An odds ratio is a relative measure of effect, which allows the comparison of the intervention group of a study relative to the comparison or placebo group. So when researchers calculate an odds ratio they do it like this: The numerator is the odds in the intervention arm. The denominator is the odds in the control or placebo arm = Odds Ratio (OR). To put it simply, this is the ratio of the amount (profit) won to the first wager, which indicates that you will certainly obtain your stake ($1) in addition to the earnings ($6), resulting in a total return of $7. If you bet $10 at 6/1, you get a complete return of $70 ($60 revenue + $10 stake). In betting, odds represent the ratio between the amounts staked by parties to a wager or bet. Thus, odds of 3 to 1 mean the first party (the bookmaker) stakes three times the.
Odds are an essential element of sports betting. Recognizing just how to read odds is a vital action to becoming an effective sports wagerer. From establishing just how much money you intend to bet to figuring out which bets provide the most value, all of it starts with a strong understanding of the probabilities.
What you might not have known is that there are several different ways of expressing odds, or that odds are carefully connected to the chance of a wager winning.
We SportsDiction.com cover whatever you need to learn about odds in this article. We prompt you to take the time to go through all this information, particularly if you are fairly new to sports wagering.
Generally, odds are used to identify the amounts paid on winning bets. This is why they are commonly described as the 'cost' of a wager. A wager can have a cost that's either odds on or odds against.
- Odds On – The possible quantity you can win will certainly be less than the amount you bet.
- Odds Against – The possible quantity you can win will certainly be higher than the amount you bet.
Probably, you'll encounter every one of these formats when playing online. Some sites allow you to pick your layout, but some do not. This is why recognizing all of them are very valuable.
This is the format most generally used by wagering sites and used mostly in Europe. Because it is the simplest and most basic of the three formats. Decimal odds, which are typically shown making use of two decimal locations, show specifically how much a winning bet will certainly return per unit staked.
When using decimal odds, the estimation required to function out the potential return is very simple.
If you intended to put a $100 bet on the PSG at 3.00 you would simply require to increase your $100 bet by the 3.00 chances (100 x 3.00) to find out that the payment is $300. It is necessary to understand that with decimal style odds it includes the quantity you bet, so to discover revenues you would require to deduct your bet ($300-$100) to find out your possible payment is $200 in revenues.
If you wished to position a $100 bet on Barcelona you would certainly once more simply increase ($100 x 1.55) to figure out that you would win $155 total amount of $55 in revenues.
American odds are utilized mostly in the United States. There are several various versions of sports betting chances, but these American Odds are the most typical odds used. Reading and also recognizing sports wagering odds can be a little confusing to newbies, so we have given an example listed below making use of two football teams:
American odds can be either positive (the appropriate number will certainly become before by a + indication) or negative (the appropriate number will certainly be preceded by a – indication).
Positive American odds show how much earnings a winning bet of $100 would make. In this example you can see Everton is listed at +150, it means that a $100 wager could win you $150. You'd also obtain your stake back, for an overall return of $250.
Negative American odds show how much you require to bet to make a $100 revenue. In this example Manchester city is listed at -120, it means that a wager of $120 might win you $100. Again you would obtain your stake back, for an overall return of $220.
Fractional odds are most frequently used in the UK, and also when banking on equine auto racing. Here are some simple examples of fractional odds.
- 6/1 (six to one)
- 5/2 (five to two)
- 15/8 (fifteen to eight)
A fractional listing of 6/1 (six-to-one) odds would suggest that you win $6 against every $1 you wager (in addition to obtaining your dollar back, i.e. $1– the amount you wagered). To put it simply, this is the ratio of the amount (profit) won to the first wager, which indicates that you will certainly obtain your stake ($1) in addition to the earnings ($6), resulting in a total return of $7. If you bet $10 at 6/1, you get a complete return of $70 ($60 revenue + $10 stake).
The following calculation is used, where 'a' is the first number in the fraction and 'b' is the second.
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…
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
How To Interpret Betting 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
How To Read Betting Odds
The odds ratio by Bland and Altman, of Bland-Altman plot fame
Wikipedia aka source of all statistical knowledge
