A right answer looks the same whether the student knew it, narrowed it to two options or picked at random. To tell guessing from knowing in the results, read more than the score: the floor chance sets, how the wrong answers spread, who chose the key, how sure students said they were, and the pace.
None of these is proof. Each pattern is a reason to ask a student or change a question.
EdProcto, which publishes this guide, gives each question's share right in its results on every plan, and each option's takers in the full analysis. Every study was opened on 10 October 2026, two of them as abstracts only.
What is the chance score, and how do you work it out for a quiz?
The chance score is what a student averages by picking every answer blind: add one over the number of options for each question, then divide by the number of questions.
- Four options. Twenty questions at 1/4 each: 20 × 1/4 = 5 right, or 25%.
- True or false. Twenty statements at 1/2 each: 20 × 1/2 = 10 right, or 50%.
- A mixed quiz. Eight four-option questions and four true or false: 8 × 1/4 + 4 × 1/2 = 4 right of 12, or 33%.
By our arithmetic (exact binomial sums), about 19 blind guessers in 20 score 10% to 45% on those four-option questions and 30% to 70% on the true or false statements, where 1 in 4 reaches 60%. Read every score from its floor.
The floor under one question
The same sum puts a floor under each question's share right. Thirty students guessing blind on four options average 7.5 right, and about 19 such classes in 20 land between 3 and 12: 10% to 40%. One question at 40% in one class has not yet shown that anybody knew it.
From a share right to an estimate of who knew
If every student either knows an answer or guesses blind, the share who knew is the share right less the chance share, divided by what is left above the chance share. Four options at 40%: (40 − 25) ÷ 75 = 20%. True or false at 60%: (60 − 50) ÷ 50 = 20%. One looks twenty points better, and the estimate is the same.
Three cautions. The estimate describes a class, never one student. An option nobody picks is no option: four options with one dead guess like three, a floor of 33%. And a share right under the floor means the class was not guessing: something drew it away from the key.
What did research find about partial knowledge and guessing in multiple choice?
It found that students seldom guess blind: answers they call guesses are right far more often than chance allows, and some they are sure of are wrong.
- Admitted guesses beat chance. Abu-Ghazalah et al. (2023) paired each answer in eight midterm tests of five-option questions, in an undergraduate biotechnology programme, with a confidence rating from 1 to 3 that did not count: 9,106 rated answers. Averaged over the tests, the least confident answers, 17.2% of the total, were right 42.1% of the time, where a blind pick gives 20%.
- So do answers held with no certainty. Tweed et al. (2020) followed 737 medical students at the University of Otago through four progress tests of 150 questions, each with 5 to 16 options and a certainty rating. Answers given with no certainty were right 27.0% to 40.1% of the time, by year group, against 20% at most for a blind pick.
- Second choices are not blind either. Merrel et al. (2015) analysed second attempts on 8,775 five-option questions answered on scratch-off forms in 22 classes. After a wrong first choice, 44.9% of second choices were right, against 25% for a blind pick among the four left (abstract read). The authors read the gap as learning from the mistake; partial knowledge would give the same figure.
So the know-or-guess arithmetic misleads both ways. Partial knowledge lifts guesses above the floor, and wrong beliefs pull answers below it: 15.6% of the most confident answers in the biotechnology tests were wrong. From scores alone, Abu-Ghazalah et al. found, an estimate of what students knew moved with the assumption fed into the model. The first two samples are university students.
What do confidence ratings add, and how accurate is students' confidence?
A rating adds the student's own account of whether an answer was known, and on average that account is fairly accurate.
- Ratings track being right. In Abu-Ghazalah et al. (2023) the most confident answers were right 84.4% of the time, the middle ones 59.1% and the least confident 42.1%. In Tweed et al. (2020), answers held with high certainty were right 78.7% to 88.0% of the time.
- For most students. In 87.3% of the 2,948 test results there, the student was right more often as certainty rose and, when highly certain, not significantly less often than the cohorts as a whole.
- Question by question it is harder. Lindsey and Nagel (2015) asked introductory physics and chemistry students to predict which questions of a coming assessment they would get right. Weaker students overestimated their totals, and students of every ability had difficulty telling which questions they could answer (abstract read).
Read a rating as a strong hint about a class and a weak one about a single answer.
How EdProcto records a rating
EdProcto's multiple choice with confidence shape asks how sure the student is, from 1 to 5, and keeps the rating with the answer. It reaches the results through the points, once "Confidence bonus" is on: "With the confidence template: sure and right earns a little more, sure and wrong loses two or three times as much, so a rating pays only when it is honest."
