The cost of a broken rule is not the trade. It is the series.

A repeated deviation from a stated plan costs a specific, computable amount of currency, and the amount is a property of the deviation, not of the trader. To get it you need one thing most writing on this subject never supplies: a control. Take a fixed series of trades, run it twice — once under the plan and once under the plan plus one deviation — and hold the market identical between the two runs. The market path is exogenous; only the decision rule changes. The gap between the two ending balances is what the decision cost, and because the two runs faced the same trades, it cannot be luck.

Done that way on the model plan defined in §01 — 200 setups, 1.00% of equity risked per trade, a 1.00R stop and a 2.00R target on a $50,000 account — the five common deviations price out like this, per single occurrence:

That marked row is also why this is a price list and not a league table. The cost of a decision is not a property of the decision alone: it moves with the risk fraction — a quantity with its own arithmetic — with the horizon, and with how often the deviation happens. Every figure below therefore carries its parameters with it.

Every number on this page is derived from a stated model and is an output of that model, not a measurement of any real trader or any real firm. The model, its parameters, its closed-form probabilities and its limits are all in §01 and §07, and the instrument in §04 recomputes every figure live from the controls you set.

It costs the difference between two ending balances produced by the same trades. That sentence is the whole method, and the word doing the work is same. If you compare a month in which you widened stops to a month in which you did not, you have compared two different markets and learned nothing. The only way to isolate a decision is to freeze the market and vary the rule.

Freezing the market means being precise about what a "trade outcome" is. It is not a profit-and-loss figure — a P&L figure is already the product of a decision. The exogenous object is the price path: what the market did after entry, which is the same whether or not you were still in the position. A decision rule is then a function that maps a path to a P&L. Two rules, one path, two numbers.

The model plan below is deliberately ordinary, and every quantity in it is declared rather than fitted to make a point.

The price path is a random walk in risk units with a step of 0.05R, and it has two regimes. While the trade has never touched −1.00R, the walk carries a small upward drift: this is the plan's edge, and it is what the entry is for. The moment the path touches −1.00R, the drift is set to zero. That switch is the model's single most consequential assumption and it encodes an ordinary idea: a stop is placed where the reason for the trade stops being true. Below it, the trader has no view. Zero drift is the assumption most generous to every deviation in this article — a negative drift would make them all more expensive — so every cost below is a floor, not a ceiling.

Two barriers close the path at −1.75R and +2.00R, the widest levels any rule here uses, so every trade resolves. That makes the model exactly solvable: the probability of touching one barrier before another in a walk with drift is the classical two-barrier result, and it needs no simulation.

Read the last line as the price of everything that follows: a trade under this plan is worth just over a fifth of a risk unit, which is $103 at the opening risk size. It wins 40.2% of the time. It is a perfectly unremarkable plan, and it is deliberately unremarkable, because a plan with a spectacular edge would make every deviation look cheap by comparison.

Because if the price path carries no edge from the stop level onward, then every exit rule you could apply from that point has exactly the same expected value — including the rule you were supposed to follow. This is not a modelling convenience. It is the optional stopping theorem: for a martingale, the expected value at a stopping time equals its starting value, provided the stopping time is well behaved. Applied to a gambler's fortune, it says that nothing can be gained on average by choosing when to walk away.

Work it through at the level the decision is actually made. The trade is at −1.00R. The plan says exit. The alternative is to move the stop to −1.75R and give it room. If the remaining path is driftless, the probability of reaching +2.00R before −1.75R is the distance to the lower barrier over the total distance: 0.75 / 3.75 = 0.20.

Not approximately equal. Equal. And the same thing happens if instead of widening you double the position at −1.00R and put the combined stop at −1.75R: the outcomes become +5.00R with probability 0.20 and −2.50R with probability 0.80, which is again exactly −1.00R. The theorem does not care how baroque the re-decision is.

So the popular account of these decisions — that they are expensive because they lose money on average — is, under the assumption most favourable to them, simply false. What is true is narrower and more interesting. The break-even rescue probability for the widened stop is p* = 0.75/3.75 = 0.20, and the driftless path supplies exactly 0.20. Widening only adds expected value if the residual drift is positive — that is, only if the stop was in the wrong place to begin with. The decision is therefore not really about the stop. It is a bet on where your edge lives.

Which leaves the obvious question: if the expected value is identical, what exactly is the reader paying for? Two things, and the figure below prices the first of them. The widened branch has a standard deviation of 1.50R where the honoured stop has none, and an account that compounds does not value those equally. Solve for the certain outcome that would leave a 1%-risk account with the same compounded position — the certainty equivalent, c, satisfying ln(1 + f·c) = E[ln(1 + f·r)] — and the widened branch is worth −1.0112R against the stop's −1.0000R. That difference, 0.0112R, is $5.60 at $500 a unit. It is small. It is also charged every single time.

