~ Divisive Data Resorting ~

This research was conducted together with Mike Poluektov

1. Data sample

Let us consider elementary Monte-Carlo simulation. We generate random number $x$ with uniform distribution from the range $[3, 30]$ and then another value $y$ as an average of 7 uniformly distributed random numbers from the range of $[0, x]$. We consider $y = f(x)$ as a stochastic system with aleatoric uncertainty. The sample of 120 points generated in this way is shown in the picture below.

Obviously, these 120 points is a sample from multinomial distribution (since both $x$ and $y$ are random), but we consider it as input dependent distribution of the output of some stochastic system. The goal is to build data generation model capable of producing samples from the same population providing only data shown in the picture.

2. The challenge

The data in the picture does not provide enough features to make judgements about the type of distribution. By looking at the data it is possible to assume that expectation model can be a straight line, but variance depends on input $x$.

3. Divisive Data Resorting

The Divisive Data Resorting is a new simple but effective algorithm of building multinomial stochastic models using short data samples. Its full version can be found in archived article . Here I provide very basic explanation of the concept in terms introduced only for this specific example.
• Step 1. We select deterministic component or expectation model. In this case it is a straight line defined by parameters $y = Ax + B$.
• Step 2. We build model by error minimization technique and sort records according to residual values $r_i = y_i - \hat{y}_i$ (residual is a difference between modelled and actual values).
• Step 3. We split records into two clusters over the median residual, build two models $M_1$ and $M_2$ for each cluster, resort records within each cluster as explained in step 2.
• Step 4. We continue this process of dividing and resorting until each model for each cluster becomes accurate, which means show very low residual values.
• Step 5. We use multiple models built for each cluster as an ensemble for modelling of the sample for each given input, that means we pass an input to each model and consider these multiple results of ensemble as a sample from the same population as provided training data, which are points in the picture.
For better understanding of the process the C# coding example is provided.

4. The result of modelling and accuracy estimation

We built the ensemble of 19 linear models according to above DDR algorithm. Below a comparison of 3 samples for $x = 28.0$ is provided. First column is a sorted Monte Carlo simulation according to section 1, which is average of 7 uniformly distributed values from the range $[0,28]$. Second column is another sorted Monte Carlo simulation. Two samples are provided to give an idea how random samples are different from each other. Third column is a sample generated by 19 DDR models.

 Monte Carlo 1 Monte Carlo 2 DDR model 9.44 10.44 9.99 11.44 10.60 11.09 12.20 11.76 11.64 12.64 11.96 11.92 12.84 12.00 12.04 13.08 12.28 12.17 13.28 12.32 12.29 14.56 13.12 13.05 14.72 13.16 13.69 14.80 13.32 14.22 14.92 14.28 14.69 15.44 15.08 15.26 15.52 16.20 15.63 15.68 16.28 15.98 16.44 17.28 16.66 17.36 17.48 16.67 17.76 18.24 16.80 18.28 18.40 17.18 19.32 18.48 17.52

As it can be seen, the ensemble built by DDR from the provided short data sample predicts near the level of original Monte Carlo simulation.

5. From a simple case to a challenging one

It is absolutely wrong to assume that DDR works well only as an ensemble of simple approximations of linear models with one input. In the archived article much more complex model with 5 inputs was used for Monte-Carlo simulation of the training data $$y = \frac{2 + 2 X_3}{3\pi} ( \operatorname{arctan}( 20( X_1 - \frac{1}{2} + \frac{X_2}{6})\exp(X_5)) + \frac{\pi}{2}) + \frac{2 + 2 X_4}{3\pi} ( \operatorname{arctan}( 20( X_1 - \frac{1}{2} - \frac{X_2}{6})\exp(X_5)) + \frac{\pi}{2}).$$ The outputs $y$ were computed for uniformly distributed random inputs $X_1, X_2, X_3, X_4, X_5$. The input dependent density distributions were asymmetric and even having multiple peaks. The expectation model was chosen as Kolmogorov-Arnold representation $$y = F\left( X_1, X_2, X_3, X_4, X_5 \right) = \sum_{k=1}^{11} \varPhi^k \left( \sum_{j=1}^{5} f^{kj} \left(X_j\right) \right),$$ where $\varPhi^k$ and $f^{kj}$ are functions determined in training. Approximately 70% of all generated by DDR output samples passed Kolmogorov-Smirnov goodness-of-fit test when they were compared to Monte-Carlo simulations.

6. Practical application

We needed a simple example to show that accurate prediction of probability of stochastic system can lead to a profit. After some research we decided to try sports betting for British Premier League. At first, I explain why and how it is possible to make money by accurate prediction of probabilities.

Assume that bookmaker's estimated probability of a particular outcome is 0.25. The typical betting value in this case will be +280, that means that bettor pass 100 to a bookmaker and in case of success bookmaker returns 100 + 280, otherwise keeps 100. The number +280 assumes 5% commission, which is clear, since each 4 statistical games bring bookmaker 20 units, while bettors provide 400. It is called Dutch booking and 5% is a typical commission. But what happens if actual probability is 0.30 and our model estimated it correctly. In this case statistical monetary gain becomes $0.30 * 280 - 0.70 * 100 = 14$, which is 14% per a bet.

When expected probabilities are above 50%, bookmakers use negative numbers in published bets, like -200 means that bettor is asked to bet 200 against 100.

To assume that bookmakers' models are not accurate enough is very naive. The sports betting industry is a very complex social system with multiple competing groups with opposite interests. Bookmakers compete and trying to lower commission to attract bettors. Bettors are biased and bookmakers have to make some bets more attractive contrary to their models. Certainly, they are very well aware that artificial intelligence can be used for making profit and simply disallow this. Bettors should agree with some arms twisted rules in order to open an account in a system and start betting.

In the matches of British Premier League one team plays at home and another team plays away. There are 20 teams and 380 matches. The bet that we chose is called '1X2', which is 'home win', 'draw' or 'away win'.