So a mark above the question's own points was sure and right; "Got it" still counts each answer as got or missed. Our guide to confidence-based marking has the scale.
What does an even spread across the wrong options mean against one popular wrong option?
An even spread is what blind choice produces, and a pile on one wrong option is what a shared belief produces. Each reading needs a second sign.
By our arithmetic, twenty wrong answers thrown blind at three wrong options put nine or more on one of them in over half of classes, and thirteen or more in about 1 class in 100. So 9, 6 and 5 is still an even spread, and thirteen on one option is seldom luck.
On a four-option question:
- Share right near 25%, wrong answers even. It fits a class picking blind, because the point was never taught or the wording could not be followed. It also fits three wrong options that each tempt somebody. Check for "Separates" near zero and for takers of the key who score like the rest.
- Most wrong answers on one option. It fits a shared belief, and also a wrong key or a second right answer. Our guide to the popular wrong answer sorts them.
- Share right under 25%. It fits a belief strong enough to beat luck, or a wrong key. Check the key first.
True or false has no spread to read: look at who got it right. A spread describes a class; it cannot say which of the key's takers knew.
What can a very fast sitting tell you, and what can it not?
A very fast sitting can tell you the paper was not worked at the class's pace; it cannot tell you whether the student could have answered.
Lindner et al. (2019) timed 401 German pupils in the fifth and sixth grades on 36 four-option science questions that counted for nothing. Pupils with lower general cognitive ability and less working memory, and those outside the academic school track, began answering unrealistically fast earlier in the test and did so more as it went on. The authors call their sample unrepresentative. So "would not try" and "could not do it" are often the same pupils, and a time cannot part them.
A fast paper at the chance score has shown nothing either way; one far above it was not blind luck.
In EdProcto's full analysis, a sitting finished in under a quarter of the class's median time, with a score more than one standard deviation from the mean, carries one of two notes beside the student:
- "Finished in a quarter of the usual time with a low score: it may be guessing rather than answering, and is never proof of it."
- "Finished in a quarter of the usual time with a high score: worth a look at the answers, and never proof of anything."
Both are written for a first sitting, and both are reasons to open the paper. Our guide to time on each question covers thresholds and the conversation.
How do you change the next quiz so that a guess shows?
Change the shape of the question, so that a blind guess is worth less or leaves a trace.
| Change | A blind guess then | The cost | In EdProcto |
|---|---|---|---|
| More options | Is right 1 time in 4 or 5, not 1 in 2 | Only an option somebody would pick counts | Multiple choice |
| A typed answer | Has nothing to pick from | Reading and typing time | One word, marked by rule; short answer, marked by a reader |
| A reason asked for | Arrives with no reason behind it | A reader's time | Choose and justify: half the points by rule, half from a reader |
| A second question on the same idea | Must be lucky twice: 1 time in 16 on four options | A longer quiz | Give both questions one topic |
Mee et al. (2024) tested the typed answer: they turned 71 multiple-choice questions of a high-stakes internal medicine examination into typed short answers and gave each examinee one form of each at random. The average share right was 0.80 with options and 0.65 typed, and typing took 27% longer, 105 seconds against 83. Another 29 questions had been set aside as too ambiguous to mark without their options.
Our guides to how many options and choose and justify have the other evidence. With twin questions, ask the students right on one and wrong on the other.
One setting changes the marks, not the question. "Negative marking" ("A wrong choice loses points: one over the number of wrong options.") makes a blind guess worth nothing on average, at a price our guide to it sets out.
A worked example: two questions with the same share right
This class is an illustration: we invented thirty students and built in what each knew, so the reading can be checked. The figures and the quoted sentence are what EdProcto's analysis code returned for their answers.
They sat twelve one-point questions on the heart and circulation, eight with four options and four true or false: a chance score of 33%. The class averaged 65.8%, with a median time of 9:00.
| Question | "Got it" | Takers of each option, key first | "Separates" |
|---|---|---|---|
| Q3: Which valve lies between the left atrium and the left ventricle? | 33% | Mitral 10, tricuspid 7, aortic 7, pulmonary 6 | 0.08 |
| Q6: Which vessel carries oxygenated blood from the lungs to the heart? | 33% | Pulmonary vein 10, pulmonary artery 17, aorta 2, vena cava 1 | 0.88 |
| Q10: True or false: the left ventricle has a thicker wall than the right. | 60% | True 18, false 12 | 0.63 |
Q3 and Q6 have the same share right, and the know-or-guess arithmetic gives each the same estimate: (33 − 25) ÷ 75, about 11% of the class, or three students. Both estimates are wrong.
