How the numbers are made

A row is ranked once its win rate is known to within 10 points either way.

What this measures

Every battle, kept: Battles come from the official PvP feed every few minutes. Nothing is deleted as it ages, so the archive runs from February 2026 to today and keeps growing. That is what lets the same history be sliced by patch. The feed is caught up, so a battle reaches the site within minutes of being fought.
Where the data comes from: Every battle, profile and catalog entry comes from the official Polandball Go API, read with the developers' permission. Nothing is scraped or estimated from outside it.
Two separate leagues: Open and Rarity are different competitions with their own standings, and a battle belongs to exactly one. Tier names are shared between them, so Crystal in Open and Crystal in Rarity are different populations. The league switch is the first control on every page that has one.

Win rates

Attacking and defending are counted apart: A single blended win rate would mostly measure how often something gets played on offense, so every aggregate keeps the two sides separate and reports both.
Side-adjusted is the mean of the two: Tables rank on this figure, and it is what Overall means on the tier list. It is an unweighted mean: a typing with 400 attacking and 20 defending appearances has its defensive rate counted equally. Whether that is right, or whether the two sides should be pooled by volume, is still an open question. It will be revisited when battle-time snapshots become available.
Ranked on the 95% Wilson lower bound: Ranking on the raw rate hands the top of every table to the thinnest sample: 75% over 43 games would outrank 58% over 1,136. Tables sort on the lower bound of the confidence interval and display the raw rate. The order then shows what is reliably good, and the number on screen is still the real one.
A row ranks once its result is known: There is no fixed game count. A flat threshold treats fifty coin-flip games and fifty one-sided ones as equally trustworthy, and they are not: the first pins the true rate no better than 36-64%, the second to within a few points. An entry ranks once its 95% interval is inside 10 points either way, however many games that took. Entries seen on only one side of the fight never rank. Everything else is shown below the rest, grayed out.

Tier lists

A ball's primary type is part of its ranking: For dual-typed balls, Fire/Water and Water/Fire are separate entries. The primary type receives an additional damage bonus, so averaging the two orientations would hide a real build difference.
Bands are cut from the distribution: Each band is a distance from the list's own average, in standard deviations. S starts 1.5 above the average, A at 0.75 and B at 0.25. C runs down to 0.25 below, D to 1 below, and F is under that. Fixed win-rate thresholds go stale the moment the game is patched, so the bands move each time the stats update. The distribution and its cuts are on the tier list page, folded shut.
High elo means Crystal and above: It covers players in Crystal, Aurora and Ethereal. A literal top 5% would fall inside Diamond, and slicing a division in half is unstable: division I promotes and division IV demotes every week.
Thin tiers say so: Under 200 battles a tier's table cannot carry weight on its own; under 1,000 its rankings will move noticeably between updates. Both are flagged on the page.

Ball owners

CP decides: The owner ranking is not a weighted blend. A higher CP outranks a lower one, even by a single point, whatever else the other owner is carrying.
Same CP goes to the item, then the win rate: Copies with exactly the same CP are separated by item, higher tier first, then by win rate, then barely by games played.
A win rate counts for more in a higher league: Seventy percent in Bronze and seventy percent in Ethereal are not the same claim, so the Ethereal one carries seven times the weight. A win rate needs ten games before it counts at all.

Raid luck (Luckiest and Unluckiest Players)

