*This was originally posted on our Facebook Group by a Trademate customer who we will refer to as JCM. Because the post was so good, we thought we’d post it on our blog for everyone to see. Thank you JCM and enjoy everyone!*

Hello guys. I've seen a few posts lately (some are actually mine), with poor results, wondering about variance, etc. I'm myself in a pretty sick downswing, and my only way to cope with it is by making sure I'm doing things the right way and having some extra assurance that I'm having just "bad variance" at the moment. I normally use this betting simulator to forecast future results and check if my EV is in-line. However it's based on pure averages, not on concrete data.

I found recently that I can download my own trades on a CSV with the Trademate Sports Analytics package, so I downloaded it and built a script to perform a simulation. The program goes one by one through all my trades, using the actual edges and odds I was offered for the past 1.5k trades, and runs the outcome randomly hundreds of times according to the parameters I enter.

I can choose to simulate as many trades as I want, and with as many samples as I choose. The results are insane. Variance is way, way bigger than I expected before getting into value betting. Placing 1k trades is a drop in the ocean, and I found that the proper threshold we need to cross in order to really beat variance is over 10k trades. Let me show you some results.

So I ran the script with the following parameters:

- 1500 trades in total
- Simulate it 500 times
- Calculate proper bet size on each trade according to current bankroll, using 30% kelly and rounding to the nearest €5 amount.
- €5.3k starting bankroll (BR)
- Max bet of 1.33%, 2% if I drop below €2.5k BR and 1% if I go over €10k BR.
- My average closing edge is 3.6%.

As you can see on the graph, anything can happen. I actually lost €1.5k during my first month. These are the actual probabilities of different profit outcomes:

**Probability of making more than -1250:** 99. % of the runs

**Probability of making more than -1000:** 99.2% of the runs

**Probability of making more than -750:** 98.2% of the runs

**Probability of making more than -500:** 96.0% of the runs

**Probability of making more than -250:** 94.2% of the runs

**Probability of making more than 0:** 92.8% of the runs

**Probability of making more than 26:** 92.6% of the runs

**Probability of making more than 250:** 88.4% of the runs

**Probability of making more than 500**: 83.6% of the runs

**Probability of making more than 750**: 76.6% of the runs

**Probability of making more than 1000**: 71.6% of the runs

**Probability of making more than 1250**: 64.8% of the runs

**Probability of making more than 1500**: 59.0% of the runs

**Probability of making more than 1750**: 52.0% of the runs

**Probability of making more than 2000:** 45.2% of the runs

**Probability of making more than 2500:** 29.200000000000003% of the runs

**Probability of making more than 3000**: 20.200000000000003% of the runs

**Probability of making more than 3500**: 10.400000000000006% of the runs

**Probability of making more than 4000**: 5.200000000000003% of the runs

**Probability of making more than 5000**: 0.7999999999999972% of the runs

So my results had less than 0.4% probability of happening. I should definitely not have more months like this in the next 10 years. We'll see about that. It was actually twice as likely to have won +5k than losing -1.5k. Insane. In theory, I should only have a losing month 8% of the time, so once a year.

So I ran the script with the following parameters:

- 5000 trades in total
- Simulate it 500 times
- The rest of the parameters are kept the same

It starts shaping up to an upward trend, however the possible results are all over the place:

**Probability of making more than 0:** 98.8% of the runs

**Probability of making more than 26:** 98.6% of the runs

**Probability of making more than 250:** 98.6% of the runs

**Probability of making more than 500:** 97.8% of the runs

**Probability of making more than 1000:** 96.6% of the runs

**Probability of making more than 2000:** 92.4% of the runs

**Probability of making more than 2500:** 88.6% of the runs

**Probability of making more than 3000:** 82.6% of the runs

**Probability of making more than 5000**: 60.8% of the runs

**Probability of making more than 6000**: 46.0% of the runs

**Probability of making more than 7500**: 22.799999999999997% of the runs

**Probability of making more than 10000**: 3.4000000000000057% of the runs

**Probability of making more than 15000**: 0.20000000000000284% of the runs

It should be very unlikely to be losing money after 5k trades, just 1.2% of the time, so that's about once every 99 times you put in 5k trades. It's more likely to make over +10k by then. Let's hope that's the case.