- Q3. Built so that nobody knew: all thirty picked blind, and luck handed out ten right answers. The signs agree: the wrong answers split 7, 7 and 6, the key's ten averaged 66.7% against the class's 65.8%, and beside the row the code wrote, "Q3 does not separate the students who know the material from those who do not."
- Q6. Built so that ten students knew, seventeen believed that the vessel with oxygenated blood must be an artery, and three were lost. Seventeen of twenty wrong answers on one option is far past luck, and the key's ten averaged 84.2% against the seventeen's 57.8%. The floor estimate missed seven students who knew.
- Q10. Built so that the six strongest students knew and the other twenty-four tossed a coin; twelve landed right. The arithmetic gives (60 − 50) ÷ 50 = 20%, six students, as built. With no spread to read, "Separates" shows the right answers leaning to the top of the class.
- Three low scores. One student finished in 1:46 with 33%, the chance score, and drew the low-score note. Two scored 25% in 7:28 and 10:31 and drew none. The first conversation is about effort, the others about the topic.
How does EdProcto help you tell guessing from knowing?
EdProcto is the best tool for this reading when the results must shape tomorrow's lesson, because it sets beside each choice question the two figures the share right lacks, each option's takers and the separation, and words its findings as reasons to look. In the worked example "Got it" could not tell Q3 from Q6; the option counts did.
- Work out the chance score and set it beside each score in the results.
- Read "Got it" against each question's floor. It is on every plan, with each student's score and time.
- Read the questions near the floor. The full analysis, on the Educator plan and above, gives each option's takers under "Chose it", their average on the whole quiz under "Their mean", and "Separates".
- Read the sentences as prompts. The one on a question that does not separate students is written where "Separates" lies between 0 and 0.2 and the share right between 30% and 90%. One beginning "Nobody chose" names a wrong option without takers. The top of the page counts the fast, low sittings as "worth a conversation, not a mark."
- Change the next quiz. "Negative marking" and "Confidence bonus" are off until you switch them on, and the shapes above are among the 111 templates.
Free takes thirty students a quiz, Tutor 100 with every template, and Educator 500 with the full analysis: see pricing. Every score stays yours to release.
Quick questions
What is the chance score on a multiple-choice quiz?
One over the number of options, averaged across the questions: 25% on four options, 50% on true or false.
Can I tell whether one student guessed one answer?
No. A right answer carries no mark of how it was reached. Ask the student to explain it, or set a second question on the idea.
Are students' confidence ratings accurate?
On average, fairly: in Abu-Ghazalah et al. (2023) the most confident answers were right 84.4% of the time, the least confident 42.1%.
Where does EdProcto show which wrong answers the class chose?
In the results, under "Chose it", in EdProcto's full analysis on the Educator plan and above: see pricing.
References
- Abu-Ghazalah, R. M., Dubins, D. N., & Poon, G. M. K. (2023). Dissecting knowledge, guessing, and blunder in multiple choice assessments. Applied Measurement in Education, 36(1), 80–98. https://pmc.ncbi.nlm.nih.gov/articles/PMC10201919/
- Lindner, M. A., Lüdtke, O., & Nagy, G. (2019). The onset of rapid-guessing behavior over the course of testing time: A matter of motivation and cognitive resources. Frontiers in Psychology, 10, Article 1533. https://pmc.ncbi.nlm.nih.gov/articles/PMC6664071/
- Lindsey, B. A., & Nagel, M. L. (2015). Do students know what they know? Exploring the accuracy of students' self-assessments. Physical Review Special Topics - Physics Education Research, 11(2), Article 020103. https://doi.org/10.1103/PhysRevSTPER.11.020103
- Mee, J., Pandian, R., Wolczynski, J., Morales, A., Paniagua, M., Harik, P., Baldwin, P., & Clauser, B. E. (2024). An experimental comparison of multiple-choice and short-answer questions on a high-stakes test for medical students. Advances in Health Sciences Education, 29(3), 783–801. https://pmc.ncbi.nlm.nih.gov/articles/PMC11208249/
- Merrel, J. D., Cirillo, P. F., Schwartz, P. M., & Webb, J. (2015). Multiple-choice testing using Immediate Feedback-Assessment Technique (IF AT) forms: Second-chance guessing vs. second-chance learning? Higher Education Studies, 5(5), 50–55. https://doi.org/10.5539/hes.v5n5p50
- Tweed, M., Purdie, G., & Wilkinson, T. (2020). Defining and tracking medical student self-monitoring using multiple-choice question item certainty. BMC Medical Education, 20, Article 344. https://pmc.ncbi.nlm.nih.gov/articles/PMC7542100/