# How to Calculate the Expected Deductible From Probability

by Walter Johnson

The analysis of insurance deductibles as a matter of probability is best accomplished using a simple regression analysis program. Using these is simple, so long as your data are reliable. The concept of probability here refers to the chances that a claim will exceed the deductible, and hence be a claim on insurance company resources. If this probability is high, then a firm might not issue the policy, or it might increase the deductible. It might also make the monthly premiums high.

1. Gather the data for all variables. In dealing with such probabilities, you must deal with the activity being covered, the track record of the proposed client and those like him, and existing company resources. This is just a beginning. Most insurance firms have much of this data already encoded, so entering it into a STATA or SPSS probability regression package is simple.

2. Define your dependent variable. In this case, it is the probability that a claimant, in a given year, will go over the proposed deductible for an insurance policy. Therefore, the dependent variable will amount to the proposed deductible. You can plug in \$1,000, and the probabilities will be lower than if you used \$2,000, since the chances of going over that is less than \$1,000. Once this is clarified, the rest is easy.

3. Look at your p score once you have run the regression. In all regression software, “p” refers to "probability." It means that each independent variable will have a probability that it will, by itself, cause the deductible to be exceeded. For example, you want to see what will cause a claim for a certain class of policies to lead to a drain on company funds. If you have as independent variables things like the danger of certain activities, and it has a p score of 0.6, then this is highly significant. More than half the time, in other words, will the nature of the activity cause the deductible to be exceeded on each claim. This means that if a company is going to insure someone involved in dangerous activities, it should charge more per month or make the deductible suitably high.

4. Use different deductible rates for your dependent variable. This will show how the causal variables can be related to different deductible packages. A health insurance policy for a professional football player normally has a high deductible, because NFL players make lots of money and chances of injury are high. If the deductible is \$20,000 dollars per year and you get a p score of 0.3 as a result, then this shows that there is a low probability that football injuries, by themselves, will drain funds from the insurance firm. If you plug in a \$10,000 yearly deductible, the score should go up, since the probability that an NFL player will go over this deductible in a given season is likely higher.

#### Tip

• For more accurate readings, add more independent variables. These might include the psychological profile of the person being covered, the regulation of the covered activity -- such as the use of protective equipment -- laws in force that regulate the proposed activity, or anything that will impact on the safety of the activity being covered. The more variables you use, the more accurate your "p" scores.

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