How the HotS numbers work

1. Where the numbers come from

Statistics need match data. Heroes of the Storm publishes none, and Whetstone builds only on data it owns or that is openly licensed, plus its own analysis. So Heroes of the Storm pages show theory: matchups derived from ability and talent text plus hand-written notes. The statistics rules below stay ready for a match-data source that meets that bar; any page that shows its numbers credits it right next to them. Theory is always labelled as theory and never mixed into a statistic.

Every number on a page shows how many games (n) it rests on and where it came from.

2. Confidence ranges (Wilson interval)

A win rate from a few games is unreliable: 3 wins out of 4 is “75%”, but the truth could easily be 40%. Wherever we show a range, we use the Wilson score interval at 95% confidence (z = 1.96). It behaves sensibly for small samples and never leaves 0–100%.

For k wins in n games, with p = k / n:

• centre = (p + z²/2n) / (1 + z²/n)
• half-width = z · √(p(1 − p)/n + z²/4n²) / (1 + z²/n)

3. Hero win rates: shrinkage

A hero with 30 wins in 50 games (60%) is almost certainly not the best hero in the game. Most of that 60% is luck. We therefore shrink every hero’s win rate toward the average. Heroes with few games move a lot, and heroes with thousands of games barely move.

This is called empirical-Bayes shrinkage. It works in three steps:

1. Average (μ): all wins divided by all games (about 50%).
2. Real spread (τ²): how much heroes truly differ. We take the observed spread between heroes with at least 50 games and subtract the spread that luck alone would cause (μ(1 − μ)/n for each hero).
3. Strength of the pull (κ): κ = μ(1 − μ)/τ² − 1, measured in “pseudo-games”. When heroes truly differ a lot, κ is small and we trust each hero’s own record. When they barely differ, κ is large.

Each hero’s shrunk win rate is then (wins + κ·μ) / (games + κ).

Example, with κ = 400:

Patch-aware starting point. Early in a patch there are few games. A hero whose kit did not change in the patch starts from its own shrunk win rate last patch instead of the average, at half the pull (κ/2). A hero that changed starts from the average. The first days of a patch are therefore steadier without hiding real changes.

Guards. If there is no data, or the data shows no real spread beyond luck, κ falls back to a large value (everyone close to the average). It never becomes infinite or negative.

4. Counters and synergies

4.1 Why not “win rate against X minus win rate”?

The naive counter number, “A’s win rate against B minus A’s overall win rate”, hides a trap. A hero that is simply strong looks like it “counters” everyone. A weak hero looks like it loses to everything. We want the part of the matchup that is specific to the pair.

4.2 The expected result

We first ask what A should win against B if neither had any special interaction, using both heroes’ shrunk win rates (p̃A, p̃B). We treat a team’s chance as the sum of its heroes’ strengths on the log-odds scale:

• Counter (A against B): expected = σ(logit p̃A − logit p̃B)
• Synergy (A with B on the same team): expected = σ(logit p̃A + logit p̃B)

Here logit(p) = ln(p / (1 − p)) and σ is its inverse. Close to 50%, the counter expectation is roughly p̃A − p̃B + 50%. A 53% hero facing a 49% hero is expected to win about 54%.

4.3 Shrinking toward the expectation

Pair samples are much smaller than hero samples, so we shrink again. This time the pull is toward the expected result, not toward 50%:

• shrunk = (wins + k · expected) / (games + k)
• Δ = shrunk − expected, in pp. A positive Δ means A does better against (or with) B than their strengths predict.

The pull k is estimated from the data the same way as κ. It uses the spread of observed minus expected over pairs with at least 30 games, beyond what luck explains. It is kept between 25 and 2,000. Each pair also gets a z-score, (wins − games · expected) / √(games · expected · (1 − expected)). This measures how surprising the raw result is, before shrinking.

Example, expected 52%, k = 500:

The same raw 60% means little after 100 games and a lot after 1,000.

4.4 Consistency

• Counters are two-sided. If A gains Δ against B, then B must lose Δ against A. We average the two directions: Δ(A,B) = (Δ(A,B) − Δ(B,A)) / 2. This removes small mismatches between the two ways the data is recorded.
• Synergy is symmetric. “A with B” and “B with A” describe the same games, so we average them and store the pair once.

Each statistic carries one reason line, for example: “Wins 54.1% vs Muradin (expected 50.9%), n=812”. The 54.1% is the raw rate. Δ, shown next to it, is the shrunk effect.

5. The 1–100 score ring

Matchup rings use a 1–100 score with 50 as neutral:

score = round(50 + 50 · tanh(Δ / 4 pp)), clamped to 1–100.

This is the same as tanh(Δ / 0.04) when Δ is written as a proportion.

We always show Δ in pp and n next to the ring, because the ring alone hides how much data backs it.

6. What gets shown: sample-size gates

When no pair passes, the page says there is no reliable data yet and shows the theory notes.

An optional extra gate, |z| ≥ 2.5, is available (see §7). It is off by default.

