Close matches often feel meaningful. A one-point difference, a late goal, or a narrow margin can create the impression that an assessment was “almost right” or that expectations were accurately aligned with reality. Statistically, however, closeness does not indicate accuracy. It reflects where an outcome happened to land within a distribution, not how well it was anticipated.
This article explains why close matches feel informative—and why that feeling does not translate into statistical relevance.
Closeness Is an Outcome, Not a Measurement
Accuracy implies a measurable relationship between expectation and result. Closeness, by contrast, is simply a description of the final margin.
A narrow result:
Does not confirm correct anticipation
Does not validate assumptions
Does not imply reduced uncertainty
It describes distance, not alignment.
Margins Are Not Signals
In probabilistic systems, margins are not signals of correctness. Outcomes are drawn from a range of possibilities, many of which cluster near the center of that range.
Because of this:
Close outcomes are common by design
Wide margins are not required for accuracy
Proximity does not imply intent or precision
This behavior is further explored in the paradox between volatility and expected value, where frequent near-center outcomes are shown to mislead perceptions of predictability. Often, the confusion arises when people mistake momentum swings for statistical variance, attributing structural meaning to what is essentially random noise within a distribution. The system does not reward or track how close an outcome was to an expectation.
The Illusion of Predictive Nearness
Humans intuitively associate nearness with progress. In skill-based tasks, being close often means improvement. This intuition is mistakenly transferred to probabilistic outcomes, where it does not apply.
A close match feels like evidence of accuracy because:
The result is easy to rationalize after the fact
Small differences feel controllable
Narratives fit neatly around narrow margins
These factors shape perception, not probability.
Why Expected Values Do Not Require Close Results
Expected values describe long-term averages across many events. They do not imply that individual outcomes should land near any specific number.
An outcome can be:
Far from expectation and still consistent with the model
Close to expectation and still uninformative
Single events do not validate or invalidate expectations based on margin alone.
Boundary Effects and Misinterpretation
Many systems use thresholds to classify outcomes. Results near these boundaries often feel significant because the difference appears minimal.
However:
Boundaries are classification tools
Proximity to a boundary has no statistical privilege
Outcomes on either side belong to the same distribution
The perceived importance of closeness is created by the boundary, not by the data. This misinterpretation is closely related to outcome bias, where results are judged by how they feel rather than by the process that generated them.
Memory Bias Amplifies Close Results
Close matches are remembered more vividly than decisive ones. They invite analysis, replay, and explanation, which reinforces the belief that something meaningful occurred.
Over time, this creates a distorted memory pattern:
Close outcomes feel frequent
Accuracy feels higher than it is
Wide deviations fade from recall
The statistical record remains unchanged.
Repetition Does Not Convert Closeness Into Accuracy
Multiple close outcomes do not accumulate informational value unless they demonstrate consistent deviation from expectation across a large sample.
Without repetition and structure:
Near results remain independent
No learning signal emerges
Perceived accuracy does not become real accuracy
Closeness does not compound.
Accuracy Requires Structure, Not Proximity
True accuracy involves:
Consistent alignment with expectation
Measurable deviation across many events
Stability beyond random fluctuation
Close matches provide none of these on their own. They are outcomes, not evidence. This distinction helps explain why favorite teams still lose frequently even when expectations appear well calibrated.
Close matches feel meaningful because humans interpret proximity as precision. Statistically, however, closeness is not a measure of accuracy. It does not confirm expectations, reduce uncertainty, or provide predictive insight.
A narrow result is simply one realization within a broader distribution. Understanding this distinction helps explain why close matches feel informative while remaining statistically neutral.
