to use were (until relatively recently), absurdly cheap to run.
To give you a demonstration, I’m going to show you how Essence orb is currently balanced. The Level 150 version spends 75 HP to heal 89 SP. How?
Essence orb uses the overvalued form of HP, meaning that 75 HP is worth ~50% Melee. 196 SP is worth 50% Melee at this level. An “always useful” penalty of *0.9 is added to this conversion (it’s always useful because this is equally effective against any opponent). Finally, a *0.5 modifier is added to get 88 (there’s a bit of rounding involved):
196 * 0.9 * 0.5 = 88.2 SP
You may be thinking “Why the 0.5 modifier?”. The answer might surprise you. Essence orb was considered so overly powerful despite being balanced, the staff decided it needed that penalty to keep things even somewhat fair. This is a great example of how sometimes the model can’t handle certain situations. Even with this penalty, Essence orb could (until recently) be used with Discount Mogloween Candy Bag and Pixel Ether to generate infinite resources!
Long ago, I proposed treating all HP cost items as if they were being used in the second way in order to solve this problem. In that scenario, Essence orb would be able to convert:
75 * 1.125 * 0.9 = 76 SP
This wouldn’t be much lower than the current value, but it would remove the need for the unwarranted *0.5 Penalty (there are of course other issues with Essence orb).
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