Odds, Probabilities and the Vig explained

In this article, we will get into details about Odds and Probabilities. We know this is not a reader-friendly article, but for the sake of betting knowledge, you should read it.

Introduction to probability theory

The first step in calculating the probability of a single random event is to define events and outcomes. In more detail, the probability is the likelihood of one or more events happening, divided by the number of possible outcomes.

Considering two totally equal football teams A and B, in order to get the percentage chance for team A to win, we divide 1 by 3 = 33.33%. Apparently, we divide 1 by 3 = 33.33% to get the Draw and B’s percentage. Then, we must divide 100 by the percentage figure to get the odds. In this simplified case, we have: A – 3.00, Draw – 3.00, B – 3.00.

The Vig

Also called Margin or Juice, is the commission the bookie or bookmaker makes when offering odds for a game or an event. Please note that the above odds would never be offered by a bookmaker due to the vig, the commission of the bookmaker. In a nutshell, bookmakers try to balance the total amount of a bet and apply the vig so as to secure a certain profit on any event, regardless of the outcome. For a two outcome event, the vigorish percentage is:

p*q

V = 1 –

p+q

where p and q are the decimal payouts for each outcome.

For example, if the odds for Over (2.5) and Under (2.5) are 1.70 and 2.20 respectively, the vig percentage is about 4.1%.

The relevant calculation is a little bit more confusing in cases of three-way events, where the following formula is applied:

V (1/p + 1/q + 1/t) – 1 = (1/p + 1/q + 1/t)

where “t” is the decimal payout for the third outcome.

Consider now a full-time result bet is offered under the odds: Home win – 4.00, Draw – 3.6, Away win: 1.8. In this example, the vig percentage is 7.4%. In many cases, only the upper part of the equation is used, leading to slightly higher percentage results than the vigorish calculation. However, it provides quick results and allows comparison between odds offered by different bookies.

Determining probabilities and own odds

Reverting back to probabilities, the assumption of equal teams is more theoretical than an empirical case. Many factors have the potential to affect the outcome of a game. In our opinion, the list of the most significant factors is as follows:

• Current Form
• Head to Head Records
• Styles of Play/coaching staff
• Home & Away Records
• Weather
• Schedules
• Injuries & Suspensions – team depth
• Overall Team Quality
• Motivation & Psychology
• Third-party intervention

In general, it is difficult to assess quality factors (such as the weather or team depth) and estimate probabilities on the outcome of a game. However, the “current form” or the “Home and Away records” can be easily quantified and constitute a base for probability estimation.

Consider teams X and Y. In this instance, we will be looking at X’s previous 10 home games and Y’s previous 10 away games. The table below also displays the current form of both teams at the last 5 games (home or away).

We add X’s 5 home wins to Y’s 7 away losses (sum = 12). We also add X’s home losses (2) to Y’s away wins (2), which is equal to 4. The total number of draws for both teams is 4. Therefore, X’s individual score is 12, Y’s individual score is 4 and the relevant score for draw is also 4. By dividing each score by the total number of matches, we get:

• X’s percentage = 60% (12/20)
• Y’s percentage = 20% (4/20)
• Draw percentage = 20% (4/20)

As already mentioned, the odds are calculated by dividing 100 by the percentage figures. In this case, we have:

• X – 1.66 (100/60.00)
• Y – 5.00 (100/20.00)
• Draw – 5.00 (100/20.00)

If we take into account the current form of both teams, the assessment of probabilities provides extremely different percentages and odds. By applying the same methodology, the relevant percentages (scores) are 40% (4/10), 10% (1/10) and 50% (5/10) for X, Y and Draw accordingly. Therefore, the odds are compiled as follows: X (2.50), Draw (2.00) and Y (10.00).

This example indicates that our odds may be biased because they depend heavily on the selected factors. Therefore, it is obvious that a statistical tool is necessary to weigh the results of different processes and provide a final estimation of the odds.

For instance, if the “Home & Away Records” and the “Current Form” are weighted by 0.6 and 0.4 respectively, our final odds are:

• X – 2.00 (1.66*0.6 + 2.50*0.4)
• Draw – 3.80 (5.00*0.6 + 2.00*0.4)
• Y – 7.00 (5.00*0.6 + 10.00*0.4)

So, the weights are of high significance for calculating odds. However, their determination by intuition or feeling is also a biased process. The implementation of a statistical – econometric model (like a betting bot) estimates the relevant weights by integrating historical data for a large number of parameters like Injuries and Suspensions, Head to Head Records, etc.