That was a quick introduction for those who are new to the subject.

Here is explanation of the concept. Assume that we are trying to predict outcome for the second match of the season 2020-2021, which was Crystal Palace - Southampton. It took place on 09.12.2020 and ended with the score 1:0. We can find some recent history for these two teams in standings for the previous season.

Standings for 2019-2020, British Premier League

The top 17 teams from the previous season 2019-2020 are playing also in 2020-2021, Crystal Palace and Southampton are among them. The bottom 3 are relegated. If we take all results for 2019-2020

and make table holding goal differences for only top 17 teams, we receive the following table:

 L M M C L T W A S B Southampton E N C B W A Liverpool 4 Manchester City 1 Manchester Utd 0 Chelsea -2 Leicester -1 Tottenham 1 Wolve 0 Arsenal 0 Sheffield Utd -1 Burnley 3 Southampton 0 Everton 0 Newcastle 1 Crystal Palace -1 -2 -2 -1 -2 0 0 0 -1 -1 -2 0 1 0 0 1 1 Brighton -2 West Ham 2 Aston Villa -2

The order matches standings table, the scores are replaced by goal differences and only results for two mentioned teams are shown. Zero values are placed conventionally on diagonal elements (it means if playing against self the team must theoretically have a draw). The name attached to the row is the team playing at home and name attached to column is away team. 17 numbers in each row and 17 numbers in each column is good performance characteristics of these two teams, however 34 inputs to a model would be too heigh. We reduce these 17 elements in a row or in a column to 3. This reduction is called feature extraction technique. We compute the sum of all negative numbers (and use its magnitude), the sum of all positive numbers and number of draws, so our input figures for predictive model are the following values: $12, 3, 6, 10, 12, 5$.

The records from the recent season are used for prediction, and the records from 16 prior seasons (totally 16 * 17 * 17 = 4624) are used for training of the model. After processing the prediction, new value replaces the old one in the table, so -2 is replaced by 1 and in this way the data is updated while the new season continues.

The model is an ensemble of 23 Kolmogorov-Arnold representations. It predicts 23 goal differences as real numbers. They are rounded and used as voting in estimation of probabilities for home win, draw or away win. The bet has been chosen according to maximal money gain computed as: $$M = P * B - (1.0 - P) * 100.$$ Success or failure was determined according to actual outcome. Since only top 17 teams participated in modelling, only 272 games were used for prediction out of 380. Typical average gain is between 15 and 20%, which is near 5000 points for a season. The data is obtained from publicly available source OddsPortal.

