Use a new algorithm using the median average deviation

module/config/actorConfig.mjs

@@ -507,14 +507,11 @@ export const subclassFeatureLabels = {
  */
 
 /** 
- * @type {Record<string, Record<2 | 3 | 4, TierData> & Record<1, { damage: number[] }>} 
+ * @type {Record<string, Record<2 | 3 | 4, TierData>} 
  * Scaling data used to change an adversary's tier. Each rank is applied incrementally.
  */
 export const adversaryScalingData = {
     bruiser: {
-        1: {
-            damage: [8, 11]
-        },
         2: {
             difficulty: 2,
             majorThreshold: 5,
@@ -522,7 +519,6 @@ export const adversaryScalingData = {
             hp: 1,
             stress: 2,
             attack: 2,
-            damage: [12, 16]
         },
         3: {
             difficulty: 2,
@@ -531,7 +527,6 @@ export const adversaryScalingData = {
             hp: 1,
             stress: 0,
             attack: 2,
-            damage: [18, 22]
         },
         4: {
             difficulty: 2,
@@ -540,13 +535,9 @@ export const adversaryScalingData = {
             hp: 1,
             stress: 0,
             attack: 2,
-            damage: [30, 45]
         }
     },
     horde: {
-        1: {
-            damage: [5, 8]
-        },
         2: {
             difficulty: 2,
             majorThreshold: 5,
@@ -554,7 +545,6 @@ export const adversaryScalingData = {
             hp: 2,
             stress: 0,
             attack: 0,
-            damage: [9, 13]
         },
         3: {
             difficulty: 2,
@@ -563,7 +553,6 @@ export const adversaryScalingData = {
             hp: 0,
             stress: 1,
             attack: 1,
-            damage: [14, 19]
         },
         4: {
             difficulty: 2,
@@ -572,13 +561,9 @@ export const adversaryScalingData = {
             hp: 2,
             stress: 0,
             attack: 0,
-            damage: [20, 30]
         }
     },
     leader: {
-        1: {
-            damage: [6, 9]
-        },
         2: {
             difficulty: 2,
             majorThreshold: 6,
@@ -586,7 +571,6 @@ export const adversaryScalingData = {
             hp: 0,
             stress: 0,
             attack: 1,
-            damage: [12, 15]
         },
         3: {
             difficulty: 2,
@@ -595,7 +579,6 @@ export const adversaryScalingData = {
             hp: 1,
             stress: 0,
             attack: 2,
-            damage: [15, 18]
         },
         4: {
             difficulty: 2,
@@ -604,13 +587,9 @@ export const adversaryScalingData = {
             hp: 1,
             stress: 1,
             attack: 3,
-            damage: [25, 35]
         }
     },
     minion: {
-        1: {
-            damage: [1, 3]
-        },
         2: {
             difficulty: 2,
             majorThreshold: 0,
@@ -618,7 +597,6 @@ export const adversaryScalingData = {
             hp: 0,
             stress: 0,
             attack: 1,
-            damage: [2, 4]
         },
         3: {
             difficulty: 2,
@@ -627,7 +605,6 @@ export const adversaryScalingData = {
             hp: 0,
             stress: 1,
             attack: 1,
-            damage: [5, 8]
         },
         4: {
             difficulty: 2,
@@ -636,13 +613,9 @@ export const adversaryScalingData = {
             hp: 0,
             stress: 0,
             attack: 1,
-            damage: [10, 12]
         }
     },
     ranged: {
-        1: {
-            damage: [6, 9]
-        },
         2: {
             difficulty: 2,
             majorThreshold: 3,
@@ -650,7 +623,6 @@ export const adversaryScalingData = {
             hp: 1,
             stress: 0,
             attack: 1,
-            damage: [12, 16]
         },
         3: {
             difficulty: 2,
@@ -659,7 +631,6 @@ export const adversaryScalingData = {
             hp: 1,