7. Calibration: does this actually work?

The thresholds above were first chosen by judgement. We check them with a simulation that runs on every test run (src/core/stats.sim.test.ts):

• 90 synthetic heroes with known strengths and popularity.
• A known, sparse set of real counter relationships.
• 5v5 games simulated at two volumes over a 30-day patch window: about 330 Storm League games a day (the low public estimate) and about 3,000 a day (the high estimate).
• The exact pipeline above runs on the simulated games, and we count what a hero page would list.

What we found:

• Hero win rates. At 330 games a day, shrunk win rates are about 1.4 pp from the truth on average, closer than raw rates. At 3,000 a day they are about 0.6 pp away.
• Low volume. The gates list essentially nothing: well under one false counter per hero page, and almost no true ones either. At this volume Whetstone honestly says “not enough data” and leans on theory.
• High volume, effects like those reported for real counters (a few pp, in a few percent of pairs). False counters stay well under one per page. Roughly half to three-quarters of the large effects (6 pp or more) on pairs with 400+ games are found.
• High volume, stronger and denser effects. Shrinkage is weaker here, and the default gates can list 1–5 false counters per page. Adding the |z| ≥ 2.5 gate brings this back under one per page while keeping most large effects. We will switch that gate on if measured data looks like this case.

Once real data exists, we will also check the gates against a held-out patch.

8. Tier lists

Tiers use fixed bands, not “top 10%”. A hero keeps its tier when other heroes move, so the list does not reshuffle every day.

Heroes of the Storm: the band is set by shrunk win rate minus 50%, in pp.

• Heroes with fewer than 200 games are marked early data instead of getting a tier.
• Each hero shows its change since the previous patch (up, down or same) and the win-rate difference in pp.
• An optional ban-rate nudge adds 0.1 × (ban rate − average ban rate) to the win rate before banding, for games where bans signal strength. It is off by default.

9. Community votes (if they ever exist)

If Whetstone ever collects votes, a vote score will be round(100 × Wilson lower bound) of up-votes out of all votes, at z = 1.96. This is the formula heroescounters.com used, and we matched it on 27,700 of 27,700 rows. Rows whose raw lower bound is below 0.30 go behind “View more”.

The formula rewards certainty. A 4–0 matchup scores only 51.

10. Draft suggestions

The draft tool scores every hero you could pick or ban right now.

1. Signals. Each kind of evidence produces signals:

   • win rate, counters against the enemy’s picks, synergy with your picks, map fit and tier;
   • theory, votes, role needs, and your personal hero pool.

   Each signal has a value on one shared scale, where 1.0 ≈ a 4 pp edge: Δ / 4 pp for statistics, or the inverse of the ring formula for 1–100 scores. A signal also carries the reason that explains it. Counters and synergies use statistics when they exist, and otherwise theory, labelled as theory.

2. Weights. A sort mode is just a set of weights:

   Mode	Weights
   Composite (default)	win rate 1 · counters 1 · synergy 0.8 · map 0.6 · tier 0.3 · theory 0.5 · votes 0.5 · role 1 · pool 0.5
   Win rate	win rate 1
   Counters	counters 1
   Synergies	synergy 1
   Map	map 1
   Tier	tier 1
   Community	votes 1 (only when votes exist)

3. One key cannot drown the rest. Many small edges of one kind (five enemies each countered a little) used to add up to 2–3 and outweigh the role guardrails. So all signals of one key from one provider are soft-capped together: their sum becomes KEY_CAP · tanh(sum / KEY_CAP) with KEY_CAP = 1.0 (about a 4 pp edge), shared out in proportion, so every reason keeps its share and its sign.

4. Score. Total = Σ weight × value. The displayed score is round(50 + 50 · tanh(total)), on a 0–100 scale.

5. Why and watch-out.

   • Up to three reasons are shown, from the largest positive contributions. A theory edge shows its headline line only (curated first); its other lines stay in the breakdown, and lines from the same rule (ignoring the evidence in brackets) count once across edges.
   • Statistics are worded as a verdict (“Beats your Valla”, “Struggles against”, “Works well with”, “Does well on”) only when they pass the list gate of §6 (n ≥ 50 and |Δ| ≥ 1.5 pp). Below it the line is neutral (“+0.5 pp against your Valla: too small to call”), stays in the breakdown and keeps its small value.
   • A reason that depends on a talent or a situation says so: “Only when …”, each condition once.
   • At most one warning is shown: the most negative contribution, if it is worth more than about 0.4 pp.

6. Ties. Heroes are sorted by total, then by the uncapped evidence behind it (for bans, the summed strength of every counter), then by name. When the top three or more shown scores lie within 2 points, the list says it is a shortlist, not an order.

Bans. A ban step ranks heroes by how much they would hurt your team:

• Breadth: 0.45 · (1 − e^(−S / 12)) · min(1, picks the other side has left ÷ 5), where S sums the strength of every hard counter the hero has among the heroes the other side can still pick. Smooth and never flat, so a hero that counters 26 heroes outranks one that counters 6. The reason names the hardest-countered heroes first.
• Pro bans (theory mode only, when there are no match statistics): the share of pro maps that banned the hero, shrunk toward the average ban rate with 20 pseudo-maps, adds (shrunk − average) × 3 on the tier key. It is credited to Liquipedia (CC BY-SA 3.0) where it is shown.

