Odds Explained

Fixed-odds betting is a form of wagering against odds offered by a bookmaker or an individual or on a bet exchange. It involves betting on an event in which there is no fluctuation on the payout. In Australia, the practice is usually known as 'SP betting' Calculating fixed odds. Sports betting lines on FanDuel Sportsbook are presented in what is called the 'American. Horse Racing Odds Explained What Do Horse Racing Odds Mean? If you see a horse listed at 7-2 odds for the first time, or a mutuel payoff amount of $5.00, you may not quite understand what that means if you want to place a bet. But understanding how to read horse racing odds is actually simple. Odds are the return you can expect to get if the.

Fractional odds are British, Ratio, or Traditional odds. You can spot them because they are represented with a hyphen (-) or a colon (:) between two numbers. Of the fraction, the denominator, represents how much profit you earn if you bet the the second part of the fraction, the nominator.

Written by Clay Smith

Idiot’s Guide

That’s right - I will be your guide. The good thing about having an idiot for a guide is that I have to make it simple to understand it myself, which means, hopefully, you will understand it as well.

Probability or Odds

Probability
Probability means the risk of an event happening divided by the total number of people at risk of having that event. I will use the example in a recent JAMA article. In a deck of 52 cards, there are 13 spades. So, the risk (or probability) of drawing a card randomly from the deck and getting spades is 13/52 = 0.25 = 25%. The numerator is the number of spades, and the denominator is the total number of cards.

Odds
Odds seems less intuitive. It is the ratio of the probability a thing will happen over the probability it won’t. In the spades example, the probability of drawing a spade is 0.25. The probability of not drawing a spade is 1 - 0.25. So the odds is 0.25/0.75 or 1:3 (or 0.33 or 1/3 pronounced 1 to 3 odds).

Moving back and forth
To go from odds to probability, simply take the numerator/(denominator + numerator). In the spades example, the odds of 1/3 is converted by taking 1/1+3 = 0.25 - and now we are back to probability. To go from probability to odds, simply take the numerator/(denominator-numerator). In the spades example, given that the probability of drawing a spade is 1/4, take 1/(4-1) = 1:3 odds or odds = 0.33.

Statistical Significance
If an odds ratio (OR) is 1, it means there is no association between the exposure and outcome. So, if the 95% confidence interval for an OR includes 1, it means the results are not statistically significant. Example, exposure to colored vs white Christmas lights was associated with an increase in jocularity score, OR = 1.2 (95%CI 0.98-1.45). Sorry, this is not statistically significant. Let’s just go with white lights…

Use
Either the OR or risk ratio (RR) could be used in many study types. However, only the OR can be used in case-control studies. Because in order to calculate the RR, one must know the risk. Risk is a probability, a proportion of those exposed with an outcome compared to the total population exposed. This is impossible in a case-control study, in which those who already have the outcome are included without knowing the total population exposed.

Risk Ratio

RR is a very intuitive concept. It is the probability (or risk) of one outcome over the probability (risk) of another. Let’s use a study we covered on JF to discuss this concept. Survival was lower in pediatric patients intubated during arrest compared with those not intubated: 411/1135 (36%) vs 460/1135 (41%). So, the RR is 36.2%/40.5% = 0.89. This means survival was reduced by a factor of 0.89 for pediatric arrest patients who were intubated during arrest vs. those who were not. As an example, if survival was expected to be 40%, then intubating during arrest would reduce it to: 40% x 0.89 = 35.6%.

Let’s do one more example. Supination-flexion (SF) vs hyperpronation (HP) to reduce nursemaid’s elbow was more likely to fail. The risk of failure with SF was 96/351 (27%) vs. 32/350 (9%) with HP. The RR was 3. This has a very intuitive meaning: risk of failure with SF was three times more likely than HP.

Odds Ratio

The OR is a way to present the strength of association between risk factors/exposures and outcomes. If the OR is <1, odds are decreased for an outcome; OR >1 means the odds are increased for a given outcome. Let’s look at the examples again and consider odds.

For pediatric arrest, the risk of survival if intubated during arrest was 411/1135 (36%) vs 460/1135 (41%) if not intubated. Let’s convert to odds and calculate an OR.

• Intubated: 411/1135-411 = 411/724 = 0.57 odds.

• Non-intubated: 460/1135-460 = 460/675 = 0.68 odds.

• So, the OR is 0.57/0.68 = 0.83.

Note, this is very close to the RR (0.89) but is a slight overestimate of the effect on the outcome. This is always the case with the OR compared to the RR - it overestimates the effect.