             stress: 1,
             attack: 2,
-            damage: [15, 18]
         },
         4: {
             difficulty: 2,
@@ -668,13 +639,9 @@ export const adversaryScalingData = {
             hp: 1,
             stress: 1,
             attack: 1,
-            damage: [25, 35]
         }
     },
     skulk: {
-        1: {
-            damage: [5, 8]
-        },
         2: {
             difficulty: 2,
             majorThreshold: 3,
@@ -682,7 +649,6 @@ export const adversaryScalingData = {
             hp: 1,
             stress: 1,
             attack: 1,
-            damage: [9, 13]
         },
         3: {
             difficulty: 2,
@@ -691,7 +657,6 @@ export const adversaryScalingData = {
             hp: 1,
             stress: 1,
             attack: 1,
-            damage: [14, 18]
         },
         4: {
             difficulty: 2,
@@ -700,13 +665,9 @@ export const adversaryScalingData = {
             hp: 1,
             stress: 1,
             attack: 1,
-            damage: [20, 35]
         }
     },
     solo: {
-        1: {
-            damage: [8, 11]
-        },
         2: {
             difficulty: 2,
             majorThreshold: 5,
@@ -714,7 +675,6 @@ export const adversaryScalingData = {
             hp: 0,
             stress: 1,
             attack: 2,
-            damage: [15, 20]
         },
         3: {
             difficulty: 2,
@@ -723,7 +683,6 @@ export const adversaryScalingData = {
             hp: 2,
             stress: 1,
             attack: 2,
-            damage: [20, 30]
         },
         4: {
             difficulty: 2,
@@ -732,13 +691,9 @@ export const adversaryScalingData = {
             hp: 0,
             stress: 1,
             attack: 3,
-            damage: [30, 45]
         }
     },
     standard: {
-        1: {
-            damage: [4, 6]
-        },
         2: {
             difficulty: 2,
             majorThreshold: 3,
@@ -746,7 +701,6 @@ export const adversaryScalingData = {
             hp: 0,
             stress: 0,
             attack: 1,
-            damage: [8, 12]
         },
         3: {
             difficulty: 2,
@@ -755,7 +709,6 @@ export const adversaryScalingData = {
             hp: 1,
             stress: 1,
             attack: 1,
-            damage: [12, 17]
         },
         4: {
             difficulty: 2,
@@ -764,13 +717,9 @@ export const adversaryScalingData = {
             hp: 0,
             stress: 1,
             attack: 1,
-            damage: [17, 20]
         }
     },
     support: {
-        1: {
-            damage: [3, 5]
-        },
         2: {
             difficulty: 2,
             majorThreshold: 3,
@@ -778,7 +727,6 @@ export const adversaryScalingData = {
             hp: 1,
             stress: 1,
             attack: 1,
-            damage: [5, 12]
         },
         3: {
             difficulty: 2,
@@ -787,7 +735,6 @@ export const adversaryScalingData = {
             hp: 0,
             stress: 0,
             attack: 1,
-            damage: [13, 16]
         },
         4: {
             difficulty: 2,
@@ -796,7 +743,22 @@ export const adversaryScalingData = {
             hp: 1,
             stress: 1,
             attack: 1,
-            damage: [18, 25]
         }
     }
 };
+
+/** Scaling data used for an adversary's damage */
+export const adversaryExpectedDamage = {
+  basic: {
+    1: { medianDamage: 7.5, damageDeviation: 1 },
+    2: { medianDamage: 13, damageDeviation: 2 },
+    3: { medianDamage: 15.5, damageDeviation: 1.5 },
+    4: { medianDamage: 27, damageDeviation: 3 }
+  },
+  minion: {
+    1: { medianDamage: 2, damageDeviation: 1 },
+    2: { medianDamage: 5, damageDeviation: 0.5 },
+    3: { medianDamage: 6.5, damageDeviation: 1.5 },
+    4: { medianDamage: 11, damageDeviation: 1 }
+  }
+};

