• Can a sample tell you if a betting approach is profitable?
• Sample size… how much is enough?

I’ve written previously about using raw profit to combine PoT and sample size to determine your confidence in the profitability of a betting approach or analyst. Now I want to delve more into sample size and enter some real numbers into the equation.

#### Large Sample Size

We know that the larger the sample size is, the more confident you can be that the results of the sample are a true reflection of how good the approach is.

The reason a large sample provides you confidence is because the larger the sample size is, the less that variation (and therefore luck) plays a role in the results.

Take for example a sample of 10 bets versus 1000 bets. Anything could happen over 10 bets, ranging from a large loss on turnover to a large profit. You certainly couldn’t be confident in something based on 10 bets.

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Take a 1000-bet sample on the other hand, combine it with a decent PoT and you can be very confident that what you have is profitable. That’s because 1000 bets will have considerably less variation in PoT, compared to a random 10 bets.

#### Simulations

So that’s the theory… but the real question is how much is enough?

1000 bets is plenty in most cases… but what about 200 bets?

Are sample size and PoT the only important factors?

The tables below provide the results of various simulations, which demonstrate the effect of sample size, PoT and price on the chance a set of results is profitable.

The simulation in Test 1 (for example) assumes that every bet is rated at \$2 (50/50 chance), the edge on each bet is 10% (i.e. the bet price is \$2.20), 1000 bets are simulated under those conditions and those 1000 bets are simulated 10,000 times. Under those conditions, 99.8% of the 10,000 simulations (9980 simulations) resulted in a final bank of more than the \$10,000 starting bank (profit) and 0.2% (20 simulations) resulted in a loss.

#### Running the numbers

Starting Bank: \$10,000

Number of Simulations: 10,000 simulations

Bank % Return Per Bet: 5.0%

Staking: Flat Stakes

 Test Rated Price PoT Sample Chance Profit 1 \$2 10.0% 1000 99.8% 2 \$2 10.0% 500 97.9% 3 \$2 10.0% 200 91.0% 4 \$2 10.0% 100 81.7% 5 \$2 10.0% 50 75.8%

 Test Rated Price PoT Sample Chance Profit 6 \$2 5.0% 1000 93.3% 7 \$2 5.0% 500 84.9% 8 \$2 5.0% 200 73.3% 9 \$2 5.0% 100 68.8% 10 \$2 5.0% 50 66.2%

 Test Rated Price PoT Sample Chance Profit 11 \$3 10.0% 1000 97.8% 12 \$3 10.0% 500 92.1% 13 \$3 10.0% 200 82.5% 14 \$3 10.0% 100 72.2% 15 \$3 10.0% 50 63.3%

 Test Rated Price PoT Sample Chance Profit 16 \$3 5.0% 1000 86.1% 17 \$3 5.0% 500 78.0% 18 \$3 5.0% 200 67.7% 19 \$3 5.0% 100 65.8% 20 \$3 5.0% 50 63.3%

#### Results

As you can see, the following conditions increase your chance of a profit:

• Larger PoT
• Larger number of bets
• Shorter rated price (i.e. higher strike rate)

Any factor that increases variation will reduce the chance of profit. There are other factors apart from PoT, sample size and average rated price that increase variation. These include different prices in a set of bets and different edges on each bet. Based on that knowledge, you can view the above chances of profit as best-case scenarios.

One of the key points is that it all comes down to confidence. And the level of confidence you are willing to accept. 50 bets rated at \$3 with a 10% PoT (Test 15) may well produce a profit over the next 50 bets. But it’s only a 63.3% chance to do so, which I wouldn’t be happy to accept.

500 bets rated at \$3 with a 10% POT. (Test 12) will produce a profit 92.1% of the time. I’m willing to accept the 7.9% risk that I will lose over 500 bets.

The question is though, are you?

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