The Law Of Large Numbers In Medical Cost Sharing

December 9th, 2014

One medical incident can cost thousands of dollars; a sum that doesn't fit into the most household budgets. However, rather than trying to manage these expenses alone, individuals can come together to take advantage of the law of large numbers, a mathematical principle that has significant implications for healthcare.

The law of large numbers says that the more times a process is carried out, the closer to the expected average the results become. For example, when flipping a coin, the expected average is to get heads half the time and tails half the time, but in just 10 coin flips, it would not be too extraordinary to end up with 3 heads and 7 tails. However, if a coin was flipped 1,000 times, the result would be much closer to the 50/50 average that was expected.

Where healthcare is concerned, the law of large numbers can be applied to the medical costs of people who come together as a group, such as the membership of Liberty HealthShare. In any given month, a few of these individuals might have very high costs, but many of the other individuals will have lower costs. The law of large numbers says that the larger the group, the closer it will be to arriving at a steady average cost per person, each month.

Rather than having to bear the full cost of monthly medical bills, Liberty HealthShare members are able to share their medical expenses with a group of like-minded individuals. This approach to healthcare allows members to follow the Christian principle of meeting one another's needs, according to the sharing guidelines of the group. Each member has an incentive to be generous and cooperative by caring for the needs of others because there may be a time when they also need someone to help care for them.

The law of large numbers involves quite a bit of math to track the results over time. Because of this, healthcare sharing ministries whose systems are based on the law of large numbers need to have systems in place to calculate what the average costs will be and how to distribute them among sharing members.

Liberty HealthShare utilizes a sophisticated algorithm to match eligible medical bills to members who pay shares each month. The algorithm takes the amount of each giving member's regular share and matches it to a member who has a bill that is eligible for sharing. Each month, the giving member is notified about the member who will receive their share. With the click of a button inside the member ShareBox, that month's share is passed along to pay the eligible medical bills.

While the law of large numbers has to do with averages, we recognize that the real world does not always abide by this theory. Some months, there are fewer medical expenses than there are share amounts. In these months, members hold onto the funds in their ShareBox. In months that have more expenses than shares, the algorithm draws on funds that were previously held in member ShareBoxes and uses these to pay the expenses.

The medical field changes every year and the costs of care fluctuate. Therefore, Liberty HealthShare must recalculate the ideal share amounts each year. We look at the total number of members and shared costs and then divide these costs between the members to calculate the monthly share amount. As a result, sometimes share amounts will increase from one year to the next, and other times, they will decrease. We always follow the principle of meeting needs while maintaining the lowest possible average costs to our members.

If you or someone you know would be interested in medical cost sharing call us at (855) 585-4237, take a look at our three sharing programs, or request our free decision guide to learn more.