The question: Given every raid a player was in, did they get more items, or fewer, than the measured drop chances say they should have? Each time a Mymic is defeated, every member of the party gets one chance at each item it drops. Who lands the last hit does not matter.
The drop chance per kill: For each Mymic, star level and item, the chance per kill p is the maximum-likelihood estimate from all recorded raids. A raid in which the Mymic was defeated k times holds the item with probability 1 − (1 − p)^k, and p is the value that makes the observed raids most likely (the log-likelihood is concave in p, solved by golden-section search). A rate is used only once it rests on at least 100 raids and 5 drops. Items two defeated Mymics both drop in the same raid are left out of that raid, since the drop cannot be credited to either one.
Each raid is measured against its own patch: A game update can change a drop chance, so p is also estimated from each patch's raids alone, and every raid is compared with the p of the patch it was played in. Where that patch's raids fall short of the 100-raid and 5-drop bar for an item, the raid uses p from all patches together, and its margin (below) also carries how far chances move between patches: a relative variance τ² on ln p, estimated across every item measured in two or more patches (a DerSimonian–Laird method-of-moments estimate). Raids before October 1 are compared with their own patch's drop share instead (below).
Your own raids are taken out of the rate: A heavy raider must not be measured against a rate they built. Before scoring a player, their own raids are removed from every rate (a leave-one-out estimate). Where little is left without them, that item is not scored for them.
Raids before October 1: Raids from September 18 to October 1 record which Mymics were defeated but not how many times. For those, the chance that the raid held the item is the share of fully recorded raids of their own patch, at the same Mymic and star level, that held it, with the player's own raids taken out. That is the average of 1 − (1 − p)^k over the real spread of kill counts, measured rather than assumed. Where that patch has too few raids, the share of later raids with recorded kill counts is used. Raids before September 18 are not used: until then a raid was often stored only when a player looked up their own history, which favors the raids that paid.
The expected number and its spread: Each (raid, item) pair is one trial: the item came (X = 1) or did not (X = 0), with chance q from the steps above. Quantity does not count: two of an item in one raid is one success. Trials are treated as independent given their kill counts and the true drop chances. The expected count is E = Σ q and, if the chances were known exactly, its variance would be Σ q(1 − q): a Poisson-binomial distribution, because every trial has its own chance.
Rarer tiers count for more: Each item is weighted by its tier, w = 2^(tier − 1): ✦ 1, ✦✦ 2, ✦✦✦ 4, ✦✦✦✦ 8, ✦✦✦✦✦ 16. The score uses the weighted sum S = Σ w·X, with mean Σ w·q and variance Σ w²·q(1 − q). An item's rarity is already in its chance q, so a 1-in-200 drop adds little to the expected total and moves the score a lot when it comes. The weight adds how much the game values it.
The drop chances are estimates too: Each p rests on a finite number of raids, so it has a standard error, from the Fisher information of the same likelihood: SE(p) = 1/√I(p), I(p) = Σ k²(1 − p)^(k − 2) / (1 − (1 − p)^k) over the raids behind it. An item measured from a handful of drops has a wide margin; one measured from thousands, almost none. This carries into each trial's chance by the delta method, ∂q/∂p = k(1 − p)^(k − 1). All of a player's trials of one Mymic, star level and item share one estimate, so its error moves them together: their margins add before squaring, V_rate = Σ over items (Σ w·∂q/∂p)²·SE(p)², not as independent terms. A patch's own estimate and the all-patch one share raids, and are combined with their correlation SE(all)/SE(patch). The spread used is √(Σ w²·q(1 − q) + V_rate).
The test: The exact distribution of S is computed by dynamic programming over the possible sums, one trial at a time, with no normal approximation. The player's observed total O is compared with it using the mid-p tail probability P(S < O) + ½·P(S = O), which corrects for S taking whole-number values. The drop chances' own margin is then added as a normal error ε with variance V_rate, independent of S: the tail becomes Σ_s P(S = s)·Φ((O − s)/√V_rate), which is the mid-p tail exactly when V_rate = 0. That probability is turned into standard deviations with the inverse normal distribution, z = Φ⁻¹(mid-p), so ±1.5 and ±2 keep their usual meaning as tail chances even when the distribution is skewed. A record measured against thinly measured items moves less far from 0 than one measured against well-measured items with the same gap.
Badges and the boards: Lucky starts at z = 1.5 and Extremely lucky at 2; Unlucky at −1.5 and Very unlucky at −2. Between them: Above average from 0.5, Below average from −0.5, and Average luck from −0.5 to 0.5. A player needs at least 60 raids since September 18 and at least 10 expected items (counted without weights) before any rating or badge, so one rare item cannot carry a small record. Each board lists everyone past ±1.5 SD on its side: Luckiest at z = 1.5 or higher, Unluckiest at −1.5 or lower. When fewer are past it, Luckiest still shows its top 10 above 0 and Unluckiest its top 25 below 0. Each board ranks by z, then by weighted points above or below expected. With hundreds of players scored, a few will sit past ±2 by chance alone (about 2.3% on each side), so a badge says the record is unusual, not that anything is wrong.
What it does not cover: Clear rewards and crafting materials are not scored, only items with a measured rate. Raids past the daily reward limit, raids an admin left out, and duplicate copies of a raid are excluded. Players with sharing off keep their place but show as Anonymous.

What the numbers cannot do

Builds are battle-time only for recent battles: Since 23–24 September 2026 the game records each ball's level, CP, orb upgrades, skin and item as they were when the battle was fought. Older battles carry the build from the owner's roster at the moment we read them: usually within the hour for the live feed, but much later for older battles filled in afterward. The stats include both, so an item swapped since an older battle is still credited to that fight.
Incomplete lineups are left out: A battle is five against five. A side missing a ball loses about twenty points of win rate, and that would count unfairly against the balls that were there. Those battles are left out of the stats. They still show on player pages.
Raid history depends on what has been imported: Opening a profile pulls that player's latest raids from the game, and a global feed of recent raids fills in the rest over time. Only raids that were won are recorded, so raid numbers are clears, not attempts. A boss's first clear is the earliest one on record, not necessarily the first ever.