The code and data is published for those who wish to research this topic deeper PremierLeague7 . Below is an example of program printout. Interesting detail that the model placed bets on underestimated underdogs. The deterministic models are the models of expectations, and they usually point to a favorite, but since it is a preference of many people, bookmakers usually reduce the return and even 60% of right predictions may not be enough for making profit. In our case 78 right predictions out of 272 already provide profit near 20%. However, betting on underdogs in all cases lead to a money loss, same as betting always on favorites.
Prediction for British Premier League
1. Crystal Palace-Southampton, 9/12/2020 2:00:00 PM, 1:0, 1X2 = 209,225,146, right prediction
2. West Ham-Newcastle, 9/12/2020 7:00:00 PM, 0:2, 1X2 = 100,260,282, right prediction
3. Tottenham-Everton, 9/13/2020 3:30:00 PM, 0:1, 1X2 = 106,243,283, wrong prediction
4. Sheffield Utd-Wolves, 9/14/2020 5:00:00 PM, 0:2, 1X2 = 227,189,161, wrong prediction
5. Brighton-Chelsea, 9/14/2020 7:15:00 PM, 1:3, 1X2 = 499,342,-179, wrong prediction
6. Manchester Utd-Crystal Palace, 9/19/2020 4:30:00 PM, 1:3, 1X2 = -270,409,794, right prediction
7. Arsenal-West Ham, 9/19/2020 7:00:00 PM, 2:1, 1X2 = -200,351,570, wrong prediction
8. Southampton-Tottenham, 9/20/2020 11:00:00 AM, 2:5, 1X2 = 237,240,125, right prediction
9. Newcastle-Brighton, 9/20/2020 1:00:00 PM, 0:3, 1X2 = 164,219,191, wrong prediction
10. Chelsea-Liverpool, 9/20/2020 3:30:00 PM, 0:2, 1X2 = 243,285,106, wrong prediction
11. Leicester-Burnley, 9/20/2020 6:00:00 PM, 4:2, 1X2 = -182,322,542, right prediction
12. Aston Villa-Sheffield Utd, 9/21/2020 5:00:00 PM, 1:0, 1X2 = 146,220,217, right prediction
13. Wolves-Manchester City, 9/21/2020 7:15:00 PM, 1:3, 1X2 = 592,359,-208, wrong prediction
14. Brighton-Manchester Utd, 9/26/2020 11:30:00 AM, 2:3, 1X2 = 442,320,-159, wrong prediction
15. Crystal Palace-Everton, 9/26/2020 2:00:00 PM, 1:2, 1X2 = 254,235,120, wrong prediction
16. Burnley-Southampton, 9/26/2020 7:00:00 PM, 0:1, 1X2 = 225,241,127, wrong prediction
17. Tottenham-Newcastle, 9/27/2020 1:00:00 PM, 1:1, 1X2 = -238,384,668, wrong prediction
18. Manchester City-Leicester, 9/27/2020 3:30:00 PM, 2:5, 1X2 = -312,488,831, right prediction
19. West Ham-Wolves, 9/27/2020 6:00:00 PM, 4:0, 1X2 = 234,231,127, wrong prediction
20. Liverpool-Arsenal, 9/28/2020 7:00:00 PM, 3:1, 1X2 = -204,413,486, wrong prediction
21. Chelsea-Crystal Palace, 10/3/2020 11:30:00 AM, 4:0, 1X2 = -192,337,557, wrong prediction
22. Everton-Brighton, 10/3/2020 2:00:00 PM, 4:2, 1X2 = -127,277,371, wrong prediction
23. Newcastle-Burnley, 10/3/2020 7:00:00 PM, 3:1, 1X2 = 141,227,216, right prediction
24. Leicester-West Ham, 10/4/2020 11:00:00 AM, 0:3, 1X2 = -120,295,323, wrong prediction
25. Arsenal-Sheffield Utd, 10/4/2020 1:00:00 PM, 2:1, 1X2 = -200,336,613, wrong prediction
26. Manchester Utd-Tottenham, 10/4/2020 3:30:00 PM, 1:6, 1X2 = 106,265,259, right prediction
27. Aston Villa-Liverpool, 10/4/2020 6:15:00 PM, 7:2, 1X2 = 579,392,-217, right prediction
28. Everton-Liverpool, 10/17/2020 11:30:00 AM, 2:2, 1X2 = 321,322,-127, wrong prediction
29. Chelsea-Southampton, 10/17/2020 2:00:00 PM, 3:3, 1X2 = -172,353,449, wrong prediction
30. Manchester City-Arsenal, 10/17/2020 4:30:00 PM, 1:0, 1X2 = -185,379,467, wrong prediction
31. Newcastle-Manchester Utd, 10/17/2020 7:00:00 PM, 1:4, 1X2 = 363,319,-139, wrong prediction
32. Crystal Palace-Brighton, 10/18/2020 1:00:00 PM, 1:1, 1X2 = 212,224,146, wrong prediction
33. Tottenham-West Ham, 10/18/2020 3:30:00 PM, 3:3, 1X2 = -156,320,442, wrong prediction
34. Leicester-Aston Villa, 10/18/2020 6:15:00 PM, 0:1, 1X2 = 138,261,196, wrong prediction
35. West Ham-Manchester City, 10/24/2020 11:30:00 AM, 1:1, 1X2 = 575,415,-227, wrong prediction
36. Manchester Utd-Chelsea, 10/24/2020 4:30:00 PM, 0:0, 1X2 = 163,249,173, wrong prediction
37. Liverpool-Sheffield Utd, 10/24/2020 7:00:00 PM, 2:1, 1X2 = -455,631,1221, wrong prediction
38. Southampton-Everton, 10/25/2020 2:00:00 PM, 2:0, 1X2 = 206,259,133, right prediction
39. Wolves-Newcastle, 10/25/2020 4:30:00 PM, 1:1, 1X2 = -120,248,392, wrong prediction
40. Arsenal-Leicester, 10/25/2020 7:15:00 PM, 0:1, 1X2 = -105,256,316, right prediction
