Websites abound with information about how to translate moneyline prices into the bookmaker’s implied probabilities.
These webpages also include some discussion about how moneyline prices are read and what they mean. A few also have discussions about the concept of a vig or vigorish (the “over rounding” that a bookmaker does to the probabilities to bake in a profit for itself).
All of these websites speak to bettors.
In keeping with the project to theoretically model a sportsbook that takes bets on trading card game events, we want to model such variables as the house.
If we’re the sportsbook, we want to know the probable outcomes of different over round percentages, splits in the over round, competitor win probabilities, total money wagered on either side, and what our expected financial outcomes should be.
In this project, we accomplish all of these things with an Excel Calculator.
The Excel TCG Sportsbook Financial Calculator
If you’d prefer to see the Excel calculator first and skip (or save for later) the discussion on how it works and why, you can find it below:
Excel TCG Sportsbook Financial Calculator
Breaking Down the Tunable Parameters
The Excel Calculator gives us five parameters that can be changed. These are found under the Assumptions heading.
Let’s take a look at each of them.
Vig
The vigorish, or “over round”, is the markup the house puts on the probabilities it uses to quote the bettors its bet prices.
This can be viewed as the long term profit margin the house expects on the outcomes of events with similar probabilities.
For most popular sporting events, the over round hovers a bit below 5%.
The Excel Calculator allows a vig of between 0 and 25%.
(We should expect that if trading card game bet prices were set, the vig would be on the higher side, as they are more thinly traded.)
Matches Played
Here, the user can set the number of matches played between competitors.
This is a simplification, for illustrative purposes, because the probabilities are identical for each match played (whereas, in real life, we’d wish to go further into developing a Bayesian predictive model to account for changes in win probabilities for either side given a series of N matches).
A more complex model deserves its own project, which will come soon enough.
These are tunable between 1 and 1,000,000 matches.
Vig Split
This allows the user to split the vig between the two competitors.
Often times, the book maker will not apply the vig equally to both, so as to help limit liability on one side of the event. Placing more of the over round weight to one side (one competitor) over another can make that side seem less attractive than the other, enticing bettors to place their money elsewhere.
Only the vig split on Player A is tunable. The vig split on Player B is automatically updated based on the input for Player A.
The Vig split for Player A can be between 1 and 100% (with Player B having the remainder).
Win Probability
The Calculator assumes that we know the win probabilities for either player.
How to arrive at these win probabilities in trading card games, at least, is the subject of another project. Here, we assume that we know them.
Only the win probability for Player A is tunable. The win probability for Player B is automatically updated based on the input for Player A.
The win probability for Player A can be between 0 and 1, inclusive (with Player B having the remainder).
Total Money Wagered
The parameters for total money wagered for either side of the matches played can be set to any amount between $1 and $1,000,000 in even dollar increments.
As noted in the Calculator, the total money wagered on either side is per match played.
Reading Financial Outcomes
After the five tunable parameters have been set, we can see the financial outcomes of the selected series of matches.
Let’s assume we set our assumptions as follows:
- Vig: 10%
- Matches Played: 50
- Vig Split: 70%/30%
- Win Probability: 0.674/0.326
- Total Money Wagered: $24,500/$47,850
Fair Probability & Over Round Probability
The fair probabilities are carried over from the Assumptions we placed in the Calculator.
Note that the sum of these probabilities will always sum to 1. There are fair probabilities, because they reflect our true beliefs about the winner of the matches.
The over round probabilities apply the vig and the vig split to each probability.
Since we placed the vig at 10% and weighted 70% of that vig on Player A and 30% on Player B, the Calculator applies those figures to each side accordingly.
Note that the probabilities sum to 1.1, meaning the fair probability sum of 1, plus the vig of 10%.
Moneyline
The Calculator gives us the moneyline for the players.
As we discussed in the post about setting odds and betting prices for trading card games, these prices use the American moneyline system for bet prices.
We see that Player A has a price of -291 (meaning that a bettor must bet $291 to win $100), while Player B has a price of +181 (meaning that betting $100 will win the player $181; plus the staked $100, in both cases).
Player A, as we should expect from our probabilities, is the favorite (with a negative quoted price), and Player B is our underdog (with a positive quoted price).
Money Wagered & Bettors to Win
The Calculator gives us the total money wagered on both sides for all events (remember, we put $24,500 on Player A and $47,850 on Player B on each of 50 matches).
It also gives us the bet liability for each side, or what bettors stand to win if they’re right.
The Bettors to Win calculation takes the total money wagered for each side and applies the moneyline price for each side to arrive at the liability figures.
Wins
The wins for each side simply applies the fair probability for each player as a proportion of the total number of matches we input.
Since we selected 50 matches, given probabilities of 0.674 for Player A and 0.326 for Player A, we expect Player A to win 34 matches and Player B to win 16 matches.
Financial Outcomes
Finally, given all of our assumptions, we have the expected financial outcomes for our venture.
With 50 matches, assuming our probabilities are correct, we expect to pay out the bettors on Player A a total of $1,109,379 and the winners on Player B a total of $2,191,674.
Our total handle, or the total money wagered by bettors, came to $3,617,500, on which we paid out $3,301,052.
That leaves us, the sportsbook, with a gross gaming revenue (GGR) of $316,448 for a profit margin of 8.7%.
Not too shabby!
Conclusions
Our Calculator allows us to model some basic assumptions about the financial viability of our sportsbook.
We can tune a number of parameters about each competitor and how we choose to price the bets we offer to bettors. We can experiment with how much money we’d need on either side to maintain profitability given these assumptions.
We’ve seen that, if it all works out more-or-less according to plan, the bookmaking business is good to us.
Please let me know if you have any questions or comments in the comments section below!
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You can find a link to the completed Excel TCG Sportsbook Financial Calculator below: