How these numbers are made

A player page makes two kinds of claim.

Both are worked out below, with the arithmetic shown.

It is the reference group behind the Distance from pool panel and behind every named leak.

It is built in five steps.

1. 1

   Cut the data to one game.

   Same currency, same stake, same table size — and the same room, wherever that room has enough players to stand on its own.

   NL2 and NL200 are not the same game and neither are two rooms: measured, pool VPIP at NL2 6-max differs by 6.3 points between rooms.

2. 2

   Drop anyone with under 500 hands in that game.

   A player seen for twelve hands has a VPIP of 0% or 50% or 100% and none of those describe them.

3. 3

   Work out each surviving player’s own percentage.

   From their counters — actions divided by opportunities.

4. 4

   Take the median of those percentages.

   One number per player, then the middle one.

5. 5

   Publish only if 30 players qualified.

   Below that the “typical player” is a handful of people.

The whole of it, in two lines:

Why the median, and not the average

Only the second is a description of the opponent you are likely to be sitting with, and poker populations always have a long loose tail to drag an average around.

Nine players at one stake, sorted by how often they enter a pot:

Illustrative figures, chosen to make the arithmetic followable — not a measurement.

Why one number per player, and not one big pile of hands

Lumping every hand together and dividing once would let a single grinder with 200,000 hands outvote three hundred casual players.

Each player gets one vote regardless of volume, because the question is what a typical person does, not what a typical hand looks like.

That choice is exactly what the next section has to undo, on purpose. The field →

The field is the reference group in What makes money here and on the radar. It is the same people as the pool, counted differently, and it exists to stop the site claiming something it cannot support.

The problem it solves

Winners play roughly twice the volume of a median player. High-volume players also behave differently from everyone else — tighter, more aggressive, fewer limps — whether or not they win. So “winners vs the pool” mixes two effects together, and mostly measures the wrong one.

Measured on a real segment: comparing winners to the raw pool reported them folding to 3-bets 8.4 points less than everyone else. Holding volume level, the real figure is 4.0 points. More than half of the “winning” effect was a regular-versus-everyone effect wearing its clothes.

How the reshaping works

1. 1

   Sort every qualifying player into a volume bucket.

   Doubling bands, so 1,024–2,047 hands is one bucket and 2,048–4,095 the next. Volume spans three orders of magnitude, and doubling bands keep the busy tail from collapsing into one lump.

   bucket(player) = floor( log₂( hands ) )
2. 2

   Give each player their bucket’s winner share.

   Not their own result — the share of that bucket which is made of winners.

   weight(player) = winners in their bucket / players in their bucket
3. 3

   Take the weighted median.

   The same median as the pool, with each player counting as much as their weight rather than once.

   field = weighted median of every qualifying player’s value

The field is the whole population, wearing the winners’ volume profile.

Worked through

A thousand qualifying players in three volume buckets. Everyone in a bucket shares a VPIP, to keep the sums visible:

Illustrative figures, chosen to make the arithmetic followable — not a measurement.

Same thousand people, same thousand values. Counting each of them once gives 28.0; counting them in the winners’ volume proportions gives 24.0. Neither is wrong — they answer different questions, and putting the second beside a winner median is the only one of the two that is a like-for-like comparison.

A second, smaller difference

The field also has a higher entry bar. A player needs 500 hands in the half of their hands used for measuring — about 1,000 overall — where the pool asks for 500 in total. (Why there are halves at all is the next section.) So the smallest-sample, loosest slice of the population is missing from the field before any weighting happens, and that pushes the same direction as the weighting does.

A winner is a player whose EV-adjusted win rate is positive in that game. Two details do the real work, and both exist because the obvious version of this panel was measurably wrong.

1. Luck is removed where it can be

Selection uses EV-adjusted winnings, not actual ones. If a player gets all-in with aces against kings and loses, the actual result says they lost the pot; the EV-adjusted result gives them the ~81% of it the cards said was theirs. All-in variance is the one chunk of luck that can be measured exactly, so it is not allowed to decide who counts as a winner.

2. Nobody is measured on the hands that got them picked

Each player’s hands are split in two by a hash of the hand id — effectively a coin flip per hand, independent of time, table, session and stake. Winners are chosen on one half and measured on the other.

Illustrative figures, chosen to make the arithmetic followable — not a measurement.

Without the split the panel flatters itself. Picking winners by money won and then reporting statistics made of money won counts the same good luck twice:

Measured. Selecting and measuring on the same hands put winners 2.9 points above the field on won-money-at-showdown. Split across separate halves, the gap collapsed to 0.4 — about seven-eighths of it was never skill. One statistic, won-when-saw-flop, changed direction outright. Published as-is, that panel would have told almost every ordinary player they had a showdown leak they did not have.

3. What “winning” is scoped to

• Per stake and room, not per situation.“Wins at NL50” is a property worth selecting on;“wins inside limped pots” is noise wearing the same word.Winner status is decided once for the game and applied to every pot type within it.
• 500 measured hands minimum — so a published winner row rests on the same evidence a pool row does.
• 30 winners minimum before a segment publishes at all.

Tested on a large sample at one stake, provably losing players sat about twice as far from the winner profile as provably winning ones — so the comparison carries real signal.

The gap between them is not an error. On a real NL25 full-ring segment, the same people counted two ways — with the casual, low-volume slice counted the way the winners’ own volume profile counts it:

That contrast is the fingerprint of the difference:regulars limp and cold-call far less, and raise about as often.

Both numbers exist for every statistic in every game, so which one a panel shows is a decision, not an accident. One rule decides it:

Distance from pool → the pool, unweighted

This panel asks a descriptive question: does this player differ from the people you will actually be sitting with?