41. Burnley-Tottenham, 10/26/2020 8:00:00 PM, 0:1, 1X2 = 473,336,-172, wrong prediction
42. Wolves-Crystal Palace, 10/30/2020 8:00:00 PM, 2:0, 1X2 = 106,216,330, wrong prediction
43. Sheffield Utd-Manchester City, 10/31/2020 12:30:00 PM, 0:1, 1X2 = 981,503,-345, wrong prediction
44. Burnley-Chelsea, 10/31/2020 3:00:00 PM, 0:3, 1X2 = 463,326,-167, wrong prediction
45. Liverpool-West Ham, 10/31/2020 5:30:00 PM, 2:1, 1X2 = -233,419,611, wrong prediction
46. Aston Villa-Southampton, 11/1/2020 11:00:00 AM, 3:4, 1X2 = 159,258,171, right prediction
47. Newcastle-Everton, 11/1/2020 1:00:00 PM, 2:1, 1X2 = 240,235,127, right prediction
48. Manchester Utd-Arsenal, 11/1/2020 3:30:00 PM, 0:1, 1X2 = 100,262,291, right prediction
49. Tottenham-Brighton, 11/1/2020 6:15:00 PM, 2:1, 1X2 = -169,326,484, wrong prediction
50. Brighton-Burnley, 11/6/2020 4:30:00 PM, 0:0, 1X2 = 102,242,319, wrong prediction
51. Southampton-Newcastle, 11/6/2020 7:00:00 PM, 2:0, 1X2 = 114,248,252, wrong prediction
52. Everton-Manchester Utd, 11/7/2020 11:30:00 AM, 1:3, 1X2 = 219,266,123, wrong prediction
53. Chelsea-Sheffield Utd, 11/7/2020 4:30:00 PM, 4:1, 1X2 = -263,401,776, wrong prediction
54. Leicester-Wolves, 11/8/2020 1:00:00 PM, 1:0, 1X2 = 136,218,237, wrong prediction
55. Manchester City-Liverpool, 11/8/2020 3:30:00 PM, 1:1, 1X2 = -108,321,264, wrong prediction
56. Arsenal-Aston Villa, 11/8/2020 6:15:00 PM, 0:3, 1X2 = -154,337,401, wrong prediction
57. Newcastle-Chelsea, 11/21/2020 11:30:00 AM, 0:2, 1X2 = 612,379,-217, wrong prediction
58. Aston Villa-Brighton, 11/21/2020 2:00:00 PM, 1:2, 1X2 = 129,254,213, right prediction
59. Tottenham-Manchester City, 11/21/2020 4:30:00 PM, 2:0, 1X2 = 320,313,-123, right prediction
60. Sheffield Utd-West Ham, 11/22/2020 1:00:00 PM, 0:1, 1X2 = 213,221,147, wrong prediction
61. Liverpool-Leicester, 11/22/2020 6:15:00 PM, 3:0, 1X2 = -127,312,334, wrong prediction
62. Burnley-Crystal Palace, 11/23/2020 4:30:00 PM, 1:0, 1X2 = 168,212,193, right prediction
63. Wolves-Southampton, 11/23/2020 7:00:00 PM, 1:1, 1X2 = 135,225,231, wrong prediction
64. Crystal Palace-Newcastle, 11/27/2020 7:00:00 PM, 0:2, 1X2 = 116,220,285, wrong prediction
65. Brighton-Liverpool, 11/28/2020 11:30:00 AM, 1:1, 1X2 = 393,325,-149, wrong prediction
66. Manchester City-Burnley, 11/28/2020 2:00:00 PM, 5:0, 1X2 = -833,921,1926, wrong prediction
67. Southampton-Manchester Utd, 11/29/2020 1:00:00 PM, 2:3, 1X2 = 289,274,-105, wrong prediction
68. Chelsea-Tottenham, 11/29/2020 3:30:00 PM, 0:0, 1X2 = 100,267,277, wrong prediction
69. Arsenal-Wolves, 11/29/2020 6:15:00 PM, 1:2, 1X2 = 108,231,289, right prediction
70. West Ham-Aston Villa, 11/30/2020 7:00:00 PM, 2:1, 1X2 = 135,252,204, right prediction
71. Burnley-Everton, 12/5/2020 11:30:00 AM, 1:1, 1X2 = 278,257,104, wrong prediction
72. West Ham-Manchester Utd, 12/5/2020 4:30:00 PM, 1:3, 1X2 = 243,250,118, wrong prediction
73. Sheffield Utd-Leicester, 12/6/2020 1:15:00 PM, 1:2, 1X2 = 309,256,-104, wrong prediction
74. Tottenham-Arsenal, 12/6/2020 3:30:00 PM, 2:0, 1X2 = 121,250,237, right prediction
75. Liverpool-Wolves, 12/6/2020 6:15:00 PM, 4:0, 1X2 = -169,334,463, wrong prediction
76. Brighton-Southampton, 12/7/2020 7:00:00 PM, 1:2, 1X2 = 145,240,200, right prediction
77. Wolves-Aston Villa, 12/12/2020 11:30:00 AM, 0:1, 1X2 = 160,227,191, wrong prediction
78. Manchester Utd-Manchester City, 12/12/2020 4:30:00 PM, 0:0, 1X2 = 363,325,-139, wrong prediction
79. Everton-Chelsea, 12/12/2020 7:00:00 PM, 1:0, 1X2 = 380,329,-147, right prediction
80. Southampton-Sheffield Utd, 12/13/2020 11:00:00 AM, 3:0, 1X2 = -154,301,448, wrong prediction
81. Crystal Palace-Tottenham, 12/13/2020 1:15:00 PM, 1:1, 1X2 = 323,283,-118, wrong prediction
82. Leicester-Brighton, 12/13/2020 6:15:00 PM, 3:0, 1X2 = 104,254,280, wrong prediction
83. Arsenal-Burnley, 12/13/2020 6:15:00 PM, 0:1, 1X2 = -222,372,641, right prediction
84. Wolves-Chelsea, 12/15/2020 5:00:00 PM, 2:1, 1X2 = 442,281,-145, right prediction
85. Arsenal-Southampton, 12/16/2020 5:00:00 PM, 1:1, 1X2 = 118,254,241, wrong prediction
86. Leicester-Everton, 12/16/2020 5:00:00 PM, 0:2, 1X2 = 112,254,252, wrong prediction
87. West Ham-Crystal Palace, 12/16/2020 7:00:00 PM, 1:1, 1X2 = 116,242,254, wrong prediction
