Most monsters in Kingdom of Loathing have 4 quantifiable stats:
Historically, Attack and Defense were typically the same, with HP being 80% of that. This is no longer a reliable rule of thumb, although many of the oldest monster may still have those stats.
There are a number of effects and equipment that give modifiers to Monster Level. In most cases, this translates to bonuses to the monster's stats (above).
For a normal combat monster:
- Actual attack is equal to (base attack + ML Modifiers + Random Variation), rounded down.
- Actual defense is equal to (base defense + ML Modifiers + Random Variation), rounded down.
- The number of stat points gained is:
XP = (Attack + Variation)/4 + (ML Modifiers)/3
- The above formula does not always work for "bosses" and other special cases.
- If the above formula gives a fractional result, the amount of stat gain is randomly rounded up or down based on the size of that fraction.
Some monsters scale to your level. Whether ML Modifiers have any effect on such monsters is defined on a case by case basis.
Monster Level Variance
Sometime in the summer of 2006, monster level variance was added to the game. Monsters' Atk, Def, and HP are all now found to vary by ±5 points.
- All three statistics independently vary by 5% of their base value, rounded down and capped at 5.
- Variance has a triangular distribution (that is, you are much more likely to see 0 than -5 or 5).
- Variance does not occur on monsters whose base ML, attack and defense are less than 20.
- Stat gains are affected. (As of July 2010.)
- Fernswarthy's Basement monsters, scaling monsters, and bosses do not vary.
Raw monster damage is given by:
- Total Damage =
- Diff = (Monster Attack - Player Moxie), minimum 0
- AbsorbFrac = (√(Damage Absorption/10) - 1)/10 (with minimum 0, maximum 0.9)
- ElementalFrac: see Elemental Resistance to determine the value based on resistance strength; remember that Mysticality classes get an innate 5% bonus
Monster Hit Chance
Monster hit chances are not linear. Use the chart below for exact values; However, this approximation is very roughly okay for most purposes:
- Base % = (55 + (Atk-Mox)*5.5), (minimum 0%, maximum 100%)
- Crit % = 6 % flat
- Fumb% = 6 % flat
- Hit % = (base%) (1 - (crit% + fumb%)) (minimum 0%, max 88%)
- Miss % = (1-base%) (1 - (crit% + fumb%)) (minimum 0%, max 88%)
With -9 or lower Moxie (relative to monster level) you will always be hit; with +10 or more Moxie (relative to monster level) you will always dodge. Apart from the funny flavor text, a monster fumble is no different than an ordinary miss and a monster critical is no different than an ordinary hit.
A graph showing the exact probabilities of this is located here.
- The way this probably works is as follows. To see if monster hits:
- find the monster's Awesomeness, defined as Attack-Moxie.
- determine critical hit or critical miss with 6% probability. If neither occurs,
- roll two ten-sided dice; add the first and subtract the other.
- If the result is negative, the monster misses; if the result is 0 or more the monster hits.
- For math geeks: by "10-sided die" we mean "computer-generated discrete uniform pseudorandom variate from 1 to 10." The resulting curve is not linear but rather the CDF of a triangular distribution, though the linear formulas given above are a decent approximation.
- Character hit rate is almost certainly determined in a similar manner.
- For the original spading and graphs showing Hit Rate vs. Awesomeness, see this HCO forum thread.
- For more recent spading of the monster hit chance, see this KoL Spading forum thread.