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1*2 DRAW FIXED MATCHES
Date: 01.09.2022 Day: Thursday
League: AUSTRIA OFB Cup
Match: Allerheiligen vs Rapid Vienna
Tip: Over 2.5 goals
Odds: 1.35 Fulltime 0:2
Date: 01.09.2022 Day: Thursday
League: NETHERLANDS Eredivisie
Match: AZ Alkmaar vs Nijmegen
Tip: Over 2.5 goals
Odds: 1.75 Fulltime 1:1
Date: 01.09.2022 Day: Thursday
League: ITALY Serie A
Match: Atalanta vs Torino
Tip: Over 1.5 goals
Odds: 1.25 Result: 3:1
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At the most basic level, The 1*2 DRAW FIXED MATCHES making money from betting requires two things. Skill and luck. Whilst many bettors fail to acknowledge the influence of the latter, measuring the former is also often overlook. This article shows why it is important to understand the different methods of assessing betting skill and how results can differ depending on your approach.
Bayes’ Theorem can be used by sports bettors to make better predictions. We can also use it to help us determine what the likelihood of us actually being any good at making those predictions and finding positive expected value. I’ve previously investigated how to evaluate the quality 1*2 DRAW FIXED MATCHES using a frequentist approach (t-test). This article will compare and contrast the two methods.
Degrees of belief
In probability theory Bayes’ Theorem describes the chances of an event happening conditional on another event occurring also. For example, suppose I believe that I have a 50% probability of being a skill bettor capable of finding value. If I win my next bet, how will this influence my belief in this proposition? In other words, how does the evidence of winning a bet change the probability of me being a skilled bettor?
Bayes’ Theorem interprets probability as a ‘degree of belief’ in a proposition or hypothesis, and formalises mathematically the relationship between the prior degree of belief before the evidence is know (the prior probability) and the degree of belief after accounting for the 1*2 DRAW FIXED MATCHES (the posterior probability). It is write as follows:
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{equation} – P(A|B)= P(A)*P(B|A)/P(B)
In our example here:
P(A) = the prior probability that I am a skilled bettor
P(B) = the prior probability of winning my bet
P(B|A) = the probability I win my bet conditional on me being a skilled bettor.
P(A|B) = the probability I am a skilled bettor conditional on me winning my bet.
Let’s try an example. Let’s assume that the definition of a skilled bettor is someone who can consistently achieve a return on investment of 110%. For even-money wagers that would imply 55 winners out of every 100. Hence, P(B|A), the probability I win my bet conditional on me being a skilled bettor, is 55%.
For an unskilled bettor, the probability of winning a fair even-money wager, P(B), will be 50%. However, let’s assume I hold a prior belief that I have a 50-50 chance of being skill {P(A) = 50%}, and P(B) for such a bettor is 52.5% (half way between 50% and 55%).
Should I win my bet, imputing these numbers into Bayes’ Theorem yields a posterior probability – P(A|B) – of 52.38%. Winning my bet leads me to believe there is a greater probability than before that I am skill.
1*2 DRAW FIXED MATCHES can be apply iteratively. Having won my first bet and update my probability of being a skill bettor, I now place another bet. The posterior probability calculate in the first step becomes the new prior probability.
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The new posterior probability of me being a 1*2 DRAW FIXED MATCHES will now be conditional on me winning (or losing) my next bet. If I win, the probability of me being skill will increase again; if I lose, it will decrease. In this example, should I win my second bet, the probability that I am a skill bettor increases to 54.75%.
This process can be repeate indefinitely with each update conditional probability falling somewhere between 0% and 100%. I have run this iteration 1,000 times, i.e. 1,000 wagers, and the chart below shows the betting history achieving the (blue line) alongside the Bayesian probabilities of me being a skill bettor after each wager (red line).
One significant problem with a Bayesian interpretation of probability is that it requires strong prior knowledge or belief in an event or situation. But do we really have that in assessing the probability that I might be skill at betting? My choice of 50% in this example was purely arbitrary and based on nothing else than guesswork. Look what happens if I now change the initial prior probability to 1%.
Furthermore, it is completely arbitrary what 1*2 DRAW FIXED MATCHES actually means in this context. Arguably a bettor capable of 105% return on investment is highly skilled if he can achieve that over 10,000 wagers – you can read about the Law of Small Numbers to find out why sample size matters. It’s also equally unclear how to define P(B) for each iterative step, given an updated value of P(A).