88. Liverpool-Tottenham, 12/16/2020 7:00:00 PM, 2:1, 1X2 = -120,296,326, wrong prediction
89. Aston Villa-Burnley, 12/17/2020 5:00:00 PM, 0:0, 1X2 = -118,279,332, wrong prediction
90. Sheffield Utd-Manchester Utd, 12/17/2020 7:00:00 PM, 2:3, 1X2 = 638,376,-222, wrong prediction
91. Crystal Palace-Liverpool, 12/19/2020 11:30:00 AM, 0:7, 1X2 = 437,312,-156, wrong prediction
92. Southampton-Manchester City, 12/19/2020 2:00:00 PM, 0:1, 1X2 = 512,368,-192, wrong prediction
93. Everton-Arsenal, 12/19/2020 4:30:00 PM, 2:1, 1X2 = 169,245,167, right prediction
94. Brighton-Sheffield Utd, 12/20/2020 11:00:00 AM, 1:1, 1X2 = -112,247,358, wrong prediction
95. Tottenham-Leicester, 12/20/2020 1:15:00 PM, 0:2, 1X2 = 110,250,263, right prediction
96. Burnley-Wolves, 12/21/2020 4:30:00 PM, 2:1, 1X2 = 249,209,135, right prediction
97. Chelsea-West Ham, 12/21/2020 7:00:00 PM, 3:0, 1X2 = -172,337,479, right prediction
98. Leicester-Manchester Utd, 12/26/2020 11:30:00 AM, 2:2, 1X2 = 200,259,134, wrong prediction
99. Aston Villa-Crystal Palace, 12/26/2020 2:00:00 PM, 3:0, 1X2 = -122,288,334, wrong prediction
100. Arsenal-Chelsea, 12/26/2020 4:30:00 PM, 3:1, 1X2 = 384,292,-133, right prediction
101. Sheffield Utd-Everton, 12/26/2020 7:00:00 PM, 0:1, 1X2 = 242,231,125, wrong prediction
102. Manchester City-Newcastle, 12/26/2020 7:00:00 PM, 2:0, 1X2 = -769,860,1969, wrong prediction
103. West Ham-Brighton, 12/27/2020 1:15:00 PM, 2:2, 1X2 = 137,233,218, wrong prediction
104. Wolves-Tottenham, 12/27/2020 6:15:00 PM, 1:1, 1X2 = 261,235,118, wrong prediction
105. Crystal Palace-Leicester, 12/28/2020 2:00:00 PM, 1:1, 1X2 = 239,243,122, wrong prediction
106. Chelsea-Aston Villa, 12/28/2020 4:30:00 PM, 1:1, 1X2 = -123,301,329, wrong prediction
107. Southampton-West Ham, 12/29/2020 5:00:00 PM, 0:0, 1X2 = 104,259,275, wrong prediction
108. Burnley-Sheffield Utd, 12/29/2020 5:00:00 PM, 1:0, 1X2 = 139,220,227, right prediction
109. Brighton-Arsenal, 12/29/2020 5:00:00 PM, 0:1, 1X2 = 271,249,108, wrong prediction
110. Manchester Utd-Wolves, 12/29/2020 7:00:00 PM, 1:0, 1X2 = -182,330,528, wrong prediction
111. Newcastle-Liverpool, 12/30/2020 7:00:00 PM, 0:0, 1X2 = 963,504,-357, wrong prediction
112. Everton-West Ham, 1/1/2021 4:30:00 PM, 0:1, 1X2 = 122,249,234, wrong prediction
113. Manchester Utd-Aston Villa, 1/1/2021 7:00:00 PM, 2:1, 1X2 = -143,316,380, wrong prediction
114. Crystal Palace-Sheffield Utd, 1/2/2021 2:00:00 PM, 2:0, 1X2 = 108,227,297, wrong prediction
115. Brighton-Wolves, 1/2/2021 4:30:00 PM, 3:3, 1X2 = 184,206,179, wrong prediction
116. Newcastle-Leicester, 1/3/2021 1:15:00 PM, 1:2, 1X2 = 511,309,-169, wrong prediction
117. Chelsea-Manchester City, 1/3/2021 3:30:00 PM, 1:3, 1X2 = 240,263,114, wrong prediction
118. Southampton-Liverpool, 1/4/2021 7:00:00 PM, 1:0, 1X2 = 505,384,-200, right prediction
119. Sheffield Utd-Newcastle, 1/12/2021 5:00:00 PM, 1:0, 1X2 = 135,214,242, right prediction
120. Wolves-Everton, 1/12/2021 7:15:00 PM, 1:2, 1X2 = 162,194,218, right prediction
121. Burnley-Manchester Utd, 1/12/2021 7:15:00 PM, 0:1, 1X2 = 692,391,-238, wrong prediction
122. Manchester City-Brighton, 1/13/2021 5:00:00 PM, 1:0, 1X2 = -588,685,1612, wrong prediction
123. Arsenal-Crystal Palace, 1/14/2021 7:00:00 PM, 0:0, 1X2 = -145,285,440, wrong prediction
124. West Ham-Burnley, 1/16/2021 2:00:00 PM, 1:0, 1X2 = -128,269,394, wrong prediction
125. Leicester-Southampton, 1/16/2021 7:00:00 PM, 2:0, 1X2 = -141,290,420, wrong prediction
126. Sheffield Utd-Tottenham, 1/17/2021 1:00:00 PM, 1:3, 1X2 = 384,262,-123, wrong prediction
127. Liverpool-Manchester Utd, 1/17/2021 3:30:00 PM, 0:0, 1X2 = -105,288,278, wrong prediction
128. Manchester City-Crystal Palace, 1/17/2021 6:15:00 PM, 4:0, 1X2 = -556,661,1591, wrong prediction
129. Arsenal-Newcastle, 1/18/2021 7:00:00 PM, 3:0, 1X2 = -233,378,686, wrong prediction
130. Leicester-Chelsea, 1/19/2021 7:15:00 PM, 2:0, 1X2 = 181,249,154, right prediction
131. Manchester City-Aston Villa, 1/20/2021 5:00:00 PM, 2:0, 1X2 = -323,488,883, wrong prediction
132. Liverpool-Burnley, 1/21/2021 7:00:00 PM, 0:1, 1X2 = -312,459,911, right prediction
133. Aston Villa-Newcastle, 1/23/2021 7:00:00 PM, 2:0, 1X2 = -196,363,529, wrong prediction