Your next opponent is drawn from the population as it isa random person, not a random hand.

So the yardstick is one vote per player, with nothing weighted away — for two reasons.

1. 1

   It keeps the volume effect.

   If a 200,000-hand regular folds to 3-bets less than the pool, part of that gap is just that regulars differ from casual players. It is still true and still worth acting on — you should 3-bet that player less than you would a stranger. Matching it away would delete part of the answer.

2. 2

   And it keeps the unit intact.

   A named leak has to sit at least one interquartile range outside the pool — a distance measured in how much that statistic varies between players. That spread is a property of the same one-vote-per-player distribution the median comes from. Re-weight the population and you have changed the unit the distance is measured in, not merely the point it is measured from.

What makes money here → the field, volume-matched

This panel makes a far stronger kind of claim.

Not “these two groups differ” but“this difference is what winning looks like”— and the reader is expected to change how they play because of it.

1. 1

   Winners are not a random slice of the pool.

   They were selected, and selection correlates with volume: winners play about twice the hands of a median player. So winners and the pool differ in volume by construction, before a single statistic is compared.

2. 2

   So any gap carries two explanations at once.

3. 3

   So the volume effect is matched away.

   Here it is a rival explanation rather than part of the answer. The same effect is signal in one panel and noise in the other, because the two panels are claiming different things.

What swapping them would do

Two panels, two reference groups. The diagonal is what the site does; the other two cells are the only two ways to get it wrong.

Suppose a player c-bets the flop 38.7% where the field c-bets 60.3%. That is a gap of 21.6 points and it looks enormous.

Whether it means anything depends entirely on how many flops they actually c-bet into.

So every gap needs a companion number: how far the gap would move on chance alone. Below that, we grey it out.

The natural idea is: take a sample, compare it to the player’s converged value, and call the sample big enough once it lands within two standard deviations.

That test can never fail, because the window it checks against is built out of the sample size itself. For a proportion,

is defined so that about 95% of samples fall within two of them — at every sample size there is.

The bar has to be an absolute one, in the unit the chart plots: percentage points.

The textbook formula assumes every hand is an independent coin flip. They are not: the same session, the same table, the same opponents, the same mood.

The penalty grows with sample size

That is the opposite of intuitive and it is the crux. Measured against the formula, for VPIP:

Over 100 hands you are inside one sitting and the formula is nearly right. Over 20,000 you have accumulated many sessions of correlated behaviour, so the error falls more slowly than 1/√n and the gap widens. Large samples are less trustworthy than the formula claims; small samples are about as bad as it already says.

How steep it is depends on the statistic

A statistic a player sets once and holds compounds; one the cards decide for them does not.

What a block of hands is compared against decides what gets measured.

The difference is not small.

Score each block against the player’s lifetime average instead of its neighbour and the error stops falling: VPIP went from ±2.76 to ±2.58 points between 10,000 and 20,000 hands, where pure sampling predicts an improvement of √2.

That floor is not noise. These accounts span years, and players change — they move stakes, adjust, get better or worse. What is left is a floor:

So there is no fixed value to converge on: the target moves while you are measuring it. That is why the experiment scores each block against its neighbour and never against a lifetime average.

Two rows of the radar readout, with the winners column dropped. Illustrative figures — but each ± is the formula below run on the n beside it. The second gap is smaller than its own margin, so it is shown in amber.

How to read it

Every stat on a player page shows a gap: the player’s number minus the field’s number. The ± next to it answers one question:

If this player were actually just an average member of the field, how far from the field’s number could their observed rate land — on luck alone — 95% of the time?

If the gap they actually have is bigger than that, luck doesn’t explain it.

How it is computed

There is no fixed threshold per statistic — partly because a threshold cannot express the gap, and partly because it could not be written honestly: seven of the fifteen statistics never reached ±2 points even at the largest samples measured, so half the table would have been invented.

Instead each number carries its own margin:

That last term is why which statistic you are looking at changes the answer:

Note the crossover. At 200 opportunities fold-vs-c-bet is the least reliable of the three; it overtakes VPIP between 500 and 2,500, and by 10,000 it has drawn level with PFR. VPIP is a setting a player holds for a whole session, so its correlation compounds as the sample grows. Fold-vs-c-bet turns on the cards, so it stays close to independent and its margin keeps falling at nearly the textbook rate.

Real numbers from a live profile, arithmetic shown. Each one runs the formula above and holds the answer against the gap.

Example 3 has one fortieth of example 2’s sample and clears its margin, where example 2 does not clear its own. Neither the gap nor the sample size decides it alone; only the two against each other.

1. A high-volume player’s VPIP — comfortably real

2. The same statistic on 2,000 hands — not evidence

3. A big gap on a tiny sample — real

• Measured on PokerStars only. The constants come from one room. Other rooms have different game structures, and the correlation between hands may differ with them.
• Fitted between 100 and 20,000 opportunities. Beyond that the inflation is extrapolated — for a player with 600,000 opportunities the model predicts 4.17×, which is past anything measured. It errs toward caution, and the margins there are tiny either way.
• It is about precision, not truth. A gap clearing its margin means the hands are unlikely to have produced it by chance. It does not mean the player is still playing that way — see the drift finding above.
• The leak panel uses a different, stricter gate. A named leak must clear both one interquartile range of the player pool and two standard errors, on at least 30 observations. That gate operates at sample sizes where this inflation is only 1.05–1.25×, so it was checked against these findings and left unchanged.

Convergence measured 2026-08-05 on 40 PokerStars accounts, ~4 million hands. Pool, field and winner baselines are rebuilt nightly from the full fact table. See also the statistics guide for what each individual number means.