So I ran the script with the following parameters:

- 15000 trades in total
- Simulate it 500 times
- The rest of the parameters are kept the same

Now the upward trend is obvious. However, there is still 0.2% chance of losing money after a full year. Just about the same chance of making 30k.

**Probability of making more than 0:** 99.8% of the runs

**Probability of making more than 3000:** 99.6% of the runs

**Probability of making more than 5000:** 98.6% of the runs

**Probability of making more than 6000**: 98.0% of the runs

**Probability of making more than 7500:** 97.6% of the runs

**Probability of making more than 10000:** 94.6% of the runs

**Probability of making more than 15000:** 62.8% of the runs

**Probability of making more than 20000:** 21.200000000000003% of the runs

**Probability of making more than 25000:** 3.5999999999999943% of the runs

**Probability of making more than 30000:** 0.20000000000000284% of the runs

So I can expect to make 15-20k during my first year, more often than not, unless I'm banned from all the bookies, or I run terribly for a full year. There is only a 5.4% chance of making less than 10k, which would be a 200% bankroll growth.

So I ran the script with the following parameters:

- 30,000 trades in total
- Simulate it 500 times
- The rest of the parameters are kept the same

Now we can see a clear convergence towards the Closing EV%. There is still huge variance between the best and worst results, but now there is 0% chance of making less than 15k in two years, and a solid 91% chance of making more than 25k.

**Probability of making more than 15000:** 100.0% of the runs

**Probability of making more than 20000:** 98.2% of the runs

**Probability of making more than 25000**: 91.6% of the runs

**Probability of making more than 30000:** 73.8% of the runs

**Probability of making more than 35000:** 43.4% of the runs

**Probability of making more than 40000:** 14.400000000000006% of the runs

**Probability of making more than 50000:** 0.4000000000000057% of the runs

So I can expect to make somewhere between 25k and 40k in two years time. We'll see how it goes. I hope it helps you guys deal with your own variance. It is crazy. And this assumes that my edge is real and accurate. I have an average Closing Edge of about 3.6%. If it is indeed lower, then variance is even grosser than this. But at least this gives me a bit of peace of mind. Less than 5k trades is absolutely not enough to extract any conclusions.

But at least this simulation is run on my actual trades, not just averages, so now I'm confident that I had the grossest month I'm hopefully ever gonna have.

Disclosure: I also ran these tests with 100k samples instead of just 500, and there are extreme cases of losses after 15k and 30k trades. But the chance is 0.0000....1%. But anything is possible.

After reading my post, Neel S was kind enough to share his trade history with me so that I could run the simulation over his 9.6k trades, which is way more meaningful than my sample.

A few caveats about his simulation:

- I used £5k starting BR, 20% kelly and no limit for the max bet as he told me. He did say he sometimes lowers the suggested amounts, so these results might be more variance-y than they should by following his criteria. So take the results with a grain of salt.
- He has a mix of trades in EUR and GBP, so I unified all amounts on GBP using today's exchange rate of 1 EUR = 0.88 GBP.
- He has a mix of trades from soft and sharp bookies

He told me I could share his data publicly, so here they are. My estimation from his data and unifying amounts in GBP at today's rate indicate that he's had over the past 9653 trades:

- 22.5k GBP in profits
- 496k GBP in turnover
- 14.6k GBP in closing EV
- 4.54% ROI
- 2.94% Closing Edge

My estimations could be a bit off, I had to make some assumptions. But they shouldn’t be too far away from reality. Here are the simulations.

If he was to start all over with the exact same 9653 value bets, 1000 times, these would be all his possible outcomes.