134. Crystal Palace-West Ham, 1/26/2021 5:00:00 PM, 2:3, 1X2 = 256,236,118, wrong prediction
135. Southampton-Arsenal, 1/26/2021 7:15:00 PM, 1:3, 1X2 = 256,271,106, wrong prediction
136. Chelsea-Wolves, 1/27/2021 5:00:00 PM, 0:0, 1X2 = -154,286,488, wrong prediction
137. Burnley-Aston Villa, 1/27/2021 5:00:00 PM, 3:2, 1X2 = 342,275,-120, right prediction
138. Manchester Utd-Sheffield Utd, 1/27/2021 7:15:00 PM, 1:2, 1X2 = -357,501,998, right prediction
139. Everton-Leicester, 1/27/2021 7:15:00 PM, 1:1, 1X2 = 220,229,139, wrong prediction
140. Tottenham-Liverpool, 1/28/2021 7:00:00 PM, 1:3, 1X2 = 261,285,100, wrong prediction
141. Everton-Newcastle, 1/30/2021 11:30:00 AM, 0:2, 1X2 = -175,311,548, right prediction
142. Crystal Palace-Wolves, 1/30/2021 2:00:00 PM, 1:0, 1X2 = 195,213,164, wrong prediction
143. Manchester City-Sheffield Utd, 1/30/2021 2:00:00 PM, 1:0, 1X2 = -556,641,1705, wrong prediction
144. Arsenal-Manchester Utd, 1/30/2021 4:30:00 PM, 0:0, 1X2 = 252,257,112, wrong prediction
145. Southampton-Aston Villa, 1/30/2021 7:00:00 PM, 0:1, 1X2 = 227,270,118, wrong prediction
146. Chelsea-Burnley, 1/31/2021 11:00:00 AM, 2:0, 1X2 = -303,430,919, wrong prediction
147. West Ham-Liverpool, 1/31/2021 3:30:00 PM, 1:3, 1X2 = 252,273,106, wrong prediction
148. Brighton-Tottenham, 1/31/2021 6:15:00 PM, 1:0, 1X2 = 227,238,131, right prediction
149. Wolves-Arsenal, 2/2/2021 5:00:00 PM, 2:1, 1X2 = 267,229,117, right prediction
150. Manchester Utd-Southampton, 2/2/2021 7:15:00 PM, 9:0, 1X2 = -222,386,600, wrong prediction
151. Newcastle-Crystal Palace, 2/2/2021 7:15:00 PM, 1:2, 1X2 = 195,231,154, wrong prediction
152. Burnley-Manchester City, 2/3/2021 5:00:00 PM, 0:2, 1X2 = 1514,606,-500, wrong prediction
153. Liverpool-Brighton, 2/3/2021 7:15:00 PM, 0:1, 1X2 = -200,363,556, right prediction
154. Aston Villa-West Ham, 2/3/2021 7:15:00 PM, 1:3, 1X2 = 136,248,208, right prediction
155. Tottenham-Chelsea, 2/4/2021 7:00:00 PM, 0:1, 1X2 = 304,250,-101, wrong prediction
156. Aston Villa-Arsenal, 2/6/2021 11:30:00 AM, 1:0, 1X2 = 198,250,142, right prediction
157. Burnley-Brighton, 2/6/2021 2:00:00 PM, 1:1, 1X2 = 267,220,121, wrong prediction
158. Newcastle-Southampton, 2/6/2021 2:00:00 PM, 3:2, 1X2 = 231,250,122, right prediction
159. Manchester Utd-Everton, 2/6/2021 7:00:00 PM, 3:3, 1X2 = -161,318,459, wrong prediction
160. Wolves-Leicester, 2/7/2021 1:00:00 PM, 0:0, 1X2 = 240,227,129, wrong prediction
161. Liverpool-Manchester City, 2/7/2021 3:30:00 PM, 1:4, 1X2 = 217,266,125, wrong prediction
162. Sheffield Utd-Chelsea, 2/7/2021 6:15:00 PM, 1:2, 1X2 = 610,332,-200, wrong prediction
163. Leicester-Liverpool, 2/13/2021 11:30:00 AM, 3:1, 1X2 = 280,289,-104, right prediction
164. Crystal Palace-Burnley, 2/13/2021 2:00:00 PM, 0:3, 1X2 = 184,215,174, wrong prediction
165. Manchester City-Tottenham, 2/13/2021 4:30:00 PM, 3:0, 1X2 = -294,478,775, wrong prediction
166. Brighton-Aston Villa, 2/13/2021 7:00:00 PM, 0:0, 1X2 = 191,237,152, wrong prediction
167. Southampton-Wolves, 2/14/2021 11:00:00 AM, 1:2, 1X2 = 127,227,249, right prediction
168. West Ham-Sheffield Utd, 2/15/2021 5:00:00 PM, 3:0, 1X2 = 102,231,313, right prediction
169. Chelsea-Newcastle, 2/15/2021 7:00:00 PM, 2:0, 1X2 = -345,487,1008, wrong prediction
170. Everton-Manchester City, 2/17/2021 7:15:00 PM, 1:3, 1X2 = 1009,487,-345, wrong prediction
171. Southampton-Chelsea, 2/20/2021 11:30:00 AM, 1:1, 1X2 = 376,279,-128, wrong prediction
172. Liverpool-Everton, 2/20/2021 4:30:00 PM, 0:2, 1X2 = -263,436,702, right prediction
173. West Ham-Tottenham, 2/21/2021 11:00:00 AM, 2:1, 1X2 = 206,244,139, wrong prediction
174. Aston Villa-Leicester, 2/21/2021 1:05:00 PM, 1:2, 1X2 = 273,271,100, wrong prediction
175. Arsenal-Manchester City, 2/21/2021 3:30:00 PM, 0:1, 1X2 = 592,359,-208, wrong prediction
176. Manchester Utd-Newcastle, 2/21/2021 6:00:00 PM, 3:1, 1X2 = -294,440,875, wrong prediction
177. Brighton-Crystal Palace, 2/22/2021 7:00:00 PM, 1:2, 1X2 = -130,249,440, right prediction
178. Manchester City-West Ham, 2/27/2021 11:30:00 AM, 2:1, 1X2 = -370,532,1022, wrong prediction
179. Newcastle-Wolves, 2/27/2021 7:00:00 PM, 1:1, 1X2 = 269,215,124, wrong prediction
180. Leicester-Arsenal, 2/28/2021 11:00:00 AM, 1:3, 1X2 = 137,236,217, wrong prediction
