Out-of-Bag Sampling in Random Forests

Bootstrap Sampling

Dataset size N 32

Draws per second 12

Forest Statistics

Trees grown (B)

This tree's OOB

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Cumulative avg OOB

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Theory (1−1/N)^N

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In-bag (drawn this tree)

Out-of-bag (never drawn)

Bar height = draw count

How it works

Bagging (bootstrap aggregating) grows each tree in a random forest on its own bootstrap sample: N draws made with replacement from the N original training rows. Because sampling is with replacement, some rows get drawn multiple times and others are never drawn at all — those left-out rows are that tree's out-of-bag (OOB) set.

P(a given row is never drawn in N draws) = (1 − 1/N)^N
                                          → e^−1 ≈ 36.8%  as N → ∞

Each button press below draws N samples with replacement from the N points on the ring. Points hit at least once light up and count toward that tree's in-bag set; points never hit stay dim — that fraction is this tree's OOB rate, and it hovers near 36.8% no matter how large N gets.

Grow One Tree — runs one bootstrap draw of N samples, animated draw by draw; the bar over each point tracks how many times it was picked.
Auto-Grow Forest — repeats this tree after tree; the cumulative average OOB fraction is a Monte-Carlo estimate that converges on the (1−1/N)^N theoretical value by the law of large numbers.
Why it matters — because roughly a third of the data is OOB for every tree, a random forest can score each tree only on the rows it never trained on, giving an internal, honest estimate of generalization error with no separate validation split needed.

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