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.
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.):
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.