What Does 3 To 1 Odds Mean
Written by Clay Smith
See full list on wikihow.com. Now when a gambler says that the odds are 3to1, they mean that there are 3 chances to win to 1 chance to lose. Alternatively, the gambler express this as the chance is 3in4, that is, 3 chances to win in 4 total chances. Dec 08, 2018 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.
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
The odds ratio by Bland and Altman, of Bland-Altman plot fame
Wikipedia aka source of all statistical knowledge
Point spread betting is the most popular form of sports betting. The vast majority of sports wagers use a point spread thanks to the popularity of football and basketball. Even though this type of betting is so popular, it may take awhile to understand.
The point spread is sometimes known as an equalizer for sportsbook operators. All teams aren’t created equally, so sportsbooks can create a point spread for a game so that each team playing has an almost even chance of winning the game. In a way, the point spread will even the field for both teams.
The point spread gives a reason for bettors to risk money on both teams. The better team playing in the game is considered favorite. They have to win by the point spread offered by the sportsbook. The favorite in a game is listed as being minus (-) the point spread.
The worse of the teams playing in the game is called the underdog. The bettor wins if this team wins the game outright or loses by an amount smaller than the point spread. The underdog in a game is listed as being plus (+) the point spread.
Let’s use this past Super Bowl between the Tampa Bay Buccaneers and Kansas City Chiefs as an example.
Using this example, the Chiefs were 3-point favorites over the Buccaneers. The Chiefs needed to win by 4 or more points to cover the spread.
Likewise, the Buccaneers were 3-point underdogs. That means the Buccaneers needed to win the game outright or not lose the contest by 4 points or more. At Chiefs -3, if they won by exactly 3 points, the betting result would have been a “push” and bettors for both sides would have gotten their wagers refunded.
The Buccaneers pulled off the upset, winning by a score of 31-9, and rewarded bettors who backed them at +3.
Point spread betting odds
Point spreads are usually set with -110 odds, but pricing often fluctuates at online sportsbooks. This is the sportsbook operators’ house edge. The odds guarantee the sportsbook operator will see a little money over time. When the odds are set at -110, the bettor must wager $110 to win $100 (or $11 to win $10).
The odds on a point spread are most commonly known as the vigorish or “vig” for the sportsbook. You might hear this small profit margin for the sportsbook called the “juice” by some sports bettors.
Point spread FAQs
What does ‘pick em’ or ‘pick’ mean in NFL betting?
A “pick em” (sometimes seen as “pick”) is when the teams have a point spread of zero, meaning neither team is favored. In this instance, you’re essentially picking moneyline and your bet will be determined on the winner alone.
What does -7 and +7 mean in NFL betting?
What Does 3 To 1 Odds Mean
A spread of minus-seven (-7) means that a is favored to win the game by a touchdown (technically, a touchdown and the extra point). A team favored by -7 must win the game by eight or more points to win the bet. If the team wins by seven, the result is a “push” and the bet is refunded.
What Does It Mean When Odds Are 3 To 1
A spread of +7 means the team must win the game or lose by fewer than seven points to win the bet. A loss by seven would result in a push.
What does -3 and +3 mean in NFL betting?
A -3 spread means that the favorite must win by more than a field goal to win the wager. A three-point win would result in a push and the sportsbook would refund the wager.
A spread of +3 means the team listed as the underdog must win the game or lose by fewer than three points to cash the bet. A three-point loss would be graded as a push by the sportsbook and the bet would be refunded.
Why are point spreads in the NFL so much lower than in college?
In 2019, the Baltimore Ravens led the NFL in point differential per game at +13.7 points; the Miami Dolphins ranked last in the NFL in point differential per game at -11.7. Even Kansas City– known for their explosive offense– had an average point differential in 2019 of just 9.7 points. The net point differential in the NFL is -14.1, or -0.9 points per game. Basically, the talent differential in the NFL is so minute that even mismatched teams often draw games within a score of each other.
NFL spreads are most commonly between one point and four, with six being a heavy favorite and extremes coming out around 15-20 point favors. (For those wondering, the 1941 Chicago Bears hold the NFL record of point differential at +15.7 points per game. Conversely, Ohio State had a +33.1 average point differential in 2019.)
Point spread and odds movement
Sportsbook operators often aim to have equal money on both sides of a point spread. When the money is exactly split the sportsbook operator will see the exact vigorish as their profit margin. If all things are equal over time this will maximize how much money the sportsbook operator can make.
What Does 3 To 1 Odds Mean
In an effort to have equal money on both sides of a wager, the sportsbook operator will move the point spread to attract money on the side that customers aren’t betting on. The odds for a point spread might change before the actual point spread. There are certain point spread numbers, like 3 and 7 in football, the sportsbook operators would like to avoid moving away from since the final score margin falls on these two numbers most often.
For example, if a lot more money is wagered on the New England Patriots -3, the vig may shift from -112 to -115 and -120 before the line moves to -3.5.
Run and puck lines
Cached
Football and basketball games are mostly bet using a point spread. The less popular major sports, baseball and hockey, are mostly bet using a moneyline. In an effort to make baseball and hockey more appealing to point spread bettors, the sportsbook operators offer run and puck lines, respectively.
What Do 3 To 1 Odds Mean
These alternative lines give point spread bettors a chance to wager on other sports using a more familiar method of betting. Since points (runs and goals) aren’t as easy to come by in baseball and hockey, the odds with the lines may have a wider spread than a football or basketball game.