The Order Book Is Theater

The same eye reading the same screen is worth 2.6 points of win rate on one instrument and 10.9 on another, and nothing about the reader changed between those two figures. The size of the wall never enters the arithmetic at all: ten thousand shares and forty thousand give the same answer, because the two quantities that decide it are both invisible and neither of them is on the screen.

Prerequisites: Lesson 25, which established that the orders that matter most are the ones nobody can see, and lesson 17, because everything a signal is worth has to be cashed out as a movement in p.

What a read of the book is worth, priced

Two quantities decide it, and only two. The first is the fraction of large orders at a level that are still there when price gets there and hold when tested — call it the base rate, and note immediately that it is a property of the instrument and the hour, not of the reader. The second is how good your read is: of the walls that turn out to be real, how many you call real, and of the walls that turn out not to be, how many you call fake. Write a read as a pair, so 80/80 means eighty per cent right on each.

Then the question “you looked at this wall and called it real — what is the chance it is?” has one answer, and it is arithmetic rather than opinion:

Walls that hold	Read 50/50	Read 70/70	Read 80/80	Read 90/90
5 in 100	5.0%	10.9%	17.4%	32.1%
10 in 100	10.0%	20.6%	30.8%	50.0%
15 in 100	15.0%	29.2%	41.4%	61.4%
25 in 100	25.0%	43.8%	57.1%	75.0%
40 in 100	40.0%	60.9%	72.7%	85.7%

Read the first column first, because it is the one that is not an estimate. A 50/50 read is a read with no skill in it — you are right as often as a coin, both ways — and the column returns the base rate exactly, on every row. That is not a coincidence and not an artefact of the numbers chosen. It is the identity the whole table is built on: a signal that discriminates nothing leaves you exactly where you started, which here means holding the market’s own frequency and mistaking it for a judgement.

Now the columns, which behave more simply than the table makes them look. Written in odds rather than percentages, every column is a single multiplier: a 70/70 read multiplies your odds by 2.33, an 80/80 read multiplies them by 4, a 90/90 read multiplies them by 9, and the coin multiplies them by 1. That is the whole content of a read. It scales the number you already had.

That settles what a good eye can and cannot do, without depending on which rows this table happens to contain. Skill is a multiplier and the base rate is what gets multiplied, so the same eyes are worth what the instrument lets them be worth. Four times a small number is a small number, and no amount of looking harder changes which number you are looking at.

Cash it out in the only currency lesson 17 accepts. Suppose a wall that does hold is worth fifteen points of win rate to you — it turns a 45 per cent setup into a 60 per cent one, which is a generous assumption, and the bounds below say what happens when it is wrong. What you actually get is not fifteen points. It is fifteen points multiplied by the chance the wall is real, and with an 80/80 read that comes to 2.6 points on an instrument where 5 in 100 walls hold, 6.2 points where 15 in 100 hold, and 10.9 points where 40 in 100 do. Same eyes, same screen, same skill, and the last is worth more than four times the first.

And here is the part worth sitting with. Look back over all of the arithmetic above and find where the size of the wall entered. It did not. Ten thousand shares and forty thousand shares give the same answer, because size is not one of the two inputs. The number the screen puts in front of you, in large type, refreshing every tick, is not in the calculation at all — and the two numbers that are in the calculation are both invisible, both properties of a distribution rather than of this wall, and both things you can only get by keeping a record.

What this does not settle

That fifteen points is what a real wall is worth. Nothing here establishes that figure; it was chosen to be generous, so that the conclusion would not depend on being pessimistic. The structure of the result does not depend on it either, because the fifteen enters as a multiplier: halve it and every number in the last paragraph halves, and the ratio between the instruments — the comparison the paragraph turns on — does not move at all. What you actually need is your own figure, and problem 3 is where it comes from.

That anybody reads at 80/80. That column is in the table because it is flattering, not because anything establishes it. And a read scored after the fact is not a read at all: to claim 80/80 you have to write down real or fake before the test, thirty times, and count. Nothing in this lesson can tell you which column you are in, and until problem 2 has been done the column you are entitled to assume is the first one.