Take the example of supination-flexion vs hyperpronation for nursemaid’s. The risk of failure for SF was 96/351 vs. 32/350 with HP. Let’s convert this to odds.

• SF: 96/351-96 = 0.376 odds

• HP: 32/350-32 = 0.10 odds

• The OR is 0.376/0.10 = 3.7

Note, the OR overestimates the RR, which was 3. Although one could say the risk of failure using SF is 3 times greater than HP, one could not say, based on the OR, the risk was 3.74 times greater. The OR and RR are not the same. What could be said is that the odds of failure is 3.74 times greater.

Risk Ratio vs Odds Ratio

Whereas RR can be interpreted in a straightforward way, OR can not. A RR of 3 means the risk of an outcome is increased threefold. A RR of 0.5 means the risk is cut in half. But an OR of 3 doesn’t mean the risk is threefold; rather the odds is threefold greater. Interpretation of an OR must be in terms of odds, not probability. Again, the OR will always be an overestimate compared to the RR. However, the RR and OR will be similar for rare outcomes, <10%. But the OR increasingly overestimates RR as outcomes exceed 10%. This is easier to understand with an example.

Pretend a new vape, Vapalicious, is associated with cancer.

• 80/100 people who use it get cancer.

• 20/100 who don’t use it get cancer.

• The risk of getting cancer is 4 times greater in Vapalicious users. RR = 0.8/0.2 = 4

• Note how distorted the OR becomes in this example. OR = (80/20)/(20/80) = 16

What if Vapalicious rarely caused cancer?

• 5/1000 get cancer with Vapalicious vs 2.5/1000 for non-users.

• RR = 2.

• OR = 2 as well (actually 2.005)

• With rare outcomes, the RR and OR are very similar.

Why Does This Matter?

This matters because we often equate the OR and RR. Unwary researchers, reviewers, or news media might report a 16-fold increased risk of cancer from Vapalicious. In fact, there was a 4-fold increased risk of cancer from Vapalicous. Not that I plan to use Vapalicious (or any other vape), but a 16-fold vs 4-fold increase is a gross overestimation of the effect.

What Does the OR Mean?

So, what does an OR mean? Here it is in plain language.

• An OR of 1.2 means there is a 20% increase in the odds of an outcome with a given exposure.

• An OR of 2 means there is a 100% increase in the odds of an outcome with a given exposure. Or this could be stated that there is a doubling of the odds of the outcome. Note, this is not the same as saying a doubling of the risk.

• An OR of 0.2 means there is an 80% decrease in the odds of an outcome with a given exposure.

Summary

• Odds Ratio is a measure of the strength of association with an exposure and an outcome.

  • OR > 1 means greater odds of association with the exposure and outcome.

  • OR = 1 means there is no association between exposure and outcome.

  • OR < 1 means there is a lower odds of association between the exposure and outcome.

• If the 95% confidence interval for the OR includes 1, the results are not statistically significant.

• OR and RR are not the same.

• OR always overestimate RR, but…

• OR approximates RR when the outcome is rare but markedly overestimates it as outcome exceeds 10%.

References

1. The odds ratio by Bland and Altman, of Bland-Altman plot fame

2. Wikipedia aka source of all statistical knowledge

Getting action on a game can add a thrill factor that is hard to find in any other aspect of life. Making some money while doing it, well, it doesn’t get much better than that. But what happens when you jump onto your favorite sportsbook and they bombard you with a series of numbers (odds) which are meant to represent the chances of your team winning, when all it really looks like is math on steroids!

If this is how you feel when your trying to place a wager, read on. The following is a simple guide on how to read sports odds and give yourself the best chance of taking home some cash.

What does +200 mean? +200 is a specific set of odds attached to a given sports event. These are in the form of ‘American’ odds’. The +200 represents the amount a bettor would win if they had wagered $100. A profit of $200 and a total payout of $300. Other types of odds are Decimal and Fractional.

What Types of Odds Do Sportsbooks Use?

Globally sportsbooks use one of three types of odds:

1. American
2. Fractional
3. Decimal

There are positives and negatives in the use of all of them. One thing is for sure, if you are going to bet on sport, you will run into one of these odds formats and you NEED to know how to read, understand and eventually capitalise on them.

This article will focus heavily on American odds.

How to Read American Odds

The basis of American odds is that they reflect two different aspects to the bet:

• in the case of the underdog: how much money a gambler will win if they bet $100,
• in the case of the favorite: how much a gambler needs to bet to win $100.

