Round numbers in the order book: quotes cluster, orders do not

Two claims get repeated about round numbers. The first is that price behaves differently near them. The second is that big orders sit on them, forming the walls people point at in a depth ladder. The second claim is checkable without any theory about psychology, because a resting order is a thing you can count. We counted, on 5,295,902 recorded seconds of quotes.

1. Where quotes actually sit

Every price ends in a digit. If quotes landed anywhere with equal probability, each of the ten cent endings would appear on about 10% of seconds. They do not. A zero ending is 1.42 times more common than chance and 1.71 times more common than a three, which is the rarest ending. Endings in zero and five together took 25.08% of seconds against the 20% a uniform distribution would give. The offer side agrees: it ended in a zero on 15.31% of seconds. Whole dollars are rarer but also crowded. A bid landed exactly on a whole dollar on 1.90% of seconds, against the 1% chance would give, and an offer on 2.29%.

2. It holds on every session

Pooled numbers can hide a handful of days doing all the work, so we measured each session on its own. Every session in the sample showed it. This is about as robust as a result gets in market data, and it should be, because it is not a claim about behaviour under stress. It is a claim about how humans and the algorithms they wrote choose numbers.

3. The effect grows with the price of the stock

On a cheap stock the clustering nearly vanishes. On a $2 stock one cent is fifty basis points, so a cent is a real decision and quotes use every one of them. On a $100 stock a cent is one basis point, so the tick stops being a meaningful unit and quoting coarsens onto rounder numbers. That is the whole mechanism, and it needs no reference to psychology. Clustering is what happens when the tick is small relative to what anybody cares about.

4. The wall that is not there

Now the second claim. If round prices attract large resting orders, the money at a zero-ending price should be larger than at other endings. We compared the median dollars resting at the touch, inside each price bucket so that expensive stocks cannot skew the comparison, on both sides of the book. Five of the eight comparisons are above one and three are below, spanning 0.42 to 2.33. In the $20 to $100 bucket both sides show less money at round prices, and in the $1 to $5 bucket both show more. The two sides of the same bucket disagree in the middle. There is no consistent effect here. Whatever a wall on a depth ladder is, our recordings do not show round prices systematically holding more resting money than their neighbours.

5. Why we do not report an average here

Our first pass used averages and produced a tidy-looking answer: less money at round prices, by a clear margin. It was an artefact. A handful of enormous quotes drag a mean anywhere they like, and zero endings are more common on expensive stocks, which carry more dollars at the touch for reasons that have nothing to do with rounding. Controlling for the price bucket removed the composition problem. Switching from means to medians removed the tail problem. What survived both is the scatter in section 4, which is the honest answer: no effect we can measure. We are describing the wrong turn because the tidy version is the one that would have made the better article, and a reader has no way to tell which one they are being handed.

6. What this is good for

Do not read a round price as a queue you are joining at the back of. It is a price the quote visits more often, not a price with more money parked on it. Expect coarser quoting as the price rises. Above $20 nearly one bid in five sits on a zero, and above $100 nearly one in four. If you place limit orders on those names, your one-cent improvements are competing against a habit rather than against depth. Do not extend this to price behaviour. We measured where quotes sit and how much size is on them. Whether price stalls or turns near round numbers is a different question, and this study does not touch it.

7. What this does not measure

We see the displayed book only. Hidden and undisplayed orders are invisible to us, and if round prices attract hidden size we would not know. We measure the top of book, not the ladder behind it. A wall two cents away from the touch does not appear in these numbers. The universe is the stocks our own scan surfaced each day, the day's active movers rather than a cross-section of the market. Quiet large caps may cluster differently.

8. Sample accounting

The sample is 38 sessions drawn evenly from 264 recorded sessions between 2025-04-02 and 2026-07-27, giving 700 symbol-days and 5,295,902 quoted seconds inside the regular session. Stocks priced under $1 are excluded because their tick is a hundredth of a cent, so a cent ending does not mean the same thing. Seconds were used only where both sides of the quote were present with positive size. Size figures are medians rather than means, and are compared within price buckets. Digit shares are plain counts of seconds, so a stock that quotes at one price for an hour contributes that price for every second it stands, which is the correct weighting for the question of where a quote you look at is likely to be sitting. We did not measure returns. Nothing here says whether anything is worth trading.