That the read is independent of the size. The table assumes your accuracy is the same whether the order is large or small, and that is unlikely to be true. It could go either way — a very large order may be harder to fake and so easier to call, or it may be exactly the size somebody chooses when they want to be seen — and which way it goes changes the columns for large walls specifically. This is measurable in the same record that problem 2 builds, by splitting it by size.

That a wall which held once will hold again. The test tells you about the test. Whether the order behind it is still there, whether it was fully consumed, and whether the participant intends to keep defending are three further questions, and the mechanics of reading them from what happens during the test are lesson 28’s subject rather than this one’s.

That the error only runs one way. This lesson has been about the book showing size that is not there. It also, routinely, does not show size that is: an order can be displayed in a fraction of its true quantity, and then the screen understates rather than overstates. The arithmetic above says nothing about that case and would give the wrong answer if applied to it, which is why lesson 31 handles it separately.

That any of this is about deliberate deception. It is not, and the distinction matters as much as it did in lesson 25. Everything above holds if every participant is acting in good faith and simply changing their mind, which in a market where orders are routinely cancelled within seconds is the ordinary case rather than a suspicious one. Placing orders with no intention of filling them is a separate thing, it is an offence, and it is lesson 27’s subject.

The book is not lying to you. It is answering a question you did not ask — how much size is offered here — in place of the one you did, which is whether any of it will still be offered when you arrive.

Problems

1. Find your base rate. On one instrument, log thirty large resting orders — large meaning several times the ordinary size at a price, judged the same way each time. Each one ends in exactly one of three columns: withdrawn before price reached it, reached and broken, or reached and held. The third column over the total is your base rate, and it is the row of the table you are actually on. Log every wall that met your size threshold, not the ones that did something memorable; a record of interesting walls measures your memory rather than the book. Expect the answer to differ by instrument and by hour, which is the finding rather than a flaw in it.
2. Score your read, before the fact. Run problem 1 again, or better, run it once and keep both records at the same time: for each wall write down “real” or “fake” before price gets to it. That gives you a two-by-two: of the walls that held, the share you called real; of the walls that did not, the share you called fake. Those two numbers are your column, and until you have them the first column is the one you are entitled to. Note that the count costs nothing but attention: no position is taken, so a month of being wrong on paper is free in a way that a month of being wrong in the market is not.
3. Price your own wall. From your record, compare the win rate of the trades you took where a wall held against your overall win rate from lesson 17. The difference is your own figure for what a real wall is worth — the fifteen points in the worked example, replaced by yours. Multiply it by your posterior from problem 2, and multiply that by (b + 1) from lesson 17 to get the answer in R. Compare it against s from lesson 10, which is already in the same units. If the wall is worth less than the round trip costs, the wall is not a reason to trade and the record just told you so.

Where the problems above ask you to go and count something, How to Collect a Base Rate is the appendix that says how: define the observation, fix the criterion before you look, take consecutive cases rather than the memorable ones, and count into four cells.

Sources. Joel Hasbrouck and Gideon Saar, “Technology and Liquidity Provision: The Blurring of Traditional Definitions” (Journal of Financial Markets, 2009), for fleeting orders — limit orders cancelled within seconds of being placed — and for the argument that a book which changes constantly is a book behaving normally rather than one being manipulated. Charles Cao, Oliver Hansch and Xiaoxin Wang, “The Information Content of an Open Limit-Order Book” (Journal of Futures Markets, 2009), for the finding that depth beyond the best quotes does carry information about subsequent price movement, and for how modest that contribution is once the best quotes are accounted for. Rama Cont, Arseniy Kukanov and Sasha Stoikov, “The Price Impact of Order Book Events” (Journal of Financial Econometrics, 2014), for the other side of the same comparison: short-horizon price changes track the imbalance of order flow at the touch far more closely than they track the standing depth behind it.

This lesson assumed everyone was acting in good faith and found the book still could not answer the question. The next one drops that assumption — what deliberate deception in a book actually looks like, what has been proved in court rather than asserted on the internet, and why the version of the story you have been told gets the mechanism backwards.

Educational only. Trading involves substantial risk of loss. Not financial advice. Past performance does not guarantee future results.