Foundations of Sports Betting - Poisson & Inverse Poisson — Transcript

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1. 0:00My son Euan averages half a goal per
2. 0:02game for his school football team. So
3. 0:04what are the odds of him scoring in his
4. 0:06very next match? They're not 50/50.
5. 0:09That's a common misconception. We take
6. 0:11his average of 0.5 and we use a pluson
7. 0:14probability distribution to arrive at
8. 0:1639%
9. 0:186 to four fractional odds. But what if
10. 0:20we want to go the other way? In sports
11. 0:23betting and advanced sports betting we
12. 0:25often want to start with this
13. 0:26probability and work out what his
14. 0:28average was. That's an inverse poson
15. 0:31probability distribution and I'll show
16. 0:34you why both of those are very useful
17. 0:38processes when it comes to profitable
18. 0:40betting. My name is Tom Brownley from
19. 0:42bookiebashing.net and in these videos we
20. 0:45look at the edges and angles of
21. 0:47profitable betting. Give a man a fish
22. 0:50and he'll eat for a day. But teach a man
23. 0:52to fish and Simeon Denny who in 1837
24. 0:58wrote a paper
25. 1:00probabilities judgments on materivil
26. 1:06and he was looking at how unfair the
27. 1:09French court system was. Look, it's 19th
28. 1:12century French courts. You're pretty
29. 1:14lucky if this is the least of your
30. 1:17problems. But he had worked out that
31. 1:19because of the jury system which had 12
32. 1:22people in it, a seven to5 guilty vote
33. 1:26was enough to send people down. And Pson
34. 1:29thought there must be quite a lot of
35. 1:31innocent people who have been wrongly
36. 1:34convicted. And he came up with a
37. 1:36distribution, a proson probability
38. 1:39distribution to estimate the number of
39. 1:42innocent people that were languishing in
40. 1:45the French jails. And little did he know
41. 1:48that two centuries later it would be one
42. 1:51of the foundations of sports betting of
43. 1:55modern sports betting because we use
44. 1:58this equation to go from a lot of
45. 2:01averages or expecties and to arrive at
46. 2:06fair odds at probability of an event
47. 2:10happening. And doing it that way is
48. 2:12useful. But doing it the other way with
49. 2:16an inverse posson probability
50. 2:19distribution is arguably even more
51. 2:22useful.
52. 2:26And so here is the equation that every
53. 2:28advanced sports better should know the
54. 2:31pluson distribution. And if your eyes
55. 2:34glazed over in high school mathematics
56. 2:36it's not that difficult. There are only
57. 2:38two components in this lambda which is
58. 2:41the average for you in that is 0.5 and K
59. 2:45which is the number that we are
60. 2:47targeting. We're trying to work out the
61. 2:48probability of for example if we're
62. 2:51trying to work out the probability of
63. 2:53youing getting two goals in his next
64. 2:55match. Then P X= 2 = E to the power of
65. 3:00-0.5
66. 3:02* 0.5^ 2 / 2 factorial which gives us
67. 3:067.6%. 6% or 13.2 in decimal odds. 12 to
68. 3:10one. That's the probability of you and
69. 3:12getting two goals. Now, you might be
70. 3:14looking at this and going, "Aha, but
71. 3:16what if we were targeting zero goals?
72. 3:18We're going to end up with a divide by
73. 3:20zero error." No. One factorial is one,
74. 3:23but zero factorial is also one. That's a
75. 3:27video for another time, but it does
76. 3:29work. So, let's apply this to a real
77. 3:31world example. Here we have a bet over
78. 3:3414 goals in the second half of all 11
79. 3:37euros Irish Premier and Spanish Sakunda
80. 3:40League matches. And in the second half
81. 3:42of these games, we had an expectancy in
82. 3:45our database of 15.2
83. 3:48goals. And Pson gives us 55.5% for over
84. 3:5214 goals in the second half of these 11
85. 3:55matches, which is fair odds of 1.80.
86. 3:59and William Hill are giving us three to
87. 4:02one. We bet £500
88. 4:05on this bet and it wins which is going
89. 4:08to do 66% of the time. So there's no
90. 4:11great big surprise there. Now if you
91. 4:14want to build your own Excel spreadsheet
92. 4:17for calculating a forward person, by
93. 4:20that I mean we're going to take an
94. 4:21average and work out the odds of a
95. 4:24target. Follow me here. So in
96. 4:28A1 I've got average and in A2 what was
97. 4:31was you? He was averaging 0.5 goals per
98. 4:34game. Now let's put a target in of zero
99. 4:37goals. And here we have our odds. And to
100. 4:40work out exactly zero. It's just equals
101. 4:43pluson.ist.
