Calculating the expected value (EV) of school security

Should you bet on the Eagles to win the Super Bowl? A method for calculating the probability of gambling payouts can help school officials decide how to invest limited resources into security options.

Happy Super Bowl week! Here’s a question that many people will be asking: Is it smart to bet $100 on the Eagles to beat the Chiefs on Sunday?

That depends on how well you understand the probability of winning and the potential payout. And how does this connect to school security? Read a little more and you will find out!

Gamblers use expected value as a tool to evaluate the potential payout of bets over the long term. By calculating the expected value—which is really just multiplying each possible outcome by its probability and then summing these products—gamblers can assess whether a wager is likely to result in a positive or negative return on average. This helps gamblers make informed decisions by focusing on favorable odds and avoiding the statistically losers over the long run (just like a really expensive security solution that only addresses a very specific type of risk. An example is the AI security camera software that failed during a school shooting last week: A Nashville school district invested about $1 million in AI gun identification software leaving some to wonder what went wrong in detecting a school shooter in the halls).

Understanding expected value allows gamblers to manage risk more effectively and maximizes their chances of achieving consistent profits over time, despite the inherent uncertainties of gambling outcomes. Looking at Kansas City and Philly in the Super Bowl:

• Spread (handicapping a pick of the winner): Chiefs -1.5 which means betting on Kansas City to win by at least 2 points

• Money Line (payout from a bet on the winner): Chiefs -125 / Eagles +105 which means a $100 bet on Philly pays out $105 while you need to bet $125 on the Chiefs to win $100.

Converting the Money Line to Implied Probability:

• Eagles +105 roughly implies a 48.8% break-even probability

• Chiefs -125 roughly implies a 55.6% break-even probability

Expected Value (EV) of betting on the Eagles:

• Win probability = 56.1%

• Lose probability = 43.9%

• Win payout at +105 = +$105 on a $100 wager

• Loss = -$100

EV=(0.561×$105)+(0.439×−$100) = $58.91−$43.90 = $15.01

That translates to a +15% return on your $100 wager in the long run. This means that betting on the Eagles money line at +$105 is a positive expected-value play.

More About Expected Value

EV uses probability statistics to quantify the average outcome of a random variable over numerous trials. This shows the long-term behavior of a random process by determining where the center of the distribution lies (this point where probability and loss are highest on the graphic below). This means that expected value is a great tool to help make informed decisions under uncertainty like the randomness of if, when, and how a school shooting will occur.

Because security risks are generally uncertain, expected value is a great tool for quantifying and assessing potential risks from various threats. By calculating the expected value of different security incidents—which involves multiplying the probability of each threat occurring by the potential impact or cost if it does occur—schools can prioritize their security measures more effectively (or at least have a defensible decision-making process to show in court during civil litigation). This quantitative approach allows school officials to identify which risks pose the greatest potential loss and shows the impact of different options to mitigate them.

This process is important because school security isn’t a zero sum game. Each decision or investment to address one type of threat can end up increasing the risk from another (the Fortress Problem paradox). Calculating the expected value for school security means:

• Identifying and assessing the potential risks

• Determining their probabilities

• Estimating the costs associated with both bad outcomes from a shooting and the cost of each preventive measures.

Taking the time to calculate expected value helps in informed decisions about which security measures are cost-effective, how to allocate limited funding, and identifying which risks are the most important to address. Here’s a step-by-step guide to calculating the expected value for school security:

1. Identify Potential Security Risks

List all the bad things that could occur at your school:

• Physical Threats: School shooting, physical violence, vandalism, theft, arson.

• Natural Disasters: Earthquakes, floods, hurricanes, fires.

• Cyber Threats: Data breaches, cyberbullying, hacking.

• Health Risks: Transmissible diseases and viruses, chemical or toxin exposure.

• Other Risks: Accidents, negligence, equipment failure.

2. Estimate the Probability of Each Risk

Assign a probability to each identified risk based on historical data, expert opinions, or statistical models:

• High Probability: Incidents that occur frequently (e.g., physical fights).

• Medium Probability: Occasional incidents (e.g., severe weather).

• Low Probability: Rare but severe incidents (e.g., school shootings).

3. Determine the Impact or Cost of Each Risk

Calculate the potential cost if each risk were to occur:

• Direct Costs: Loss of life or injury, property damage, medical expenses, legal fees.

• Indirect Costs: Loss of reputation, lost hours of learning, decreased enrollment, acute psychological impact on students and staff.

• Intangible Costs: Long-term emotional distress, loss of trust, loss of future opportunities due to psychological trauma or lost learning.

4. Calculate the Expected Loss for Each Risk

Expected Loss=Probability of Risk × Cost of Risk