Lottery Analysis

For the Healthy Living Rewards Quarterly Wellness Challenge, one grand prize winner receives an $8,000 wellness retreat in Hawaii each quarter. When selection occurs randomly from the 100,000-member pilot, each member category has a specific winning probability based on their representation.

Prize Distribution Probabilities

• Large Employer Members:P(Large Employer) = 42,000/100,000 = 0.42 or 42%

• Large employer members have the highest winning probability because they represent the largest segment of eligible participants.

• Small Employer Members:P(Small Employer) = 23,000/100,000 = 0.23 or 23%

• Individual/Family Plan Members:P(Individual/Family) = 18,000/100,000 = 0.18 or 18%

• Medicare Advantage Members:P(Medicare Advantage) = 17,000/100,000 = 0.17 or 17%

• Medicare Advantage members have the lowest probability, reflecting their smaller proportion of the pilot population.

Visual Analysis

Figure 1 Grand Prize Winning Probability by Member Category

The visualization above illustrates probability distributions, showing large employer members have the highest chance (42%) while Medicare Advantage members have the lowest (17%) of winning the quarterly Hawaii wellness retreat through random selection.

Factors Beyond Random Selection

While this wellness challenge employs truly random selection for prize distribution, several legitimate business and clinical factors might influence wellness awards in other healthcare contexts.

Merit-Based Incentives: Health plans sometimes offer enhanced incentives to members with chronic conditions including diabetes, hypertension, or heart disease to encourage disease management participation. The top 5% of healthcare spenders account for approximately 50% of total healthcare costs, making targeted incentives clinically justified (Loeppke et al., 2007).

Behavioral Achievements: Offering additional raffle entries for completing health risk assessments provides valuable population health data enabling targeted interventions (Goetzel et al., 2014). Extra entries for biometric screenings measuring blood pressure, cholesterol, and glucose drive early disease detection. Members completing health coaching sessions demonstrate 40-60% higher success rates in achieving weight loss and physical activity goals (Wolever et al., 2013).

These merit-based approaches reward members investing in behavior change, though they create non-random distribution patterns where more engaged members earn more entries.

Ensuring Fair Random Selection

To maintain absolute fairness and eliminate any possibility of discrimination, UnitedHealth Group implements rigorous safeguards throughout the selection process.

The selection process uses FIPS 140-2 compliant cryptographically secure random number generators ensuring truly unpredictable outcomes (National Institute of Standards and Technology, 2019). The randomization algorithm operates on anonymized member identification numbers completely stripped of protected health information, with zero access to gender, age, race, ethnicity, diagnosis codes, or any other protected characteristics.

An independent actuarial firm with healthcare industry expertise verifies the entire selection process, certifies randomness using statistical tests, and validates compliance with HIPAA privacy regulations and ACA wellness program rules (U.S. Department of Health and Human Services, 2013).

Multiple entry pathways accommodate members with disabilities or medical limitations. Members unable to meet step-count goals due to mobility limitations can earn equivalent entries through nutrition education or stress management activities, ensuring universal access regardless of health status.

Every program interaction is logged in HIPAA-compliant data warehouses with comprehensive audit trails that can withstand regulatory scrutiny from government agencies.

Mathematical Verification

To verify fairness over time, expected frequencies can be calculated for long-term program operation. Over 100 quarterly drawings, expected winners from each category should align with their population representation:

• Large Employer: 100 × 0.42 = 42 expected wins

• Small Employer: 100 × 0.23 = 23 expected wins

• Individual/Family: 100 × 0.18 = 18 expected wins

• Medicare Advantage: 100 × 0.17 = 17 expected wins

  
  

Statistical monitoring ensures actual outcomes match expected distributions, with any significant deviation triggering immediate investigation of potential system issues.

Note: Detailed probability calculations are provided in the accompanying Excel spreadsheet showing formulas and step-by-step work.