181. Tottenham-Burnley, 2/28/2021 1:00:00 PM, 4:0, 1X2 = -200,334,626, wrong prediction
182. Chelsea-Manchester Utd, 2/28/2021 3:30:00 PM, 0:0, 1X2 = 138,237,218, wrong prediction
183. Sheffield Utd-Liverpool, 2/28/2021 6:15:00 PM, 0:2, 1X2 = 706,437,-270, wrong prediction
184. Everton-Southampton, 3/1/2021 7:00:00 PM, 1:0, 1X2 = 114,250,250, right prediction
185. Manchester City-Wolves, 3/2/2021 7:00:00 PM, 4:1, 1X2 = -455,557,1374, wrong prediction
186. Sheffield Utd-Aston Villa, 3/3/2021 5:00:00 PM, 1:0, 1X2 = 264,244,112, right prediction
187. Burnley-Leicester, 3/3/2021 5:00:00 PM, 1:1, 1X2 = 289,216,116, wrong prediction
188. Crystal Palace-Manchester Utd, 3/3/2021 7:15:00 PM, 0:0, 1X2 = 662,368,-222, wrong prediction
189. Liverpool-Chelsea, 3/4/2021 7:15:00 PM, 0:1, 1X2 = 121,252,233, wrong prediction
190. Burnley-Arsenal, 3/6/2021 11:30:00 AM, 1:1, 1X2 = 394,266,-128, wrong prediction
191. Sheffield Utd-Southampton, 3/6/2021 2:00:00 PM, 0:2, 1X2 = 281,238,110, wrong prediction
192. Aston Villa-Wolves, 3/6/2021 4:30:00 PM, 0:0, 1X2 = 162,216,194, wrong prediction
193. Brighton-Leicester, 3/6/2021 7:00:00 PM, 1:2, 1X2 = 154,220,204, right prediction
194. Manchester City-Manchester Utd, 3/7/2021 3:30:00 PM, 0:2, 1X2 = -200,346,579, right prediction
195. Tottenham-Crystal Palace, 3/7/2021 6:15:00 PM, 4:1, 1X2 = -185,316,568, wrong prediction
196. Chelsea-Everton, 3/8/2021 5:00:00 PM, 2:0, 1X2 = -159,293,512, wrong prediction
197. Manchester City-Southampton, 3/10/2021 5:00:00 PM, 5:2, 1X2 = -556,644,1648, wrong prediction
198. Newcastle-Aston Villa, 3/12/2021 7:00:00 PM, 1:1, 1X2 = 272,236,112, wrong prediction
199. Everton-Burnley, 3/13/2021 4:30:00 PM, 1:2, 1X2 = 100,234,326, wrong prediction
200. Southampton-Brighton, 3/14/2021 12:00:00 PM, 1:2, 1X2 = 223,221,141, right prediction
201. Leicester-Sheffield Utd, 3/14/2021 2:00:00 PM, 5:0, 1X2 = -189,307,646, wrong prediction
202. Arsenal-Tottenham, 3/14/2021 4:30:00 PM, 2:1, 1X2 = 167,237,177, wrong prediction
203. Manchester Utd-West Ham, 3/14/2021 7:15:00 PM, 1:0, 1X2 = -123,261,390, wrong prediction
204. Wolves-Liverpool, 3/15/2021 8:00:00 PM, 0:1, 1X2 = 476,294,-156, wrong prediction
205. Brighton-Newcastle, 3/20/2021 8:00:00 PM, 3:0, 1X2 = -139,258,474, wrong prediction
206. West Ham-Arsenal, 3/21/2021 3:00:00 PM, 3:3, 1X2 = 254,250,114, wrong prediction
207. Aston Villa-Tottenham, 3/21/2021 7:30:00 PM, 0:2, 1X2 = 211,245,137, wrong prediction
208. Leicester-Manchester City, 4/3/2021 4:30:00 PM, 0:2, 1X2 = 442,298,-147, wrong prediction
209. Arsenal-Liverpool, 4/3/2021 7:00:00 PM, 0:3, 1X2 = 190,264,140, right prediction
210. Southampton-Burnley, 4/4/2021 11:00:00 AM, 3:2, 1X2 = 102,241,304, wrong prediction
211. Newcastle-Tottenham, 4/4/2021 1:05:00 PM, 2:2, 1X2 = 448,289,-147, wrong prediction
212. Manchester Utd-Brighton, 4/4/2021 6:30:00 PM, 2:1, 1X2 = -152,295,450, wrong prediction
213. Everton-Crystal Palace, 4/5/2021 5:00:00 PM, 1:1, 1X2 = -119,248,384, wrong prediction
214. Wolves-West Ham, 4/5/2021 7:15:00 PM, 2:3, 1X2 = 189,219,164, wrong prediction
215. Liverpool-Aston Villa, 4/10/2021 2:00:00 PM, 2:1, 1X2 = -213,373,611, wrong prediction
216. Crystal Palace-Chelsea, 4/10/2021 4:30:00 PM, 1:4, 1X2 = 652,325,-200, wrong prediction
217. Burnley-Newcastle, 4/11/2021 11:00:00 AM, 1:2, 1X2 = 127,234,236, wrong prediction
218. West Ham-Leicester, 4/11/2021 1:05:00 PM, 3:2, 1X2 = 221,229,137, right prediction
219. Tottenham-Manchester Utd, 4/11/2021 3:30:00 PM, 1:3, 1X2 = 195,257,141, wrong prediction
220. Sheffield Utd-Arsenal, 4/11/2021 6:00:00 PM, 0:3, 1X2 = 463,288,-152, wrong prediction
221. Brighton-Everton, 4/12/2021 7:15:00 PM, 0:0, 1X2 = 114,249,252, wrong prediction
222. Everton-Tottenham, 4/16/2021 7:00:00 PM, 2:2, 1X2 = 254,249,114, wrong prediction
223. Newcastle-West Ham, 4/17/2021 11:30:00 AM, 3:2, 1X2 = 246,242,120, right prediction
224. Wolves-Sheffield Utd, 4/17/2021 7:15:00 PM, 1:0, 1X2 = -127,246,430, wrong prediction
225. Manchester Utd-Burnley, 4/18/2021 3:00:00 PM, 3:1, 1X2 = -278,428,777, wrong prediction
226. Chelsea-Brighton, 4/20/2021 7:15:00 PM, 0:0, 1X2 = -147,274,476, wrong prediction
227. Tottenham-Southampton, 4/21/2021 5:00:00 PM, 2:1, 1X2 = -116,283,326, right prediction
