For one trade the expectancy is a theoretical value, as it assumes probabilities for losing and winning. There is only one practical outcome, which is statistically insignificant, and you cannot calculate the expectancy without assuming ex-ante probabilities.
The R-multiple depends a bit on the mechanics of the trade. If you enter long for 2 contracts with a logical stop of -10 ticks, a 1st profit target of + 10 ticks with adjustment to breakeven, and a second profit target of +20 ticks, the outcome for a random market after a larger number of trades would be close to:
The weighted reward-to-risk is (0.125*20 + 0.125*0 + 0.25*10)/ 0.5*10 = 5:5 = 1:1 Reward-to-risk is needed to calculate the edge of a trading system. The edge is the expectancy.
Expectancy = Average winner * Winning percentage - Average Loser * Losing percentage or by requiring a positive expectancy this equation can be transformed to
(1) R-Multiple > 1/winning percentage - 1
Example: If your winning percentage is 40%, your R-Multiple required to breakeven would be 1/0.4 -1 = 1.5 This example is before transaction cost and slippage. This is the easy part.
Many similar trades
If you have a larger number of similar trades, you can calculate a statistically based expectancy. This is based on an ex post probability which is a result of the trades. Note the difference with one trade.
If you are trading an automated system, always using the same stop and the same profit targets, you can calculate the correct reward-to-risk ratio by empirically counting the number of outcomes for each of the four possible results (I stay with my no-slippage model). The relative frequency of the outcomes is an approximation of the probability, and you can again calculate the reward-to-risk ratio by comparing the added positive outcomes with the added negative outcomes:
(2) R-Multiple = (added $ of winning trades/ number of winning trades)/ (added $ of losing trades/ number of losing trades)
Many different trades
If there are many different trades, you may want to evaluate them. For technical and other reasons your risk will sometimes be 2.3%, sometimes 1.4% of your account. I think that Van Tharp wants to make these trades comparable by not using the $$ outcome, but the outcome measured in multiples of R.
This is a way of normalizing the position sizing of the trades. If an undisciplined trader doubles position size and luckily wins, this for sure affects his account. In this case Van K Tharp - as I understand him - does not want to take into account the unduly increased position size, so he measures the outcome in terms of R achieved.
Now, there is a catch.
Expectancy
The idea of calculating an average R-Multiple is mathematical nonsense. But it can be a valid educational concept. The expectancy can only be calculated by taking into account both winning percentage and R-Multiple. A scalper with a high winning percentage does not need high R-multiples, as he relies on a hihg winning percentage. The high winning percentage will even allow him to increase his position sizing, because the probability of a larger drawdown is reduced. The scalper may actually tolerate a higher risk per trade, without increasing the risk of ruin*).
So why does Van Tharp calculate R-multiples?
Psychological Barriers
Most beginning traders do not let their profits run, and achieve bad R-Multiples. You will find some journals here that show R-multiples < 1. It is psychologically easy to take a quick profit, and have a large loss every 5 trades. You are emotionally rewarded with 4 successes and only 1 failure! Van Tharp uses this method as a way to monitor the trader's performance to cope with loss aversion and not letting profits run.
It is an educational tool
And there is another reason to use this method. To complete evaluate a trader's edge you would need to know the winning percentage and the R-multiple. To get a good approximation for the winning percentage, you would need something like 100 trades if you search for statistical significance. So you cannot give the trader immediate feedback on his performance. The R-Mulitple can be used even after 1 trade and is significant. So it is a concept that can be used to train traders.
Why does he choose the median?
He could choose the arithmetic average, the geometric average, the median, the mode, etc. No importance, the median can be observed without calculating anything.
And the mathematics?
There is little valid mathematics in the books of Van K Tharp. If you are really intested in the subject you should start with "The Mathematics of Money Management" by Ralph Vince. Not an easy read though, but very important. I am slowly digging through this, interrupted again and again by other priorities.
*) not known by many traders: Let us assume two trading systems:
system 1: winning percentage 70%, R-Multiple = 2 system 2: winning percentage 42%, R-Multiple = 4
Both systems have the same expectancy of 1.1R (which is excellent, 0R stands for break-even). However, the first system has a better Sharpe Ratio, so you can actually trade it with a larger position sizing, without increasing your actual risk (measured in terms of max. drawdown).
Note that mathematics is in contradiction with the methods of Van Tharp.
Who is able to calculate the position sizing for the 1st system relative to the 2nd, so that the risk of ruin becomes equal?
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Here are some screen shots of the new journal I am working on. Thanks goes to @sam028 and @Gary for helping me with some of it.
The basic idea is an Overview panel that shows me at a glance some meaningful statistics. I still have a lot of work to do on this, so the screen shot is not complete. The idea is to be able to breakdown stats by Method (entry) and also by result (Comment field), so I can see how methods compare, and also I can track 'Comment' like followed rules/not followed rules, or any other comment I want, and see how stats breakdown. There are not many sample trades entered in this journal yet, so some pages appear empty.
The Journal panel is for data entry. Most fields are auto-populated. Just need to enter the date/time, instrument (from drop-down choice), method (drop-down choice), entry/exit price. I have VWAP here because I want to conduct a study to determine if tracking VWAP in relation to my trades is important -- stats on the Overview page reflect this, am I more successful longing above VWAP, more successful shorting below, etc? This will allow me to track that. MAE is self-explanatory. The Bench field is what I call benchmark, it is the absolute best-case scenario for a trade. If I exited at the absolute best tick possible during this trade while following my rules, I would get <xx> ticks. The next field is efficiency, it measures my actual realized exit compared with the benchmark. Minutes tracks how long the trade was, so I can breakdown my average winner and loser in minutes (on overview page). Risk, Result, Balance are self-explanatory. The Comment field will allow me to enter a few 'scenarios' perhaps and track each uniquely, getting stats per scenario. The rest of the fields are just there to make formulas easier, they are all automatic.
The Method List allows you to enter new methods that will appear automatically in the drop-down menu and the rest of the spreadsheet.
The Comment List is the same way.
The Instrument List is the same, and is necessary to define tick values and such so math calculations can be done correctly on the Journal tab.
The Internal Calcs tab/panel is just for behind-the-scenes formulas that are necessary to create some of the results in the Overview page, like the trade result per hour breakdown, the annualized returns, etc.
I will post the spreadsheet when I consider it 'ready'. I welcome feedback with what I have so far.
Looks brilliant, I will stop all my efforts in this area, and wait until you're ready. But of course, post any later improvements, if this is still possible.
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Here is a simple xcel spreedsheet that you can use to calculate your risk/reward and risk per contract. Just enter symbol, entry, stop, and target. To modify the formulas if needed the sheet password is 1234.
Some of the values look unrealistic and …
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This is excellent for assisting with discretionary trading. I know you have a keen interest in the 'state of mind' && 'state of health' when you are trading ... do you intend to incorporate those as inputs for a later version?
Jon
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Yes, the 'comments' block will be where I tag each trade with relevant info to help me track such things.
I will look at them to see if I can add anything useful to mine. The second link, I tried this last year and ran into too many technical problems. I actually still have a membership there, it was comped gratis due to the issues. But, I prefer my spreadsheet.
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No not at present. But I could have a list of pre-defined comments that should cover enough range to give me post-trade analysis info. There are two fields to classify or categorize trades, the 'method' and 'comment' field. More could be added, but this is enough for me.
But it can be a valid educational concept. The expectancy can only be calculated by taking into account both winning percentage and R-Multiple. A 
