How Are Odds Calculated In Sports

Sports betting odds are calculated with the main goal for sportsbooks being to receive equal money on both sides of a bet. For example, if the Kansas City Chiefs are a -10 point favorite against the Oakland Raiders and are getting 90% of the money, the sportsbook would likely adjust their line so. A parlay bet is a single wager that requires two or more outcomes to all win. The parlay calculator allows you to input your stake & odds in American formats to quickly calculate the payout for.

A parlay is a single bet that links together two or more individual wagers for a high payout. A 2 team parlay might pay 13/5, a three team parlay might pay 6/1, a four team parlay might pay 10/1, and so forth with the payouts getting higher with more teams or totals selected. For a single bet, 2 to 8 teams or totals can be selected.

In order for the parlay bet to win, every one of the wagers must win or push (tie). If any of the selections lose, your wager loses, regardless of the outcome or cancellation of the other games. If one or more selections is a tie, postponed, incomplete, cancelled or rescheduled for another day, then the wager reverts to the next lowest number. For example, if you place a 5 team parlay and have 4 winners and a tie, your wager pays out as a 4 team parlay. If you place a 2 team parlay and one team wins and one ties, the wager becomes a straight bet.

The resulting wager will have the same risk amount with the win being calculated to reflect the odds of the remaining team (Example: On a two team $100 parlay with team A +110 and team B -110 if A ties and B wins the resulting wager will be a straight play on B risking $100 to win $91).

I’ve been reading a lot of books about sports analytics lately. My current read is The Logic of Sports Betting by Ed Miller and Matthew Davidow. One of the first concepts discussed in the book is understanding the balanced hold of a sportsbook on a two-way market. In a two-way market, you take either one side of a bet or the other, for example Team A will win, or Team B will. The hold is simply the profit a book “holds” onto after all of the winning bets have been paid, divided by the total wagers placed. A balanced hold assumes (naively) that the book is holding balanced action on the wagers, meaning that no matter which side wins, the book will have the same amount of profit. This is rarely realty for a number of reasons. However, the concept is emphasized as important, presumably because it will be needed for later concepts. While a couple of contrived examples are presented, the how of to calculate the balanced hold is not spelled out—at least in the chapters I’ve read thus far.

I wanted to be able to quickly calculate the hold myself, so I tried a few unsuccessful Google searches. So in about 15 minutes I figured out how to calculate it myself, first via doing the math on paper, then building a spreadsheet calculator to make it easier to calculate on the fly as needed.

Here’s some examples laid out in the book in American Odds:

The last part, calculating the hold percentage is the easiest: you just divide the profit by total money wagered. The harder part is to figure out what the profit and amount wagered need to be in order for the action to be balanced. For that to happen, we need to have the amount paid to each possible winner subtracted from the amount wagered by the respective loser to be equal. For example 1 that looks like:

Profit from Team A winning = Wagers placed on Team B minus payout on Team A wagers = $108.69 - $100.00 = $8.69

Profit from Team B winning = Wagers placed on Team A minus payout on Team B wagers = $150.00 - $141.30 = $8.70

Profit from Team A winning = Profit from Team B winning

The way I tackled this problem was to start with calculating the wager to payout ratio for each bet. Since we’ll need to be calculating both the wager and payout amounts, we need this ratio to solve later variables. I won’t go into how dumb American odds are, but a quick overview of what they represent. If a wager’s odds are negative (-150), that means you have to risk $150 to win $100. If a wager’s odds are positive (+130), then if you wager $100 you will receive the odds ($130) back. Therefore, in example 1, the ratio of wager to payout for each bet is:

You can do this in a spreadsheet formula would look something like this:

In order to solve the problem, I started by assigning an arbitrary wager and payout for one side of the bet. In this case, I just set side A with potential payout of $100, so risking $150. If it was a plus bet, I’d set it to risk $100 and payout to the odds. The formula for the risk would look like:

Then for the payout you would just multiply your risk to the ratio calculated above.

Since our objective is to have the profit for both columns to be equal, we can setup the equation like this:

Since previously calculated the ratio between X and Y, we can replace Y with a factor of X:

Now we can solve for X:

Let’s plug in these new values for wagers and payouts on Team B, and calculate the profit on each outcome:

Success! If you aren’t interested in recreating this yourself, you can just grab a copy of my Balanced Sportsbook Hold Calculator Google Sheet.

Multi-way Markets

I was feeling super proud of myself until I got to the next chapter, which spelled out how it’s equally important, but much harder, to calculate a multi-way market. A two-way market takes the form of

• Who will win the 2019 NBA Playoffs?

1. Toronto Raptors
2. Golden State Warriors

• Or How many games will the 2019 Boston Red Sox win?

1. More than (Over) 94.5
2. Fewer than (Under) 94.5

A multi-way market has more than two options. Such as:

• Result of 2019 Women’s World Cup Match between USA and Thailand:
  1. USA wins
  2. Thailand wins
  3. Tie
• Or Who will win the 2019 Women’s World Cup (24 options):

How Are Odds Calculated In Sports Management

1. France
2. USA
3. Germany
4. England
5. Netherlands
6. Australia
7. et c.

How Are Odds Calculated In Sports Betting

How To Calculate Odds Ratio In Sports

After much more scratchpad/Google Sheet math, I realized that for each option in a bet, regardless of how many options there were, the sum of the wagers and payouts would be equal. In the example above, the sum of wagers and payouts were both $250. What changed for each option was the ratio of the risk and payout, and that adding the two together was the key. In the example above, the ratio of 1:1.3 became 2.3 when summed. It just so happens that 2.3 is the decimal odds version of a +130 bet. The second tab of my google sheet can calculate the hold on any bet with up to 24 positions.