Quite a big difference between the two, and definitely a little tricky to navigate at first.

The following is an example of the moneyline market using American Odds, which was offered by a sportsbook during the NBA playoffs

Note:As the Portland Trail Blazers are the home team they are listed second in this market. Interestingly in many international or offshore sports the home team is listed first. Perhaps in this case the home court advantage is what has led the sports books to install the Trail Blazers as the favoured team.

Odds Explained Synonym

We can tell Portland has favoritism as the odds have a minus sign at the front. Any time a team has minus sign out front, the bettor knows they will be receiving less than a 2 – 1 payout figure. In fact in this case, to win $100 wagering on the Trail Blazers you would need to stake $128.

In this particular example, the Oklahoma City Thunder are the outsider or underdog as they have odds with a plus sign at the front (plus money). This means if you bet $100 on OKC then you would collect $105 profit, a total return of $205.

Clearly the bookmakers considered the game to be potentially close and therefore odds were reasonably tight. As it turned out the Trailblazers dominated the second half and ran out convincing winners 114 – 92. Moneyline bettors who took Portland, go to bed with a tidy profit. In actual fact the margin of victory is irrelevant as the Moneyline requires just one condition be met, a win.

How to Do the American Odds Math?

Despite the American odds looking confusing at first sight, the underlying math is not too difficult. Having said that it could be much more user friendly.

Another key point to remember is that American odds do not include the original stake in the calculation. They only reflect the profit from the wager. The original stake needs to be added to reflect the total payout or total return figure.

Referring back to the previous example the following math applies:

The issue with this way of reporting odds is that the bettor has to do more than one level of calculation themselves. While it’s all fairly straightforward it does affect the user experience negatively.

How are American Odds Different to Decimal Odds?

The decimal odds system, which is being increasingly used by sports bookmakers across the globe, removes the extra step of calculation required by the bettor when American Odds are in use. It is a much simpler method to offer odds on the identical market and immediately gives a total return or payout figure by using one simple multiplication.

The NBA example used earlier in the article using decimal odds would read as follows:

The payout calculation is where the ease of decimal odds is highlighted:

Odds Explained Betting

Underdog:

Favorite:

It is clear that the decimal method is a much simpler way for sport bettors to calculate their potential winnings than than the American odds system.

Another downside to using American odds is that they are almost unusable when working with parlay betting. A parlay or multiplier is where a bettor takes classic bet types and parlays several of these into one wager. In order to multiply the individual odds to create the parlay payout figure, the moneyline is first converted to decimal odds. Highlighting the extra step of math sportsbooks require bettors to do when they solely offer odds in the American format.

It is hoped that one day soon most sports books will offer decimal odds instead of American odds. As legalized sports betting explodes in popularity across the US and more mobile sports betting platforms come online, it is hoped that at the very least, functionality to switch between types of odds is added to all betting apps. After all, sports betting is about entertainment, and user experience should be the number one focus from all corporate bookmakers.

How to Identify Sportsbook’s Margin When Using American Odds

Sportsbooks clearly need to make money to continue to operate and therefore it is understandable that they will take a cut along the way. Understanding when that cut is too large is critical in giving yourself the best chance of turning a profit.

When dealing with American odds on 50/50 markets like total points or point spread the margin is quite simple to recognise.

For example the market on an NBA game may be offering an over/under points total of +/-214.5 points.

In this market, without any bookmaker edge, the odds would read +100 for each option. That is a doubling of the bettors money based on the market essentially being a coin flip. $100 invested would return a profit of $100. Clearly this is not the case in reality. If you spot a market like this through a sportsbook promotion (a rare occasion), then load up!

The sportsbook is only offering -110 meaning a bettor would need to invest $110 to return a profit of $100. This equates to approximately a 4.5% margin (vig) for the book. To be profitable long term the bettor would have to correctly pick this market 53% of the time. A tall order.

Some books will offer a smaller vig, for example -108 but others will be less generous and wind their margin out to numbers like -112. These numbers are often seen in live betting markets due to the greater perceived risk the sportsbook take on with live markets.

It is best, as a rule, to avoid markets where the market is skewed too far in the favor of the book.

Horse Racing Odds Explained

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The Game Starts Now

Before you hit the confirm bet button on your mobile sportsbook make sure you are fully aware of what price you are actually buying. While American Odds can at times be confusing there is still an art to spotting and cashing in on value. Best of luck!

Odds Explained 13/10

Good Luck and as always, gamble responsibly!