module/data/actor/adversary.mjs

@@ -3,7 +3,7 @@ import { ActionField } from '../fields/actionField.mjs';
 import BaseDataActor, { commonActorRules } from './base.mjs';
 import { resourceField, bonusField } from '../fields/actorField.mjs';
 import { parseTermsFromSimpleFormula } from '../../helpers/utils.mjs';
-import { adversaryScalingData } from '../../config/actorConfig.mjs';
+import { adversaryExpectedDamage, adversaryScalingData } from '../../config/actorConfig.mjs';
 
 export default class DhpAdversary extends BaseDataActor {
     static LOCALIZATION_PREFIXES = ['DAGGERHEART.ACTORS.Adversary'];
@@ -214,18 +214,11 @@ export default class DhpAdversary extends BaseDataActor {
             source.system.attack.roll.bonus += scale * entry.attack;
         }
 
-        /** Returns the mean and standard deviation of a series of average damages */
-        const analyzeDamageRange = range => {
-            if (range.length <= 1) throw Error('Unexpected damage range, must have at least two entries');
-            const mean = range.reduce((a, b) => a + b, 0) / range.length;
-            const deviations = range.map(r => r - mean);
-            const standardDeviation = Math.sqrt(deviations.reduce((r, d) => r + d * d, 0) / (range.length - 1));
-            return { mean, standardDeviation };
-        };
 
         // Calculate mean and standard deviation of expected damage ranges in each tier. Also create a function to remap damage
-        const currentDamageRange = analyzeDamageRange(typeData[source.system.tier].damage);
+        const expectedDamageData = adversaryExpectedDamage[source.system.type] ?? adversaryExpectedDamage.basic;
-        const newDamageRange = analyzeDamageRange(typeData[tier].damage);
+        const currentDamageRange = expectedDamageData[source.system.tier];
+        const newDamageRange = expectedDamageData[tier];
         const convertDamage = (damage, newMean) => {
             const hitPointParts = damage.parts.filter(d => d.applyTo === 'hitPoints');
             if (hitPointParts.length === 1 && !hitPointParts[0].value.custom.enabled) {
@@ -248,14 +241,14 @@ export default class DhpAdversary extends BaseDataActor {
                 )
                 .join('+');
             const terms = parseTermsFromSimpleFormula(formula);
-            const mean = terms.reduce((r, t) => r + (t.modifier ?? 0) + (t.dice ? (t.dice * (t.faces + 1)) / 2 : 0), 0);
+            const expected = terms.reduce((r, t) => r + (t.modifier ?? 0) + (t.dice ? (t.dice * (t.faces + 1)) / 2 : 0), 0);
-            return { formula, terms, mean };
+            return { formula, terms, expected };
         };
 
         // Update damage of base attack
-        const atkAverage = parseDamage(source.system.attack.damage).mean;
+        const atkAverage = parseDamage(source.system.attack.damage).expected;
-        const deviation = (atkAverage - currentDamageRange.mean) / currentDamageRange.standardDeviation;
+        const deviation = (atkAverage - currentDamageRange.medianDamage) / currentDamageRange.damageDeviation;
-        const newAtkAverage = newDamageRange.mean + newDamageRange.standardDeviation * deviation;
+        const newAtkAverage = newDamageRange.medianDamage + newDamageRange.damageDeviation * deviation;
         const damage = source.system.attack.damage;
         convertDamage(damage, newAtkAverage);
 
@@ -266,11 +259,11 @@ export default class DhpAdversary extends BaseDataActor {
             for (const action of Object.values(item.system.actions)) {
                 const damage = action.damage;
                 if (!damage) continue;
-                const { formula, mean } = parseDamage(damage);
+                const { formula, expected: mean } = parseDamage(damage);
                 if (mean === 0) continue;
 