Through three doors, and only three: a change in the average trade, a change in the dispersion of trades that a compounding account has to absorb, and a change in how many trades you take at all. Any claim about the cost of a decision that does not resolve into one of those three is a claim about something else.

Execution friction is deliberately not one of the three. Spread, commission and slippage are charged on every trade taken, at the same rate, in both arms of the comparison, so they subtract from both ending balances and cancel out of the difference between them. That is what makes the gap attributable to the decision. What friction costs in absolute terms, and how many round trips a month it takes to matter, is a question with its own arithmetic.

• Expectancy. The decision changes the mean outcome. Cutting a winner at +0.80R when the plan holds to +2.00R does this: from +0.80R the trade is still working and the drift is still there, so holding is worth +1.0112R against the +0.80R you took. You gave up 0.2112R of mean, on 60% of all trades. That is real, first-order, and unrelated to compounding.
• Variance under compounding. The decision leaves the mean alone and widens the spread. Widening a stop and adding to a loser both do this. A fixed-fraction account accumulates log growth, so a wider spread at the same mean is strictly worse — the cost is exactly the gap between the two certainty equivalents, and nothing else.
• Participation. The decision removes a trade from the series. Skipping a setup does this, and it is the cleanest of the three because it needs no assumption about residual drift at all: you were not in the market, so you collected exactly nothing where the plan collected its expectancy.

The waterfall below runs all five deviations together at φ = 30% and resolves the total into those steps. It is an expectation, not a sample: each bar is the change in the compounded 200-setup result caused by adding one more deviation to the ones already applied. Because the bars are a chain of differences they sum to the total by construction. A different application order gives different individual bars and the identical total — that ambiguity is real and stating it is part of the figure.

Note the fourth bar carefully. Doubling size after a loss adds $1,362 here. That is not a recommendation and it is not a paradox: it is what happens when a risk fraction sits far below the level that maximises compounded growth, and it comes attached to a near-doubling of drawdown depth that the waterfall does not draw. §07 handles it honestly. On why win rate and expectancy diverge in general, there is a dedicated treatment; what matters here is only the currency.

Set the deviation, set how often it happens, and the instrument computes what it costs. Everything below recomputes from the controls at the moment they move. The two capital paths in the plot are generated from one shared set of trade paths, so every turn they share is a turn the market made and neither decision caused — which is the point of the whole construction. Change the sample and the shape changes; the price does not.

The headline cost is the closed-form model value, not the sample. That distinction is deliberate: a single 200-setup series is far too noisy to measure a cost this small, and the tenth-to-ninetieth range printed under the plot shows exactly how noisy. The price is what the decision is worth. The sample is what one year happens to look like.

Exactly the expectancy of one trade, with certainty, every time — and unlike every other cost in this article it requires no assumption whatsoever about what the market did next. You were not in it. The plan collected +0.206R and you collected nothing. At $500 a unit that is $103 of arithmetic and $97.79 of compounded position, and it is charged on the way in, not settled later.

The symmetry cuts both ways, and the article would be dishonest if it printed only the expensive half. The cost of a skipped setup is the expectancy you skipped — so a trader with no edge loses nothing by sitting out, and a trader with an edge pays for every one. The price of abstention is not a fact about discipline. It is a fact about the size of the edge being abstained from, which is why it cannot be quoted until the plan has been specified.

Where it becomes large is in accumulation. Skipping the setup after a loss is a rule that fires as often as losses occur, which in this plan is 59.8% of trades. At full frequency it removes 37.4% of all setups from the series — the steady-state share, because a skipped setup is not itself a loss and does not chain. Over three years at five setups a week, that abstention costs more than the account it was protecting.

Nothing in that sentence involves a bad trade. No stop was moved, no position was averaged, no size was doubled. Every trade that was taken was taken exactly to plan. The entire cost is trades that never happened, which is precisely why it never appears in a review of the trades that did.

In this model the missed one, by a factor of about seventeen. A setup skipped forfeits 0.196R of compounded position. Widening the stop on a trade already sitting at its stop forfeits 0.0112R. The decision that a trader would describe as restraint is seventeen times more expensive per occurrence than the decision the same trader would describe as a lapse.

The mechanism behind that ratio is not psychological, and it survives without any claim about how anyone feels. A missed trade forfeits the whole expected value of a trade, because you took none of it. A re-decision at the stop forfeits only the difference between two lotteries that share an expected value, because the loss was already incurred when the price got there — the trade's expectancy had already been spent. You cannot lose an edge you are no longer holding.

