JJ Simon Course Expected Value Variance Video transcript

This is a video on expected value, which honestly is the most important part of trading. It is the most important part of making a business. It is the most important part of pretty much everything you do. Uh just the reason for it is pretty much in the formula itself. So just go over the formula really quick. Expected value is your chance of a win times profit on win plus chance of loss times loss on loss. So your chance of losing times how much you lose if you lose.

This is this would be a negative value obviously because you're losing money. Or you could just do minus chance of loss times loss if this is positive. Let me just give it give you an example really quick. So if you're going to flip a coin, what's the expected value of flipping a coin? Chance of winning obviously is 50%. So you do it in decimal form. Chance of loss also 50%. Now how much do you win? Just say you're flipping a coin for 100 bucks each time.

So you win 100 bucks is that's your profit on win. This would be plus I guess your loss on loss would be minus 100. Obviously, this is 50 minus 50. 50 plus negative50, which is zero. So, you're flipping a fair coin. The outcome on either side, no matter what, is $100 or 100 plus 100 or minus 100. And it's 50/50. You're going to break even, which means you have zero expected value, which is totally fine. I guess there's no reason to flip that coin except if you're seeking that sort of adrenaline.

But, uh, the expected value that we have by trading is pretty much the same thing. So, uh, uh, it's a little bit different based on your risk-to-reward, but let's just assume for the sake of discussion the coin example. Say you're going to do plus or minus $100, something like this. What is the chance of winning? Well, maybe it's 51%. That means you're trading a little bit better than average. Your chance of loss then would be 0.49 because these two have to add up to one.

And obviously because it's win plus lose, there's no other outcome and there's nothing more than 100%. So then it would be $51 minus 49. So expected value would be $2. This is per trade I guess you could say. So my expected value in this case is positive. And what we have to understand obviously in trading and in life is you want to have a very positive expected value. Meaning this side of the equation is greater than this side.

The absolute value. Wait, that's too complex. I don't no need to go into no need to go into the math yet. But you just want this to be larger than this. And obviously there's so many ways you could do that. So to make this side larger, we increase this, we increase this, or decrease this, decrease this. So this comes with changing your risk to reward, changing your strategy, pretty much anything. Uh, expected value is literally used in anything.

Like, I mean, if a business is going to run ads, like when do you start running ads for your business? Uh, say you're selling something for 5K. So, if you win or your ad hits, say like 1% of ads hit. I don't know what a good ad rate is, but that's 50 bucks. Uh, and how much are you paying for that ad? Well, you're paying a 99% chance to lose. How much do you pay for the ad? Maybe 100 bucks. I don't know. In this case, it's minus EV to run ads because you're making $50 per, but you're losing $99.

So, you're net down 49. So, expected value is literally used in pretty much everything. It is so important to understand it. Oh, I didn't know you could do that. I know you could switch the words, but yeah, expected value is the most important thing in trading, the most important thing in business, even life. Maybe not life. Uh, there's some there's some pretty important stuff, but expected value is Where's the eraser?

I don't know expected value is is something very important. Uh what we have to understand while we're trading is we're gaining positive expected value over time just through our strategy and our risk management. So if we know we're getting positive expected value, the only way to turn that positive expected value into a negative one is by doing something emotional while you're trading uh because that increases your chance of a loss if you're taking a bad trade.

Also, overrisking obviously increases the loss of your loss, which would make this side larger, which means you're losing money, and you obviously don't want that. So, just keeping yourself in check, making sure you don't do anything that is going to increase your chance of a loss, nothing to increase the size of your loss. Obviously, you can scale up. It's totally fine to scale up. U just risking more per trade as long as you're following that positive expected value strategy and risk management in the first place.

Now in terms of trading expected value usually comes out to this exact equation and then what you do is you just put in different risk-to-rewards like your chance of win maybe 33% to make 300 or I used to be 200 and then your chance of loss would be uh 66% to lose 100 something like that. Um or would that be right? It's it's close enough I guess. U and then you would have a slightly positive expected value over time if you're able to increase this increase this which proportionately decreases these because as this goes up this goes down.

So you have four variables here that you can attack and literally just make these go up and make these go down. I know it's easier said than done but obviously by following my strategy uh you have a larger chance of win and by following my risk management you have a larger profit on win smaller this smaller this as well. So pretty much every pretty much everything as long as you're just following the strategy step by step.

Uh anything else about expected value. Honestly, just understanding that pretty much everything you do can be created by this formula of expected value. Uh it's very good to look at trading from a statistical point of view. I know most people just look at it like charts, ICT, buy here, sell here. uh if they're not taking a statistical approach, more likely than not, they're going to lose in the in the end. I'll just add another term here, variance.

Oh, variance. So, you might already know what variance means, but variance is pretty much just luck. So, I just modeled this in in an earlier video probably, but your expected value is slightly positive over time, but you have some luck obviously, which creates this sort of equity curve. And as long as you're following it though, you're gaining positive expected value by executing the strategy every day by staying focused, staying non-emotional, following the risk management.

If you give up after a big downswing like this just because of a three to five losses in a row, then you're still not going to get that expected value. Like you could come back right here, start trading again, and still get that positive expected value. But, uh, if you stop, then obviously you're done here. or if you start tilting then you're going this way. You're getting negative expected value if this is money over here.

So just think about everything in terms of expected value while you're trading. You can obviously ask me more questions about it in general in the in your dis in the discord but this is a a very good way to trade on profirm specifically. The reason for that is the let me just do the expected value of a profirm actually. So the expected value is your chance of a win times profit on win. So don't look at this in terms of risk-to-reward profit loss minus 1,000 plus,000 because that's how you would trade a live account.

