Guessing Penalty Calculator Formula

Understand the math behind the guessing penalty calculator. Each variable explained with a worked example.

Use the Guessing Penalty Calculator

Formulas Used

Expected Points from Guessing

expected_gain = guesses * (prob_correct * 1 - prob_wrong * penalty_per)

Expected Correct Guesses

expected_correct = guesses * prob_correct

Expected Wrong Guesses

expected_wrong = guesses * prob_wrong

Variables

VariableDescriptionDefault
guessesNumber of Guesses10
choicesChoices per Question4
penalty_perPenalty per Wrong Answer0.25
prob_correctDerived value= 1 / choicescalculated
prob_wrongDerived value= 1 - 1 / choicescalculated

How It Works

How to Calculate Guessing Penalty Impact

When a test penalizes wrong answers, random guessing has an expected value.

Formula

Expected Gain = Guesses x (P(correct) x 1 - P(wrong) x Penalty)

Where P(correct) = 1 / Number of Choices

If the penalty equals 1/(choices-1), guessing has zero expected value.

Worked Example

A student randomly guesses on 10 questions with 4 choices each and a 0.25 penalty.

guesses = 10choices = 4penalty_per = 0.25
  1. 01P(correct) = 1/4 = 0.25
  2. 02P(wrong) = 3/4 = 0.75
  3. 03Expected gain per guess = 0.25 x 1 - 0.75 x 0.25 = 0.25 - 0.1875 = 0.0625
  4. 04Total expected gain = 10 x 0.0625 = 0.625 points

Ready to run the numbers?

Open Guessing Penalty Calculator