Odds represent a possibility in the probability theory and statistics of indicating probabilities. For example one speaks a 1:1 of - chance that with a "„head appears "“. Mathematically Odds compute themselves as quotients from the probability that an event occurs and the probability that it does not occur:

R (A) = {P (A) \ more over {1-P (A)}}

R is the value of the Odds and P the probability that the event occurs.

In the statistics one uses the so-called Odds reason (relationship of Odds) around the difference of two Odds to evaluate and thus statements about the strength from connections to to make. These compute themselves as follows:

R (A: B) = {R (A) \ over R (B)} = \ more over {P (B) \ more over {1-P (B)}}} =

(see in addition Fahrmeir 2003, to chapter 3.2.1; there Odds reason is shown also as "“relative chances"”, but was in-patriated so far in the German shoptalk rather the English term. That seems meaningful, because "“relative chances"” easily with "“relative risks"” can be confounded [which something else is!]).

The formulas are described in the following on the basis a fictitious example with empirically determined probabilities (expressed as percentages):

We call the probability of women to have no predominance P (A), and the appropriate probability of the men as P (B). The Odds that a woman does not have a predominance, amounted to thus 60:40 or 1.5, with a man amounts to you against it only 30:70 or 0,43. In principle it shows up that a value of the Odds of exactly 1 expresses a relationship of 50:50, values >1 expresses that the category in the counter, values <1 that that exhibits the larger portion in the denominator.

The Odds reason amounts to in the example 1,5: 0,43 = 3,5. That is called the "“chances"” by women not to be over weighty is 3.5 times as large as by men. The Odds reason can be understood therefore as connection measure. A Odds reason of 1 meant that there is no difference in the Odds, is the Odds reason >1, is larger the Odds of the first group, is it <1, is smaller it than those the second group.

Here intentionally (fictitious) an example with medical or epidemiological background was selected, because straight is strongly pronounced in this range thinking in Odds and Odds reason, thus in (relative) chances (even if behind it frequently "“risks"” stand, e.g. on death by cardiac infarct, by cancer etc.). The Odds reason actually plays an important role in the meantime also in other sociological disciplines, particularly in connection with the logistic involution.

Odds and Odds reason can be expressed in each case regarding two developments. In larger than 2x2-Tabellen accordingly several Odds and Odds reason can be computed.

At Odds reason its expressed Unanschaulichkeit is problematic. As strong a connection is, for which (statistically significant) a OR was computed of 3, cannot from the number actually not be derived. The size of the OR does not only hang of the strength of the connection, but also of the basic probabilities of the examined events off. Therefore additionally always also the probabilities should be indicated to the OR.

Bets

In connection with bets, in particular with sport bets, the English term Odds is often translated briefly with, victory or profit margin or ratio. Odds represent for a long time the usual way of Buchmachern to probabilities to indicate. The representation of the Odds in the business varriert depending upon location.

If one regards an event with the probability of entrance of 1 from 5 (thus 0.2 or 20%), then is the Odds 0.2/(1-0,2) = 0.2/0.8 = 0,25. With employment of 1 in a fair bet and entrance of the event the disbursement amounts to 4, in addition the employment is paid back of 1. A bookmaker in Continental Europe indicates for this 5.0. The employment of 1, which can be paid back, is here already contained in the disbursement. A British bookmaker writes 4 to 1 approximately (or 4/1), an American bookmaker indicates as +400 the profit from an employment of 100.

Against it if the probability of entrance of an event amounts to 4 from 5 (thus 0.8 or 80%), then is the Odds 0.8/(1-0,8) = 4. With use of 4 in a fair bet and entrance of the event the disbursement amounts to 1, in addition the employment is paid back of 4. A bookmaker in Continental Europe indicates for this 1.25, who is employment here in the disbursement already contained. A British bookmaker writes 4 to 1 for (or 1/4), an American bookmaker indicates as -400 the necessary employment, in order to obtain 100 profit.

See also

• Probability theory
• Odds strategy
• Statistics
• Gambling
• Profit margin

Literature

• F. Thomas Bruss: The art of the correct decision. In: Spektrum der Wissenschaft. 06/2005. Spektrum der Wissenschaft publishing house company, P. 78-84, ISSN 0170-2971

• Fahrmeir, Ludwig; Artist, Rita; Pigeot, iris; Tutz, Gerhard: Statistics. The way to the data analysis. Heidelberg and others: Springer, 4. Edition 2003, chapter 3.2.1.

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