Logical Fallacies

LogFall

A practical logical-fallacies reference with clear explanations, usable examples, and teaching tools.

Fallacy profile

Base rate fallacy

Occurs when someone judges how likely a case is by focusing on vivid case-specific evidence while ignoring the underlying frequency of the thing in question.

Mathematical

Definition

Occurs when someone judges how likely a case is by focusing on vivid case-specific evidence while ignoring the underlying frequency of the thing in question.

Illustrative example

This fraud filter is 98% accurate and flagged my transaction, so there is almost no chance the alert is wrong.

Teaching gauges

These 0-100 gauges are teaching aids for comparing fallacies. They are editorial classroom estimates, not measured statistics.

Recurring

60

Common in today's rhetoric

Common enough that most readers will meet it often.

Tricky

40

Easy to spot

Often hides inside wording, framing, or technical detail.

Almost automatic

90

Easy to innocently commit

Very easy for well-meaning people to commit without noticing.

Foundational

25

Difficulty

Usually approachable without much prior logic background.

Middle school+Formal logic

Reference

Family

Statistical/Sampling Fallacy

The reasoning misuses rates, probabilities, samples, distributions, or other quantitative expectations.

Quick check

What numbers, rates, or probabilities are being ignored or mishandled?

Why it misleads

A fuller explanation of how the fallacy works and why it can look persuasive.

For rare conditions or rare events, even very accurate tests can generate more false positives than true positives. The missing question is not just 'How accurate is the test?' but 'How common is the condition before the test is applied?'

That's like saying...

Instead of leading with the label, this analogy answers the shape of the reasoning move directly so the mistake is easier to see in plain language.

Fallacious claim

This fraud filter is 98% accurate and flagged my transaction, so there is almost no chance the alert is wrong.

That's like saying...

That's like hearing a smoke detector beep once and forgetting you are standing in a building full of low batteries. The vivid clue feels decisive only because the background rate was ignored.

Caveat

This label is easy to overuse. The point here is not to call every weak argument by this name, but to reserve it for the exact misstep it describes.

Common misapplication

Do not use this label every time numbers, odds, or percentages appear in an argument. The problem has to be a specific misuse of rates, samples, frequencies, or statistical comparison.

Use the label only when...

Use this label only when someone judges how likely a case is by focusing on vivid case-specific evidence while ignoring the underlying frequency of the thing in question. If the real problem is that someone assumes that because something could happen, it is therefore likely or inevitable that it will happen, the better label is Appeal to probability.

Often confused with

These near neighbors are easy to mix up, so use the comparison to see the exact difference.

Comparison

Appeal to probability

Why people mix them up: Both often look like mathematical mistakes at first glance.

Exact difference: Base rate fallacy happens when someone judges how likely a case is by focusing on vivid case-specific evidence while ignoring the underlying frequency of the thing in question. Appeal to probability happens when someone assumes that because something could happen, it is therefore likely or inevitable that it will happen.

Quick split: What numbers, rates, or probabilities are being ignored or mishandled? Then compare it with What numbers, rates, or probabilities are being ignored or mishandled?

Comparison

Ecological fallacy

Why people mix them up: Both often look like mathematical mistakes at first glance.

Exact difference: Base rate fallacy happens when someone judges how likely a case is by focusing on vivid case-specific evidence while ignoring the underlying frequency of the thing in question. Ecological fallacy happens when statistics about a group are used to draw conclusions about particular individuals in that group.

Quick split: What numbers, rates, or probabilities are being ignored or mishandled? Then compare it with What numbers, rates, or probabilities are being ignored or mishandled?

Practice And Repair

Extra teaching tools that show why the fallacy is persuasive, what to look for, and how to correct it.

Why it matters

Why this mistake matters

Base rate fallacy threatens rationality because someone judges how likely a case is by focusing on vivid case-specific evidence while ignoring the underlying frequency of the thing in question.

Main reasoning problem

Someone judges how likely a case is by focusing on vivid case-specific evidence while ignoring the underlying frequency of the thing in question.

Why this kind of mistake matters

It makes quantities, probabilities, rates, or samples push confidence farther than the math permits.