It's a good topic to know in general just to help make you a better trader. But the expected value for profits is very interesting. So these variables are going to change a little bit. Now the best way for me to describe this is your chance of a win is your chance of a payout. So we'll do probability of a payout. That's your chance. Probability is the same as chance. So, your chance of a payout times obviously the size of the payout.

So, the size of the payout. So, you have a 50% chance to get a $1,000 payout. That would be $500 for this side of the equation. Now, this is a little bit different for prop firms. The reason for that is the risk is asymmetric. So your expected value, what you're losing each time is just the evaluation fee. It's hard to write into a formula because it sort of it depends on your pass rate. It depends depends on how often you're getting the payout and uh basically what you're tracking is your overall metrics, but we could just say minus the valuation minus minus the eval expense.

So if you're making money on prop firms, the probability of a payout times your average payout uh basically just means your net payouts. Net payout larger than Eval's expenses. So you can sort of create your own formula here. Find out what exactly your pass rate is. Uh because this is very related to expected value. Um if your pass rate say an evot cost 100 bucks. If your pass rate is 25%. You divide it by 0.25 you get $400.

So on average, it cost you $400 to pass a $100 eval because this means it takes four attempts if you have a 25% success rate. Uh I guess it's pretty much expected value. So this is your expected cost to achieve the funded account. Now if your probabil probability of a payout times the size for your payout is larger than $400, that means you're making money because on average this is your gain when on average your loss is minus400 on the funded account.

We're just assuming that evals you're able to you're able to pass the evals at more than 25%. My strategy just like 40%, maybe higher some days, some weeks, but tops that makes money on a 13% pass rate. I think anything above 25 means you'll make money. 20% would still mean tops that make money. Uh so they're making a ton of money if they're at 13%, but just go for above 25. Uh I know some people like you need to pass 100% of your emails.

No, you do. No, you do not. Uh, if you pass every email, your cost fund is $100, which is insane. It's statistically impossible. I guarantee no one has done that with a sample size more than five probably. Uh, but if you're still at 25%, that's not bad because you're paying $400 for this funded account. And honestly, like the the example I went over previous, if you have a 50% chance to get a payout for we'll do multiplication, a $1,000 payout.

So if you can get a $1,000 payout half a time, that's 500. That's plus 500 minus the 400 it took you on average to get the funded account. Your net expected value is plus $100. So every time you get a new funded account, you're making $100. So every time you buy an evaluation, then if it takes four times to pass, you're making $25 per evaluation. So I mean, it's just just an interesting way to think about prop firms.

Not many people do. I'm have absolutely no idea why no one does it this way. I think it's the only way to make money on proper is to actually look at your personal statistics. Now, to change this formula around to make more money, all you have to do is decrease your cost, which is just increasing your pass rate. Or I guess you can't really decrease the cost. So, you can apply discount codes, but increase your pass rate.

And then over here, increase your probability of a payout and or and or increase the size of your payout. uh it just comes with practice knowing exactly what risk parameters work for you. Obviously, if you have dashboard access, go check out the dashboard sometime soon. Uh the dashboard tells you literally the statistically optimal amount to risk on every single trade. It'll tell you exactly your probability of a payout.

It'll tell you the exact size of your average payout. It'll tell you your exact pass rate and then exactly exactly how much money. So, it it'll it literally tells you you're printing $100 every time you buy a ZBOT. as long as you follow the risk management strategy. Obviously, you can't just do whatever and make money. It's not that easy, unfortunately. But that is sort of the main overview of expected value. Uh the most important things obviously are your pass rate and your chance of a payout multiplied by the size of the payout.

The the only bad thing is it's inversely proportionate. So every time you increase if you if you're higher probability of a payout then on average that size of the payout is smaller because you can't say oh I'm going to have like a 90% chance of a 10k payout just not possible. All you have to do is make sure the left side of the equation is larger than the right side. So average payout size times chance of a payout larger than average cost of funded and you're making money.

Uh who's to complain if you're making money, right? You you obviously have to note um you can scale up in the future. The larger accounts usually offer better everything like just more value for your money. But obviously start on the 50ks to make sure you understand what you're doing. And if you make any mistakes then you're losing pretty much a third of the money that you would have lost if you're doing it on 150k. So we'll always start with 50ks.

I always recommend people start on 50ks until you prove yourself you can get the first payout. From the first payout you can risk it. you can go to the 150s u but obviously variance is much higher variance variance is luck so you could get unlucky and you could lose everything and then you're kind of screwed. So, usually when people get the first payout from 50s, I'm like, you know what? Go buy five 50s on this site, five on this site, five on this site, maybe buy 10 here or something like that.

Just you want to realize your expected value over time. And the way you do this obviously is finding your exact statistics. So, you have to start tracking these uh if you're trading my my strategy and my risk, you start tracking your pass rate, start tracking your payout, average payout size. Obviously, over like two payouts, the value is not going to be exact. is going to be I don't know it could be pretty far away from where where it actually is because these could go like average payout small one big two medium you know variance is key because you need a lot of samples to find your variance I would say at least 20 evals before you get a accurate pass rate and pay out honestly give it like five to 10 payouts uh you can after your first payout after I'd say after three payouts if you're still not making money.

If you spent more in Evals and you have three payouts, something's wrong and you should just tell me, send me a message, tell me, tell me what your stats are, and I'll be like, "Okay, uh, this is this is very far off from what it should be." Thankfully, I have all of this, all of these statistics stored for literally every single prop firm, so I know exactly what you're doing wrong, and I can help you with that. So, this is just introductory to expected value, how I use it in trading, how you should use it in trading, and yeah, that is it.