-                const deviation = (mean - currentDamageRange.mean) / currentDamageRange.standardDeviation;
+                const deviation = (mean - currentDamageRange.medianDamage) / currentDamageRange.damageDeviation;
-                const newMean = newDamageRange.mean + newDamageRange.standardDeviation * deviation;
+                const newMean = newDamageRange.medianDamage + newDamageRange.damageDeviation * deviation;
                 convertDamage(damage, newMean);
 
                 const oldFormulaRegexp = new RegExp(formula.replace('+', '(?:\\s)?\\+(?:\\s)?'));

tools/analyze-damage.mjs

@@ -0,0 +1,105 @@
+/**
+ * Internal script to analyze damage and spit out results.
+ * There isn't enough entries in the database to make a full analysis, some tiers miss some types.
+ * This script only checks for "minions" and "everything else".
+ * Maybe if future book monsters can be part of what we release, we can analyze those too.
+ */
+
+import fs from "fs/promises";
+import path from "path";
+
+const allData = [];
+
+// Read adversary pack data for average damage for attacks
+const adversariesDirectory = path.join("src/packs/adversaries");
+for (const basefile of await fs.readdir(adversariesDirectory)) {
+    if (!basefile.endsWith(".json")) continue;
+    const filepath = path.join(adversariesDirectory, basefile);
+    const data = JSON.parse(await fs.readFile(filepath, "utf8"));
+    if (data?.type !== "adversary" || data.system.type === "social") continue;
+
+    allData.push({
+        name: data.name,
+        tier: data.system.tier,
+        adversaryType: data.system.type,
+        damage: parseDamage(data.system.attack.damage),
+    });
+}
+
+const result = {
+    basic: compileData(allData.filter(d => d.adversaryType !== "minion")),
+    minion: compileData(allData.filter(d => d.adversaryType === "minion")),
+};
+
+console.log(result);
+
+/** Compiles all data for an adversary type (or all entries) */
+function compileData(entries) {
+    // Note: sorting numbers sorts by their string version by default
+    const results = {};
+    for (const tier of [1, 2, 3, 4]) {
+        const tierEntries = entries.filter(e => e.tier === tier);
+        const allDamage = tierEntries.map(d => d.damage).sort((a, b) => a - b);
+        const median = getMedian(allDamage);
+        const residuals = allDamage.map(d => Math.abs(d - median)).sort((a, b) => a - b);
+        results[tier] = {
+            medianDamage: median,
+            damageDeviation: getMedian(residuals),
+        };
+    }
+
+    return results;
+}
+
+function getMedian(numbers) {
+    const medianIdx = numbers.length / 2;
+    return medianIdx % 1 ? numbers[Math.floor(medianIdx)] : (numbers[medianIdx] + numbers[medianIdx - 1]) / 2;
+}
+
+function parseDamage(damage) {
+    const formula = damage.parts
+        .filter(p => p.applyTo === 'hitPoints')
+        .map(p =>
+            p.value.custom.enabled
+                ? p.value.custom.formula
+                : [p.value.flatMultiplier ? `${p.value.flatMultiplier}${p.value.dice}` : 0, p.value.bonus ?? 0]
+                        .filter(p => !!p)
+                        .join('+')
+        )
+        .join('+');
+    return getExpectedDamage(formula);
+}
+
+/**
+ * Given a simple flavor-less formula with only +/- operators, returns a list of damage partial terms.
+ * All subtracted terms become negative terms.
+ */
+function getExpectedDamage(formula) {
+    const terms = formula.replace("+", " + ").replace("-", " - ").split(" ").map(t => t.trim());
+    let multiplier = 1;
+    return terms.reduce((total, term) => {
+        if (term === "-") {
+            multiplier = -1;
+            return total;
+        } else if (term === "+") {
+            return total;
+        }
+
+        const currentMultiplier = multiplier;
+        multiplier = 1;
+        
+        const number = Number(term);
+        if (!Number.isNaN(number)) {
+            return total + currentMultiplier * number;
+        }
+
+        const dieMatch = term.match(/(\d+)d(\d+)/);
+        if (dieMatch) {
+            const numDice = Number(dieMatch[1]);
+            const faces = Number(dieMatch[2]);
+            return total + currentMultiplier * numDice * ((faces + 1) / 2);
+        }
+
+        throw Error(`Unexpected term ${term} in formula ${formula}`);
+    }, 0);
+}