Check yourself

The assessment area now uses mixed 10-question sets, so the fallacy is not announced in the title before the quiz begins.

What the assessment does

You will work through a mixed set of fallacy-identification questions. Focused links from a fallacy page will quietly include this fallacy among nearby look-alikes without announcing the answer in the page title.

Questions to ask

Use these category-based prompts to audit similar arguments.

Prompt 1

What numbers, rates, or probabilities are being ignored or mishandled?

Case studies

Each case study explains why the example fits the fallacy and links back to its source whenever source information is available.

Noncitizen voting, already illegal in federal elections, becomes a centerpiece of 2024 GOP messaging

AP's May 18, 2024 overview of noncitizen-voting rhetoric documented how a politically useful intuition about election fraud kept being treated as if it were established by the evidence. The report is especially useful for seeing how tiny counts, suggestive language, and moral urgency can be stretched into system-wide claims. The fallacy here is Base rate fallacy: someone judges how likely a case is by focusing on vivid case-specific evidence while ignoring the underlying frequency of the thing in question. That matters here because for rare conditions or rare events, even very accurate tests can generate more false positives than true positives. A better analysis would remember that the missing question is not just 'How accurate is the test?' but 'How common is the condition before the test is applied?'

Associated Press · 2024-05-18

Fact-check: Trump keeps claiming noncitizen voting is a big problem. It's not

NPR's October 12, 2024 fact check on noncitizen-voting claims is a good case study in the gap between isolated anecdotes and population-level conclusions. It shows how a few suspicious stories can feel decisive even when the base rates and verified counts point the other way. The fallacy here is Base rate fallacy: someone judges how likely a case is by focusing on vivid case-specific evidence while ignoring the underlying frequency of the thing in question. That matters here because for rare conditions or rare events, even very accurate tests can generate more false positives than true positives. A better analysis would remember that the missing question is not just 'How accurate is the test?' but 'How common is the condition before the test is applied?'

NPR · 2024-10-12

Iowa finds several dozen instances of noncitizens voting in a past election

AP's coverage of Iowa finding dozens of noncitizen votes is useful precisely because it reports real violations without letting the count float free of scale. The story helps show the difference between acknowledging a genuine problem and inflating it into a sweeping narrative. The fallacy here is Base rate fallacy: someone judges how likely a case is by focusing on vivid case-specific evidence while ignoring the underlying frequency of the thing in question. That matters here because for rare conditions or rare events, even very accurate tests can generate more false positives than true positives. A better analysis would remember that the missing question is not just 'How accurate is the test?' but 'How common is the condition before the test is applied?'

Associated Press · 2024-10-23

Q&A on H5N1 Bird Flu

FactCheck.org's May 2024 H5N1 explainer is a strong illustration of why people need mechanisms, prevalence, and scope before drawing practical conclusions from a scary headline. It helps distinguish real uncertainty from reasoning that jumps too fast from fragments of evidence to a preferred story. The fallacy here is Base rate fallacy: someone judges how likely a case is by focusing on vivid case-specific evidence while ignoring the underlying frequency of the thing in question. That matters here because for rare conditions or rare events, even very accurate tests can generate more false positives than true positives. A better analysis would remember that the missing question is not just 'How accurate is the test?' but 'How common is the condition before the test is applied?'

FactCheck.org · 2024-05-04

Why AP called the Arizona Senate race for Ruben Gallego

AP's explanation of why it called the Arizona Senate race for Ruben Gallego is a useful numbers-first counterexample to intuition-driven political certainty. It shows what it looks like to reason from remaining vote shares, path constraints, and actual denominators instead of headline impressions. The fallacy here is Base rate fallacy: someone judges how likely a case is by focusing on vivid case-specific evidence while ignoring the underlying frequency of the thing in question. That matters here because for rare conditions or rare events, even very accurate tests can generate more false positives than true positives. A better analysis would remember that the missing question is not just 'How accurate is the test?' but 'How common is the condition before the test is applied?'

Associated Press · 2024-11-12

Related fallacies

Nearby entries chosen by shared categories and family resemblance.