228. Aston Villa-Manchester City, 4/21/2021 7:15:00 PM, 1:2, 1X2 = 883,436,-294, wrong prediction
229. Arsenal-Everton, 4/23/2021 7:00:00 PM, 0:1, 1X2 = 104,259,277, right prediction
230. Liverpool-Newcastle, 4/24/2021 11:30:00 AM, 1:1, 1X2 = -455,631,1170, wrong prediction
231. West Ham-Chelsea, 4/24/2021 4:30:00 PM, 0:1, 1X2 = 421,299,-145, wrong prediction
232. Sheffield Utd-Brighton, 4/24/2021 7:00:00 PM, 1:0, 1X2 = 535,298,-167, right prediction
233. Wolves-Burnley, 4/25/2021 11:00:00 AM, 0:4, 1X2 = 135,212,248, wrong prediction
234. Leicester-Crystal Palace, 4/26/2021 7:00:00 PM, 2:1, 1X2 = -233,368,714, wrong prediction
235. Southampton-Leicester, 4/30/2021 7:00:00 PM, 1:1, 1X2 = 316,281,-114, wrong prediction
236. Crystal Palace-Manchester City, 5/1/2021 11:30:00 AM, 0:2, 1X2 = 901,447,-294, wrong prediction
237. Everton-Aston Villa, 5/1/2021 7:00:00 PM, 1:2, 1X2 = -103,278,281, right prediction
238. Newcastle-Arsenal, 5/2/2021 1:00:00 PM, 0:2, 1X2 = 281,266,100, wrong prediction
239. Tottenham-Sheffield Utd, 5/2/2021 6:15:00 PM, 4:0, 1X2 = -303,450,897, wrong prediction
240. Burnley-West Ham, 5/3/2021 7:15:00 PM, 1:2, 1X2 = 204,257,134, wrong prediction
241. Leicester-Newcastle, 5/7/2021 7:00:00 PM, 2:4, 1X2 = -250,392,765, right prediction
242. Sheffield Utd-Crystal Palace, 5/8/2021 2:00:00 PM, 0:2, 1X2 = 197,222,159, wrong prediction
243. Manchester City-Chelsea, 5/8/2021 4:30:00 PM, 1:2, 1X2 = 104,239,305, right prediction
244. Liverpool-Southampton, 5/8/2021 7:15:00 PM, 2:0, 1X2 = -323,500,859, wrong prediction
245. Wolves-Brighton, 5/9/2021 11:00:00 AM, 2:1, 1X2 = 292,231,108, right prediction
246. Aston Villa-Manchester Utd, 5/9/2021 1:05:00 PM, 1:3, 1X2 = 348,300,-127, wrong prediction
247. West Ham-Everton, 5/9/2021 3:30:00 PM, 0:1, 1X2 = 114,254,248, right prediction
248. Manchester Utd-Leicester, 5/11/2021 5:00:00 PM, 1:2, 1X2 = 273,257,108, wrong prediction
249. Southampton-Crystal Palace, 5/11/2021 7:15:00 PM, 3:1, 1X2 = -112,282,309, right prediction
250. Chelsea-Arsenal, 5/12/2021 7:15:00 PM, 0:1, 1X2 = -106,242,342, right prediction
251. Aston Villa-Everton, 5/13/2021 5:00:00 PM, 0:0, 1X2 = 202,234,147, wrong prediction
252. Manchester Utd-Liverpool, 5/13/2021 7:15:00 PM, 2:4, 1X2 = 179,274,145, right prediction
253. Newcastle-Manchester City, 5/14/2021 7:00:00 PM, 3:4, 1X2 = 778,484,-303, wrong prediction
254. Brighton-West Ham, 5/15/2021 7:00:00 PM, 1:1, 1X2 = 254,258,110, wrong prediction
255. Crystal Palace-Aston Villa, 5/16/2021 11:00:00 AM, 3:2, 1X2 = 213,252,129, right prediction
256. Tottenham-Wolves, 5/16/2021 1:05:00 PM, 2:0, 1X2 = -182,353,492, wrong prediction
257. Everton-Sheffield Utd, 5/16/2021 6:00:00 PM, 0:1, 1X2 = -278,416,809, right prediction
258. Brighton-Manchester City, 5/18/2021 6:00:00 PM, 3:2, 1X2 = 631,368,-217, right prediction
259. Chelsea-Leicester, 5/18/2021 7:15:00 PM, 2:1, 1X2 = -143,286,434, wrong prediction
260. Tottenham-Aston Villa, 5/19/2021 5:00:00 PM, 1:2, 1X2 = -161,350,423, right prediction
261. Newcastle-Sheffield Utd, 5/19/2021 5:00:00 PM, 1:0, 1X2 = -119,276,338, wrong prediction
262. Everton-Wolves, 5/19/2021 5:00:00 PM, 1:0, 1X2 = -127,272,386, wrong prediction
263. Crystal Palace-Arsenal, 5/19/2021 6:00:00 PM, 1:3, 1X2 = 484,312,-164, wrong prediction
264. Burnley-Liverpool, 5/19/2021 7:15:00 PM, 0:3, 1X2 = 877,531,-345, wrong prediction
265. Aston Villa-Chelsea, 5/23/2021 3:00:00 PM, 2:1, 1X2 = 598,388,-217, right prediction
266. Leicester-Tottenham, 5/23/2021 3:00:00 PM, 2:4, 1X2 = -123,324,313, right prediction
267. Wolves-Manchester Utd, 5/23/2021 3:00:00 PM, 1:2, 1X2 = 136,229,225, right prediction
268. Manchester City-Everton, 5/23/2021 3:00:00 PM, 5:0, 1X2 = -333,520,872, wrong prediction
269. Sheffield Utd-Burnley, 5/23/2021 3:00:00 PM, 1:0, 1X2 = 183,250,154, right prediction
270. West Ham-Southampton, 5/23/2021 3:00:00 PM, 3:0, 1X2 = -127,287,359, right prediction
271. Liverpool-Crystal Palace, 5/23/2021 3:00:00 PM, 2:0, 1X2 = -625,771,1567, wrong prediction
272. Arsenal-Brighton, 5/23/2021 3:00:00 PM, 2:0, 1X2 = -145,320,394, wrong prediction

Total bets 272
Right predictions 78
Total betting amount $27200,$100 per game
The ending balance, the amount obtained or lost (lost when negative) \$5462.32
Winning to betting amount ratio 0.20