Expectancy

Two ways to write it

The direct form is net P&L divided by the number of trades, after commissions and slippage. The decomposed form is win rate × average win − loss rate × average loss, which shows that a low win rate and a large average win can produce the same expectancy as a high win rate and a small average win.

The quant guide on this site works through a hypothetical example in ticks: 40% winning trades averaging 3 ticks and 60% losing trades averaging 1 tick give a gross expectancy of 0.40 × 3 − 0.60 × 1 = 0.6 tick per trade; with 0.8 tick of round-trip costs the net expectancy is −0.2 tick. The point of the exercise is that costs are subtracted from a per-trade average, so a positive gross expectancy can turn negative after execution.

Dollars, ticks or R

• In dollars, expectancy depends on contract size and instrument. It does not compare across strategies.
• In ticks, it is independent of the dollar tick value but still tied to the instrument's tick size.
• In R, each trade is divided by the distance to its stop at entry. A trade that made forty dollars with an eight-tick stop and one that made forty dollars with a forty-tick stop are the same in dollars and very different in R. Trades without a stop have no R.
• A rolling expectancy over the last N trades shows where a whole-run average hides a strategy that turned.

In Senzoukria

The Replay performance panel shows Expectancy / trade with the hint 'Net P&L divided by the number of trades', next to the win rate, the average win and the average loss that make up the decomposed form. A Rolling expectancy chart over the last N trades is drawn below it.

The backtest panel offers Expectancy per trade as one of the walk-forward objectives and draws an R-multiple chart whose summary reports expectancy in R, the median R, the share of trades at or above one R and the share of trades that had a stop. The site's journal page lists expectancy among the computed statistics of a trading record.

Common mistakes

• Quoting gross expectancy. Commissions, exchange fees and slippage are part of every trade.
• Reading a positive expectancy on a handful of trades as an edge. The average of a small sample is dominated by its largest values.
• Mixing instruments in one dollar expectancy. MNQ and ES trades do not share a tick value.
• Ignoring the distribution around the mean. Two strategies with the same expectancy can have very different drawdowns.