Rules the draft respects:

• The verified Storm League order with first-pick toggle: 3 bans per team, split 2 + 1.
• No hero on both teams, and no picking a banned hero.
• Cho’gall takes two consecutive picks of the same team and is only offered at those steps.
• Free mode places heroes on either team in any order. It can also list suggestions for the other team; adding one of those heroes puts it on that team and keeps your own target.

Role needs (src/games/hots/draft/roles.ts). A team should end with a Healer and a frontline hero (Tank or Bruiser, main or flex role). Only a short curated list of non-Healers can stand in for the Healer: Medivh and Zarya (their shields and saves carry a team through fights). The Lost Vikings and Abathur never count.

• A pick that leaves fewer pick slots than unmet needs gets a large penalty and a warning (“No Healer”).
• A pick that fills an open need gets a bonus: 0.2 + 0.3 to 0.4 × urgency, where urgency is open needs ÷ picks left. In Storm League urgency starts at 0, because your team’s later picks are planned. A need nobody available can fill any more is dropped and mentioned once.
• Smaller penalties, each with its reason: a second main-role Tank, a second (or third) Healer, a second Support, a third Melee Assassin, a fourth melee hero, a finished team without ranged damage. On a team’s last two picks these grow × 1.75 (× 1.25 in ARAM): the composition is all but decided, so a second Healer costs 0.79 instead of 0.45.
• Last-pick guardrails: a finished team with no waveclear, or with at most one hero with hard crowd control (stun, root, polymorph, sleep, taunt, fear, time-stop), gets a 0.2 penalty (0.15 in ARAM), but only when someone still available could close the gap. The warning names the heroes and tags behind it (“only Muradin (stun)”).

Draft review. When the draft is complete (all 16 Storm League steps, or both teams full in free mode) a review card shows the three strongest matchups in each direction (each net of the edge back, edges below 0.1 left out), the best synergy pair of each team, each team’s best and weakest map fit and the role verdict, with the same evidence bar as hero pages: statistics that pass the list gate when statistics are in use, theory otherwise. A copy button gives a plain-text summary for Discord, with the share link and the credits of the data it used.

ARAM helper. You choose one of the three heroes you are offered, so there is no draft order. The same role needs apply with gentler penalties, with one difference: a gap you can fill counts fully (urgency never below 1), because your teammates still to lock get random options of their own and may not be able to fill it. ARAM rankings use theory and ARAM statistics only, never Storm League numbers.

11. Theory scores and what a hero page lists

Without match statistics, matchups come from the theory layer (docs/THEORY.md): rules about what kits do to each other, plus matchups that curators wrote and checked against the current kit text. Theory scores use the same 1–100 ring, but they measure how hard one kit punishes another, not how often a matchup is won.

One list per opponent. Both heroes of a pair can have tools against each other, so the data holds two directed scores. A hero page nets them the way the draft tool does: value(you → them) − value(them → you), where value is the inverse of the ring formula (§10). The opponent appears under “strong against” if the net is positive and under “weak against” if it is negative, never under both, with the net as its score. Its reasons show both sides, the winning side first.

Within a list, curated matchups come first, then generic ones, each by score. A reason that only holds when a hero takes a certain talent or Heroic says so, naming every pick that works (“Only when Anduin takes Lightbomb or Censure”); a hand-written matchup that depends on a talent, a Heroic or a situation carries the same “Only when …” line, and is rated low confidence when the whole effect rests on that one choice. A rule that applies both ways round (both heroes blind, both rely on Basic Attacks) is a wash and only counts by how much more it favours one side. The draft tool uses every stored theory edge, weighted by its score.

Map fit. A hero page’s “Best maps” lists only maps scoring above 50. Maps whose layout or objective works against the kit (below 50) are listed separately as “Harder maps”, hardest first. Map pages split their hero lists the same way.

12. Freshness

Every page shows how old its data is. The data job runs once a day.

A source whose latest fetch failed keeps showing its last good data. It is labelled as such and is never called “fresh”. Disabled sources (for example an optional source the site owner has not switched on) are listed as disabled, not broken.

13. Known biases

• Who uploads replays. Uploaders skew toward engaged, higher-rated players, and some regions (notably China) are barely present.
• Rank. League bands come from the data provider’s own rating, not Blizzard’s rank.
• Parties. Storm League includes party games, and coordinated groups win more.
• Quick Match can contain mirror matches. We exclude them where the source allows.
• ARAM. Each player chooses from a small random set, so an ARAM win rate means something different from a draft win rate.
• Patches. We use whole-patch windows. For the first 14 days of a patch the previous patch’s data is blended in at half weight, and the page says so.

None of these numbers predict a single game. They describe tendencies over many games.