What is the Chance to Beat Control?

The Chance to Beat Control (CTBC) is a probability-based metric that quantifies the likelihood of a variation outperforming the control in an experiment. It provides valuable insights into the effectiveness of a new marketing approach and helps answer the question: “What is the probability that the variation is better than the control?”

Calculation of Chance to Beat Control

The Chance to Beat Control is typically calculated using statistical analysis, specifically Bayesian methods or Frequentist methods. One of the common approaches is Bayesian statistics, which incorporates prior knowledge and continually updates beliefs as data is collected during the experiment.

Bayesian Chance to Beat Control Formula

The formula for calculating the Bayesian Chance to Beat Control is as follows:

Chance to Beat Control = ∫ [ P(θv > θc | D) P(θv | D) dθv ]

Where:

• P(θv > θc | D) represents the probability that the variation’s effect (θv) is greater than the control’s effect (θc) based on the data collected (D).
• P(θv | D) represents the posterior distribution of the variation’s effect, which is updated as more data is gathered during the experiment.

Example

Let’s consider an A/B test where a marketing team is comparing two different email subject lines (Variation vs. Control) to determine which one leads to a higher open rate. After running the experiment and collecting data from a sample of users, the team uses Bayesian analysis to calculate the Chance to Beat Control. If the Chance to Beat Control is 90%, it means there’s a 90% probability that the Variation will outperform the Control in terms of open rates.

Best Practices for Interpreting Chance to Beat Control

• Set a Threshold: Before conducting an experiment, define a minimum threshold for the Chance to Beat Control that would indicate a significant improvement. This threshold will guide decision-making during the analysis phase.
• Consider Sample Size: Larger sample sizes generally lead to more precise estimates of the Chance to Beat Control. Ensure that the sample size is sufficient to draw reliable conclusions.

• Combine with Other Metrics: While the Chance to Beat Control is informative, it should be considered alongside other relevant metrics such as conversion rates, click-through rates, or revenue generated.