The tendency is upwards, but there is still a ton of variance here, even though his sample size is quite large. Here are the probabilities for different outcomes:

**Probability of making more than -5000:** 100.0% of the runs

**Probability of making more than -1750:** 99.2% of the runs

**Probability of making more than -1000:** 99.0% of the runs

**Probability of making more than 0:** 98.7% of the runs

**Probability of making more than 1000:** 98.1% of the runs

**Probability of making more than 2000**: 97.3% of the runs

**Probability of making more than 2500**: 96.3% of the runs

**Probability of making more than 3000:**95.9% of the runs

**Probability of making more than 4000:** 94.3% of the runs

**Probability of making more than 5000:**92.5% of the runs

**Probability of making more than 6000:** 90.7% of the runs

**Probability of making more than 7500:**86.4% of the runs

**Probability of making more than 10000:**76.4% of the runs

**Probability of making more than 15000:** 48.0% of the runs

**Probability of making more than 20000:** 21.299999999999997% of the runs

**Probability of making more than 22500:**12.900000000000006% of the runs

**Probability of making more than 25000**: 7.099999999999994% of the runs

**Probability of making more than 30000**: 1.2000000000000028% of the runs

**Probability of making more than 35000:** 0.09999999999999432% of the runs

**Probability of making more than 40000:** 0.0% of the runs

He had a 13% chance of getting the results he's actually had, so from this data we can infer that he's probably been running over EV on this sample, on the good side of variance. He had 0% chance of losing his entire BR, but he did have a 1% chance of dropping 1-2k after almost 10k trades. Slim, but possible. About 50% of the time he should have made over 15k GBP, which is about his closing EV value.

It is very likely (76% chance) that he would have made at the very least 10k GBP, which is pretty great for the first 7 months of work.

Good job Neel. Amazing results.

The trend is much clearer now. However, since the max bet % is set to 100%, variance is huge and we can see a couple of outliers who did lose the entire BR along the way. Here are the probabilities for a few different outcomes:

**Probability of making more than -1250:** 100.0% of the runs

**Probability of making more than 3000:** 99.9% of the runs

**Probability of making more than 7500:** 99.4% of the runs

**Probability of making more than 10000:** 98.8% of the runs

**Probability of making more than 15000**: 94.6% of the runs

**Probability of making more than 20000**: 85.5% of the runs

**Probability of making more than 22500**: 79.5% of the runs

**Probability of making more than 25000**: 72.7% of the runs

**Probability of making more than 30000:** 53.0% of the runs

**Probability of making more than 35000:** 33.400000000000006% of the runs

**Probability of making more than 40000**: 16.400000000000006% of the runs

**Probability of making more than 50000:** 2.5% of the runs

**Probability of making more than 75000:** 0.0% of the runs

Should he run at the same pace, he could very well end up with over 40k GBP after 14 months, 16.4% chance. Now there is virtually no possibility of ending up in a loss, actually there is almost no chance that he'd make less than 10k GBP.

There is 20% chance that he is going to break even for the next 10k trades and stay at his 22.5k profit mark. But should variance even out, he should expect to make about another 10k GBP and close the 20k trade mark with about 30k GBP profits. If his good run continues, he might even make over 50k GBP.

Really nice results. Still, variance is huge. Very huge. And as someone said in the comments, this is all based on assuming TM edges are accurate. However, there is a silver lining after seeing Neel results. If TM edges were non-existing, there'd be mathematically no way that he could have reached 22.5k profits in 10k trades. They might be slimmer than what we can see as our closing edge, but they can't be too far from that.

So as long as we keep closing edges over 2.5%, I believe we're in great shape to make some nice profits if we keep a cold head and keep putting in the volume. 10k seems like a lot but still, it's the sweet spot where variance starts to fade.

Hope you enjoyed reading this, and thank you again Neel for sharing your data with all of us. I hope you reach that 2.5% chance of hitting the 50k GBP profit mark after the next 10k trades!

PS: Should someone want to explore deeper tweaking some parameters, please let me know on the Facebook Group. It's an interesting topic to discuss!

Good trading guys!

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