102. 4:46I open the brackets. The first value is
103. 4:50the target of zero and the second value
104. 4:53is his average. finish it with a
105. 4:56cumulative false and I get odds or at
106. 5:00least probability of 0.606
107. 5:04and if I want to know more than zero I
108. 5:07would just one minus that taking the
109. 5:11reciprocal of both sides that's fair
110. 5:14odds of 1.64 64 on him getting zero
111. 5:16goals. Fair odds of 2.54 of him getting
112. 5:20one or more goals in the game. Six to
113. 5:24four. So that is a forward plus on
114. 5:27distribution where we go from average
115. 5:30expectancy to probability. But what
116. 5:33about the inverse?
117. 5:39What if we're trying to work out what
118. 5:41the expecties are, but all we have is
119. 5:44odds. When would that be the case? Well,
120. 5:46all the time when we're building our own
121. 5:48models because what can we see? We can
122. 5:50see what the markets think. We can see
123. 5:52what bet 365 traders thought. We can see
124. 5:55what the exchanges think. But all we can
125. 5:57see is the odds. So, we need to work
126. 6:00backwards to get the expecties. And to
127. 6:03do that, we use an inverse poson
128. 6:06distribution in it. Now, forward normal
129. 6:09pluson distribution has a very tidy
130. 6:12equation. It's slightly more nuanced for
131. 6:15an inverse on distribution.
132. 6:19We can't rearrange it just to isolate
133. 6:21expectancy, but we can represent it with
134. 6:24this equation here. And I'm going to use
135. 6:26an example of one of the games that's on
136. 6:28this evening. Hacken women versus
137. 6:31Chelsea women in the Women's Champions
138. 6:34League. And on the exchanges over 2.5
139. 6:37goals is a midpoint could be argued here
140. 6:41to be 1.44. 445. So let's take that
141. 6:441.445
142. 6:46for over 2.5 goals, put it into that
143. 6:50equation, and work backwards to get the
144. 6:53expectancy. And rearranging this formula
145. 6:55for a target of over two goals, we get
146. 6:58an expectancy of 3.57
147. 7:00goals in the match. That is the
148. 7:02expectancy that the markets that the
149. 7:05exchange seeders were using. And we can
150. 7:08do a reality check. We can pop over to
151. 7:10the spreads where we see in this match a
152. 7:12sell line of 3.55 and a buy line of
153. 7:153.75. So that 3.57 sits in the middle of
154. 7:19that window. And this inverse
155. 7:22probability distribution, this process
156. 7:25of using the market's probability to
157. 7:28arrive at an expectancy can be useful
158. 7:31across a heap of markets from the number
159. 7:34of 180s in the PDC World Championships,
160. 7:37the number of three-pointers that
161. 7:38someone might throw in a basketball
162. 7:40game, the number of shots on targets or
163. 7:43fouls in a football match.
164. 7:48Be aware that a plus on probability
165. 7:50distribution can only be used when
166. 7:53events are discrete meaning 01 23 goals.
167. 7:57Something like NFL point scoring,
168. 7:59cricket point scoring is not appropriate
169. 8:02for for and also that events are
170. 8:04independent and happen over a fixed
171. 8:06interval in time. Meaning that if a goal
172. 8:09is scored then that does not affect the
173. 8:12chance of another goal being scored. And
174. 8:14you could argue that it does. Or the
175. 8:16probability of a goal in the first
176. 8:18minute is the same as the probability of
177. 8:19the goal in the 89th minute. It's not
178. 8:22technically true. Goals are more likely
179. 8:25later in games. But even with those
180. 8:28observations, we can start with a plus
181. 8:30on probability distribution and then
182. 8:32just adjust it for under disposition for
183. 8:35overd disposition where the likelihood
184. 8:38of the events happening get adjusted
185. 8:41closer or further away from zero. So
186. 8:44that's an overview on how plus is used
187. 8:46in sports betting. And if you want to
188. 8:49download a spreadsheet to help you
189. 8:51calculate under or over or inverse plus
190. 8:54on, check out the link underneath this
191. 8:56video. Don't forget to like and
192. 8:57subscribe. Spreadsheet is free, but we
193. 8:59do have on and more advanced skeleum
194. 9:03calculators that run on live data over
195. 9:06at Bookie Bashing. And if you want to
196. 9:08see a more advanced video on, check out
197. 9:11this video on Dixon Coohl's that
198. 9:14calculates the correct score marker in
199. 9:17football matches based off the expected
200. 9:19goals each team is going to score. I am
201. 9:22off to my boy's football game at school
202. 9:25because there is a 1.6% chance he's
203. 9:28gonna get a hat-tick tonight.