Author
Bowtie Team
Updated on
2025-07-09
Disclaimer: This article is translated with the assistance of AI.
What’s the difference between insurance and football betting? It’s a tricky question! To answer it, we need to dive into the mathematical principles behind both. Bowtie invited actuary Mr. J to break it down for you.
How Bookmakers Calculate Football Betting Odds in 3 Steps
1. Data Collection & Probability Estimation
Bookmakers employ a team of statistical experts to analyze data. Take a football match as an example: the first step involves gathering a vast amount of data that could influence the outcome. This includes player injuries, suspensions, head-to-head records, and home/away advantages. The goal isn’t to predict the exact result—100% accuracy is impossible—but to estimate the probability of each possible outcome as the foundation for calculating odds.
For instance, in a match between Manchester City and Arsenal, both teams are at the top of the league table. However, with Manchester City playing at home and having won three of their last five encounters, the estimated probabilities might be: 50% for Manchester City, 25% for a draw, and 25% for Arsenal. The initial odds could look like this:
| Manchester City (Home Win) |
Draw | Arsenal (Away Win) |
| 1.6 | 3.4 | 3.6 |
2. Adjusting Odds for Profit Margin
After calculating the initial odds, bookmakers adjust them downward to ensure a profit margin (The Margin). These adjusted odds are what you see on betting websites (assuming a target profit margin of 5%). This explains why it’s tough for regular bettors to consistently beat the bookmakers.
| Manchester City (Home Win) |
Draw | Arsenal (Away Win) |
| 1.6 * 1.05 = 1.68 | 3.4 * 1.05 = 3.57 | 3.6 * 1.05 = 3.78 |
3. Real-Time Monitoring & Betting Trends
The final step involves real-time monitoring of betting inflows: If a bookmaker suddenly receives a flood of bets on one side, the odds for that outcome are lowered to minimize risk (Achieve a Balanced Book). Simply put, if there’s a surge of bets on Manchester City, the odds might shift like this, making the home win less attractive:
| Manchester City (Home Win) |
Draw | Arsenal (Away Win) |
| 1.68 * (1 – 10% ) = 1.51 | 3.57 | 3.78 * (1 + 10% ) = 4.16 |
On the risk management front, bookmakers also hedge their bets by placing wagers with other companies, essentially betting against their own retail customers.
Using Poisson Distribution to Calculate Odds:
Poisson Distribution is ideal for modeling the probability of random events occurring within a fixed interval. It can be used to estimate football goals per match. Start by taking each team’s average goals scored this season, then use the Poisson function in Excel to predict the number of goals in the next game. By comparing the goal-scoring probabilities of both teams, you can simulate the likelihood of various match outcomes.
(This is the simplest mathematical model and doesn’t account for factors like player injuries, suspensions, head-to-head records, or home/away advantages. Hence, the odds for both teams may appear closer than in the example above.)
Insurance Pricing Similar to Betting Odds?
Insurance companies and betting firms share a common goal: earning profits with minimal risk. From a mathematical perspective, the way odds are calculated bears striking similarities to insurance pricing.
1. Actuaries Calculate Claim Probabilities
Take car insurance as an example. Factors like car make and model, driver profile, mileage, and residential area are considered. The goal isn’t to predict when a crash will happen but to estimate the likelihood of different types of accidents (personal or third-party). For lifetime annuities, pricing might reference Hong Kong’s population life expectancy data and longevity improvement trends, alongside historical data on policyholders’ life expectancy.
However, there’s a key difference between insurance and gambling: insurance premiums don’t rise with more buyers. Since insured events are more predictable, a larger pool of policyholders tends to bring results closer to the average.
2. Like Bookmakers, Insurers Hedge Risks
For instance, if an insurer sells too many products with guaranteed minimum interest rates, they might hedge by purchasing derivatives betting on falling rates (like Interest Rate Swaps) in the market. Swaps are over-the-counter derivative contracts exchanging fixed-rate payments for floating rates based on the London Interbank Offered Rate (LIBOR). These can generate profits when interest rates drop. .
Yet, some insurance risks can’t be hedged. Take life insurance—there’s no direct market hedge for a policyholder’s death risk. The only option is to contract with a reinsurer (essentially, insurance for insurers). However, such agreements take time to finalize. Risks like policy lapses or critical illness incidence rates are also tough to hedge.
Do Agents Pose Risks to Insurers?
First, when pricing new products, agent commissions are a major expense. For participating policies, first-year commissions can take up a hefty chunk of the premium. If policyholders surrender early, the insurer can’t recover costs and takes a loss. That’s why insurers heavily analyze and estimate surrender rates. On the flip side, insurers without agents dodge this risk and can focus purely on product coverage.
Beyond commissions, launching new products involves significant fixed costs. Companies with agents must run scenario tests to account for potential losses tied to agents, like agency fraud or the loss of business when a star agent (Key Agent) jumps ship. These losses need to be quantified.
Once quantified, these losses feed into the Operational Risk Capital Requirement. Insurers factor these capital needs into pricing, ultimately passing the cost to consumers (e.g., raising premiums or reducing coverage scope for new products) .
Insurance vs Gambling: Key Differences
| Gambling | Insurance | |
| Event at Stake | Short-term events, e.g., sports matches, horse racing | Personal events, e.g., death (life insurance), illness/injury (medical insurance) |
| Nature | Primarily entertainment | Hedging long-term risks |
The main difference between the two lies in this: Gambling focuses on short-term events like sports matches or horse racing, driven by entertainment, while insurance covers personal matters such as death (life insurance) or illness/injury (medical insurance), serving as a hedge against long-term risks.
Moreover, insurance offers something unique beyond payouts—a sense of peace of mind. This emotional reassurance is something numbers and math simply can’t explain.
A Key Difference Between Gambling and Insurance: Insurable Interest
As mentioned earlier, insurance relates to events that personally affect you. However, for an insurance contract to be valid, there must be an “insurable interest” between the policyholder and the insured. This concept is another crucial distinction between gambling and insurance.
What is “insurable interest”? It exists when the policyholder would suffer a financial loss if the insured experiences an event covered by the policy. For instance, in life insurance, insurable interest typically applies to immediate family members or spouses. This is also why you can’t just buy life insurance for a random stranger.
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