THE MODEL'S FORMULAS AND ASSUMPTIONS

• Stat growth: stat(L) = base + growth×(L-1)×(0.7025 + 0.0175×(L-1)) — Riot's official formula.
• Damage multiplier: 100 / (100 + resistance). Penetration stats are subtracted before resistance.
• DPS = auto-attack DPS (AD × attack speed × crit multiplier) + ability rotation DPS (base damage + ratio×stat ÷ cooldown) — ability data is read from the current patch.
• Duel advantage = your time-to-die ÷ your time-to-kill the enemy. Above 1: you win the duel.
• Enemy model: the enemy spends gold equal to yours on stats fitting their own profile (fair duel). Healing counts as +22% effective HP; Grievous Wounds cuts it by 60%.
• Item efficiency = stat value ÷ price. Stat values are derived from the table on the right (this patch's basic items); since passive effects aren't included, efficiency is a lower bound.
• Range (kite) factor: a melee champion can apply 75% of its DPS to a ranged enemy.
• Item selection target: score = min(die, 1.25×kill) ÷ kill + 0.6×(10 ÷ kill). That is: first survive enough to win the duel; defense beyond that is waste, gains come from kill speed.
• Ratio matching: attack items must include the stat your ability ratios depend on (an AP champion isn't offered a pure AD/crit item); defensive items are open to everyone, their value set by the duel.
• Ability numbers (base damage + ratios, rank by rank) come from the community source Meraki Analytics; Riot doesn't publish these in official data, so this source is used. If unavailable, a generic rotation is assumed (150 base + 0.55×AP + 0.4×AD, 8s cooldown).
• If the enemy's real items are marked, the model uses those items' exact stats instead of a generic gold spread.
• The RUNE PAGE is chosen entirely by math: the keystone is picked from the archetype pool by duel score (with a small priority to the meta standard); minor runes by a 'duel effect + utility' score per row, and the secondary tree is the one whose best two minor runes sum highest. Rune values are derived from Riot's descriptions; utilities invisible in a duel (ult cooldown/mana) are scored separately.
• GAME STYLE (tank): 'tank' rewards absolute survival time (defense/EHP items rise), 'damage' rewards kill speed, 'balanced' both. Tank champions default to 'tank'; changeable at the top. Defense type is chosen by the enemy's damage (armor vs AD, magic resist vs AP).
• Item passives are partly modeled: max-HP burn (Liandry, Blackfire), damage amplification (Riftmaker, Shadowflame), on-hit magic (Nashor). So items with strong passives are ranked by real effect, not just flat stats. Some items' numbers are template-hidden in Riot's data (like Nashor, Demonic), so that part may be missing.
• TEAM MODE: in a live game, item score is computed weighted against the whole enemy team, not one enemy — the lane opponent 40%, the other 4 enemies share the remaining 60% equally. Each enemy is modeled with their real items; the armor/magic-resist decision is set by the team's damage split.

STAT GOLD VALUES (derived from this patch)