Here’s some information on the win distribution of MTT players with different skill levels over different sample sizes. See this post for more information on how it was generated.

ROI

Tourneys Played

Expected Earn

Chance of Loss

Chance of Earning < .5x EV

Chance of Earning > 1.5x EV

Chance of Earning > 2x EV

Standard Deviation

20%

100

$2,394.53

65%

67%

30%

28%

$18,585.18

20%

500

$11,972.65

53%

60%

30%

25%

$44,009.92

20%

1000

$23,945.30

42%

50%

36%

31%

$61,479.31

20%

2000

$47,890.60

33%

44%

35%

25%

$88,140.68

20%

5000

$119,726.50

20%

38%

30%

17%

$138,984.43

40%

100

$4,789.06

61%

65%

27%

23%

$23,262.91

40%

500

$23,945.30

37%

51%

31%

26%

$51,610.30

40%

1000

$47,890.60

29%

44%

32%

23%

$71,611.76

40%

2000

$95,781.20

14%

33%

28%

17%

$97,886.49

40%

5000

$239,453.00

6%

26%

21%

8%

$165,349.43

60%

100

$7,183.59

56%

63%

29%

24%

$25,652.40

60%

500

$35,917.95

29%

49%

31%

25%

$60,563.41

60%

1000

$71,835.90

20%

41%

27%

18%

$83,019.78

60%

2000

$143,671.80

9%

33%

26%

13%

$119,527.45

60%

5000

$359,179.50

1%

16%

17%

4%

$183,835.47

80%

100

$9,578.12

51%

62%

25%

21%

$30,978.19

80%

500

$47,890.60

24%

46%

28%

22%

$69,439.22

80%

1000

$95,781.20

12%

36%

28%

16%

$95,094.01

80%

2000

$191,562.40

5%

27%

23%

9%

$138,899.84

80%

5000

$478,906.00

0%

13%

12%

2%

$203,351.00

100%

100

$11,972.65

47%

61%

24%

18%

$32,541.62

100%

500

$59,863.25

18%

44%

25%

20%

$73,688.91

100%

1000

$119,726.50

9%

35%

25%

11%

$101,343.14

100%

2000

$239,453.00

1%

24%

18%

5%

$141,119.81

100%

5000

$598,632.50

0%

8%

10%

1%

$224,240.35

Note in particular that this data is not at all normally distributed until the sample size gets to about 5k. Typically, when people calculate things like this, they’ll approximate it by the normal distribution (go central limit theorem!), which leads to hugely inaccurate results. Here’s a comparison (I’ve sorted the data differently here. Sorry for the nasty formatting.):

Tourneys Played

ROI

Expected Earn

Standard Deviation

Chance of Loss

Incorrect Value Given by Norm Approx

Chance of Earning < .5x EV

Incorrect Value Given by Norm Approx

Chance of Earning > 1.5x EV

Incorrect Value Given by Norm Approx

Chance of Earning > 2x EV

Incorrect Value Given by Norm Approx

100

20%

$2,394.53

$18,585.18

65%

45%

67%

47%

30%

47%

28%

45%

100

40%

$4,789.06

$23,262.91

61%

42%

65%

46%

27%

46%

23%

42%

100

60%

$7,183.59

$25,652.40

56%

39%

63%

44%

29%

44%

24%

39%

100

80%

$9,578.12

$30,978.19

51%

38%

62%

44%

25%

44%

21%

38%

100

100%

$11,972.65

$32,541.62

47%

36%

61%

43%

24%

43%

18%

36%

500

20%

$11,972.65

$44,009.92

53%

39%

60%

45%

30%

45%

25%

39%

500

40%

$23,945.30

$51,610.30

37%

32%

51%

41%

31%

41%

26%

32%

500

60%

$35,917.95

$60,563.41

29%

28%

49%

38%

31%

38%

25%

28%

500

80%

$47,890.60

$69,439.22

24%

25%

46%

37%

28%

37%

22%

25%

500

100%

$59,863.25

$73,688.91

18%

21%

44%

34%

25%

34%

20%

21%

1000

20%

$23,945.30

$61,479.31

42%

35%

50%

42%

36%

42%

31%

35%

1000

40%

$47,890.60

$71,611.76

29%

25%

44%

37%

32%

37%

23%

25%

1000

60%

$71,835.90

$83,019.78

20%

19%

41%

33%

27%

33%

18%

19%

1000

80%

$95,781.20

$95,094.01

12%

16%

36%

31%

28%

31%

16%

16%

1000

100%

$119,726.50

$101,343.14

9%

12%

35%

28%

25%

28%

11%

12%

2000

20%

$47,890.60

$88,140.68

33%

29%

44%

39%

35%

39%

25%

29%

2000

40%

$95,781.20

$97,886.49

14%

16%

33%

31%

28%

31%

17%

16%

2000

60%

$143,671.80

$119,527.45

9%

11%

33%

27%

26%

27%

13%

11%

2000

80%

$191,562.40

$138,899.84

5%

8%

27%

25%

23%

25%

9%

8%

2000

100%

$239,453.00

$141,119.81

1%

4%

24%

20%

18%

20%

5%

4%

5000

20%

$119,726.50

$138,984.43

20%

19%

38%

33%

30%

33%

17%

19%

5000

40%

$239,453.00

$165,349.43

6%

7%

26%

23%

21%

23%

8%

7%

5000

60%

$359,179.50

$183,835.47

1%

3%

16%

16%

17%

16%

4%

3%

5000

80%

$478,906.00

$203,351.00

0%

1%

13%

12%

12%

12%

2%

1%

5000

100%

$598,632.50

$224,240.35

0%

0%

8%

9%

10%

9%

1%

0%

Here’s the rest of the data in some ugly graphs. The red lines indicate the expected earn:

If you’d like to provide me with some more data to play around with or you’d like the raw data, let me know.

## MTT Data

Here’s some information on the win distribution of MTT players with different skill levels over different sample sizes. See this post for more information on how it was generated.

ROITourneys PlayedExpected EarnChance of LossChance of Earning < .5x EVChance of Earning > 1.5x EVChance of Earning > 2x EVStandard DeviationNote in particular that this data is not at all normally distributed until the sample size gets to about 5k. Typically, when people calculate things like this, they’ll approximate it by the normal distribution (go central limit theorem!), which leads to hugely inaccurate results. Here’s a comparison (I’ve sorted the data differently here. Sorry for the nasty formatting.):

Tourneys PlayedROIExpected EarnStandard DeviationChance of LossIncorrect Value Given by Norm ApproxChance of Earning < .5x EVIncorrect Value Given by Norm ApproxChance of Earning > 1.5x EVIncorrect Value Given by Norm ApproxChance of Earning > 2x EVIncorrect Value Given by Norm ApproxHere’s the rest of the data in some ugly graphs. The red lines indicate the expected earn:

If you’d like to provide me with some more data to play around with or you’d like the raw data, let me know.