Abilities
Rank breakpoints, cooldowns, costs, and level scaling in one centered ledger.
Base Stats by Level
Riot curved growth: value(L) = base + growth × coef(L), where
coef(L) = (L−1)(0.7025 + 0.0175(L−1)). Attack speed scales the same coef as a % of base AS.
What this analyzer computes
Every number on the Build Analysis tab is derived from your selected items, runes, ability
ranks and the target's defenses. This is the full set of assumptions behind those figures.
Stat scaling
Per-level champion stats use Riot's curved growth:
value(L) = base + growth × coef(L)
coef(L) = (L−1)(0.7025 + 0.0175(L−1))
Attack speed applies the same coef(L) as a percentage of base AS. Level-linear
ability values are interpolated between their listed level 1 and 18 endpoints.
Physical damage mitigation
Physical damage is reduced by the target's effective armor:
mitigation = 100 / (100 + effArmor)
effArmor = max(0, armor × (1 − %pen) − lethality)
Percent armor penetration is applied first, then flat lethality is subtracted. Effective armor
never drops below zero.
Damage types
- Physical — shares the armor mitigation above, plus rune amp, Giant Slayer and
(on autos) the target's Steelcaps.
- True — ignores armor entirely.
- Magic — ignores armor; the target's magic resist is not modeled.
Autos are crit-averaged: each auto deals (1 + crit% × (critMult − 1)) of its
base, rather than rolling individual crits.
Modeled passives ★
Only four item passives change the damage numbers — all marked ★ on the
Items tab:
- Infinity Edge — increased critical strike damage.
- Kraken Slayer — bonus physical damage on every third attack.
- Lord Dominik's Regards — Giant Slayer: up to +15% damage vs targets with bonus health.
- Hubris — Eminence:
12 + 3 × stacks bonus AD while active. On the Hubris card
(bottom of the Offensive panel) set your takedown stacks with the spinner and switch the buff on or
off with the circular ✓ toggle; while active the bonus feeds Total AD and every AD ratio, and the
mid-quest +8% applies on top.
All other item passives are descriptive text only. A rune affects damage only if the analyzer
models its effect (these feed the numbers on Build Analysis); other runes are selectable but
utility-only.
Combo timing
The Combo Sequencer plays your rotation on the build's live stats. The model below is computed
from the current build — its numbers (windup, W attack speed, Harrier cooldown, procs)
update as you change items, runes and ability ranks:
These assumptions are intentionally simple — they model a clean rotation against a
stationary target. Real games add movement, mid-combo item actives and target MR, which are out of scope here.
Movement speed formula
Bonuses combine in a fixed order: flat first, then additive percent, then each multiplicative
percent in turn, then the single strongest slow. Soft caps are applied last.
(wiki)
raw = (base + flatBonuses)
× (1 + Σ additivePercent)
× Π (1 + eachMultiplicativePercent)
× (1 − highestSlow)
Only the single largest slow applies — slows do not stack. Quinn's base is
330.
Soft caps (applied to raw)
- raw > 490 →
raw × 0.5 + 230
- 415 – 490 →
raw × 0.8 + 83
- 220 – 415 → no cap (used as-is)
- 0 – 220 →
110 + raw × 0.5 (slow soft cap — raises it)
- raw < 0 →
110 + raw × 0.01 (floor ≈ 10)
The brackets are continuous: 415 and 490 and 220 give the same value on either side.
Worked examples
1 · Boots + a movement rune (flat → additive %)
base 330 + 45 (Steelcaps) = 375
375 × (1 + 0.05) = 393.75 → 220–415, no cap
final = 394
2 · A fast build hits the upper cap
raw = (330 + 60) × (1 + 0.05) × 1.20 = 491.4
491.4 > 490 → 491.4 × 0.5 + 230
final = 475.7
Past ~490 each point of raw MS is worth only half — stacking flat MS hits steep
diminishing returns.
3 · A heavy slow hits the lower soft cap
at 400 MS, hit by a 90% slow:
raw = 400 × (1 − 0.90) = 40 → 0–220
final = 110 + 40 × 0.5 = 130
The lower cap is why even a near-total slow still leaves you crawling rather than frozen.
4 · Quinn R (Behind Enemy Lines)
R out of combat grants a large flat + % MS.
e.g. (330 + 0) × (1 + 0.70) = 561 → > 490
final = 561 × 0.5 + 230 = 510.5
Quinn's roam speed is huge but soft-capped — exact R values live in the Abilities
& Stats pane; the cap math is what matters here.
Travel time to lane
The Peak movement-speed boxes on the Build Analysis tab carry two turret badges:
the estimated time to reach your lane's tier-1 (outer) turret leaving the fountain, for the selected role.
The plain turret badge uses passive movement speed only; the active-items turret badge
additionally fires your item actives on the way out, so it is the faster of the two.
Speed is not constant over the trip. The leaving-fountain buffs each last only a few seconds,
so the time is integrated over a decaying speed profile rather than distance ÷ a single speed:
- Homeguard (fountain boost) — starts at +80% (+150% after 14:00), decays to +40% (+65%)
over 4s after leaving the fountain, then holds that floor for the rest of the trip
(walking to lane stays out of combat and out of the jungle). Both badges.
- Youmuu's Ghostblade — Wraith Step +15% for 4s (ranged), if owned. With-actives badge only.
- Mercurial Scimitar — Quicksilver +50% for 2s, if owned. With-actives badge only.
Once the item actives lapse you continue at the out-of-combat (Basic) speed plus the decayed
Homeguard floor. Straight-line fountain → outer-turret distances (reference estimates):
- Top — ≈ 10,050 units
- Mid — ≈ 8,080 units
- Bot — ≈ 10,110 units
step Δt: x += speed(t)·Δt until x ≥ lane distance
speed(t) = softCap( (base + flat) × (1 + Σ%(t)) × mult(t) × R )
Σ%(t) = items + runes + Homeguard(t) + Wraith Step(t)
mult(t) = Quicksilver while active, else 1
Distances are straight-line estimates — real pathing runs a little longer. Because the
boosts fade, the badge time is noticeably higher than distance ÷ Peak speed. The lane follows the
selected role; Fill and Jungle have no single lane turret, so no badge is shown.
In-game MS is shown rounded. This analyzer does not model movement, so these figures
are reference only — they are not fed into the damage numbers.
