I'm not Ralph Vince. And I can assure you that John Kelly did not consult with Ralph Vince before writing his seminal article. If you want to understand the Kelly formula and you don't trust my presentation of it, go directly to Kelly, not to some other interpreter like Vince or Ryan Jones or whoever.
I read that paper of J Kelly years ago. I noticed that most authors ( including J Kelly ) on money management prefer to use gambling as an anolog to trading. It is OK with that . But traders must bear in mind that : trading is different with gambling . In gambling if you lose a specifit bet , you lost 100% of the stake that you put into the bet; While in trading, if you lose a specific trade, more often than not ,you only lost a part of the fund you put into the trade. Even if you risk a certain percentage x% of the account, ( a position larger than if you only put x% of your account into the trade), you still can expect to averagely lose less than x% of the account, unless you do not apply any kind of trailing stop, profit target, time exit, etc. ,and sit still waiting the market to hit your stop. So if there is a kelly f% in gambling theory, then its equivalent in trading must be "risk f% of the total account" , rather than "put f% of the total account into a trade" While many authors did not point out the difference between gambling and trading. Ralph Vince must have realized this difference ( at least subconciously ) , therefore he reminded readers not to misunderstand the correct use of kelly f%.
I read the posts in full, unless I missed it somewhere, it's unclear to me how expected return over the square of the expected return is useful as an indicator.
If you look at the formula in the OP it doesn't 'care' what the actual values of R1, R2, etc. are. They can be big or small, positive or negative. A number approximating optimality is coming out regardless. Look at Example 2 in the OP. The risk is FIVE times your Kelly fraction, because you might get the red ball. But the Kelly fraction is already sized to take this into account. Let's make the red ball riskier: if you get it, you lose 7 times your bet. The approximation becomes (7(-1) + (-7) + 2(+10))/(7(+1) + 49 + 2(+100)) = 2.34% So the Kelly approximation shrinks to account for increased risk, as desired. Now let's try the traditional 2-outcome formula: new L = (7(-1) + -7)/8 = -1.75 p - (1 - p)/(W/L) = 0.2 - 0.8/(10/1.75) = 6% A slight improvement but still overbetting for the actual 3-outcome situation. You can waste time doing it the Ralph Vince way, or you can cut to the chase and do it the Kelly way. Your choice.
OK. I did not mean or infer "indicator" in the TA sense of the word, let me re phrase. In what way is expected return over expected return squared useful as a trade management figure, what does it show, what is the use or the significance of it, why consider it?
I didn't say "expected return over expected return squared". Read the original post. It's all right there, plain as day.
OK. "expected return over expected squared return". Six little easy-to-remember words. I can not agree it's entirely clear as described in that post. Nevermind.
The point of kelly's formula is not about risk management, the point of kelly formula is about maximization of the profit. Though in practice I have been very conservative , but I still have to point out that in mathematical terms, there is only right kelly f% for the maximal output of any strategy with an edge. And that kelly f% goes with Ralph Vince's version. And in this respect, only putting f% of the whole account into a trade just does not take the enough risk that will make you full advantage. You want to trade the hell out of a profitable model, you need to stomach painful drawdowns. Then again, more profit or less risk, it is a personal choice.