Two columns of that table matter more than the first. Certainty: the two expensive decisions charge their fee every time, with no chance of a refund, while the two cheap ones are lotteries that pay out one time in five and are therefore remembered. Worst case: the abstention's downside is bounded by construction at exactly one trade's expectancy, whereas the re-decisions have a worst case that is only bounded because this model draws a barrier at −1.75R. Remove the barrier — which is what a discretionary stop is — and the left tail of that column has no defined edge at all.

That last point is where this arithmetic stops and a different one begins. A cost of $5.60 an occurrence is a rounding error until the occasion on which the −1.75R lands against a hard floor, at which moment the price of the decision is no longer measured in dollars per occurrence. Ruin has its own mathematics, and it is not this one.

Because a trading account produces only one arm of the experiment. You observe the series you traded. The series you would have traded had you followed the plan does not exist anywhere — not in the platform, not in the statements, not in the journal — so there is nothing to subtract. Every cost in this article is a difference between two numbers, and a live account supplies one of them.

The second reason is scale. The per-trade cost of the cheap deviations is on the order of 0.01R to 0.04R, and the per-trade standard deviation of the plan itself is 1.47R — roughly a hundred times larger. A single series is a measurement of the noise with the signal somewhere inside it. This is not a statement about anyone's attentiveness; it is what happens when you try to resolve a hundredth of a unit against a whole one.

Which is why the answer has to come from a model, and why the model's assumptions have to be stated louder than its outputs. Here they are, in the order in which they could be wrong.

• Zero residual drift below the stop. The load-bearing one. If the level breaking carries information, widening is genuinely negative-expectancy and its cost rises well above $5.60. If it carries the same edge as before, the stop was misplaced and widening pays. The model takes the middle, generous case and asserts nothing about markets.
• Execution friction is held constant, not ignored. Spread, commission and slippage are charged at the same rate on every trade taken in both arms, so they cancel out of the difference and none of the gap above is friction. Two residues do not cancel and are not counted here: adding a unit buys one extra fill, and a skipped setup buys none at all. Both belong to the arithmetic of friction itself, and they push the two figures in opposite directions.
• No elimination floor. The model account cannot be closed. This matters most for the size-increase result: doubling after a loss lifted compounded growth in a 1% account and roughly doubled the depth of the median drawdown alongside it. Put a floor under the account and the ordering can invert entirely, which is a question about ruin and a question about how a floor moves, not a question about decisions.
• A stationary edge and independent trades. The drift does not change and no trade knows about any other. Real edges decay and real trades cluster.
• One deviation at a time, at a fixed frequency. The instrument prices deviations singly; the waterfall composes five, and the composition is order-dependent as it says.

What survives all five caveats is the method rather than any single number. A deviation is not a character flaw and it is not free; it is a recurring charge with a rate, and the rate can be computed as soon as the plan is written down precisely enough to have a counterfactual. Most plans are not. That, rather than any bias, is the reason the invoice never arrives.

Almost everything in this article is derived, and its working is printed beside it. Three things are not, and they are listed below with what each supports.

• Optional stopping theorem Wikipedia, "Optional stopping theorem". Retrieved 27 July 2026 from https://en.wikipedia.org/wiki/Optional_stopping_theorem — supports the statement that a martingale's expected value at a well-behaved stopping time equals its starting value, its three standard sufficient conditions, and the reading that nothing can be gained on average by choosing when to stop a fair game. The specific application to a stop level in §02 is derived here.
• Two-barrier hitting probability Wikipedia, "Gambler's ruin". Retrieved 27 July 2026 from https://en.wikipedia.org/wiki/Gambler%27s_ruin — supports the closed-form probabilities used throughout: A/(A+B) for a driftless walk and the (q/p)-ratio form for a walk with drift. The algebraic re-arrangement into (1 − ρ^A)/(1 − ρ^A+B) is shown in §01's margin and was verified against a 200,000-path simulation.
• Odean, T. (1998), "Are Investors Reluctant to Realize Their Losses?" The Journal of Finance 53(5), 1775–1798, doi:10.1111/0022-1082.00072 — supports only the single, bounded statement in §06 that realising gains at a higher rate than losses is a documented pattern with a name. The publisher's PDF could not be read in text form in the environment used to prepare this article; the citation details and the qualitative finding were verified against Wikipedia, "Disposition effect", retrieved 27 July 2026 from https://en.wikipedia.org/wiki/Disposition_effect. No figure from the paper is quoted here, and no prevalence is claimed for any population.