Polar codes are capacity-achieving codes with an unprecedented diagrammatic and deterministic construction. The latter property, along with a relatively simple decoding procedure, make polar codes a popular and attractive candidate for error correction in the design of state-of-the-art communication systems. For example, polar codes were recently chosen to encode the transmission of the control channels in the 5G cellular standardization. One of the most important metrics of any error-correcting code is its scaling exponent µ. The scaling exponent quantifies, per a given target decoding error probability, how fast a rate-R code’s blocklength, N, increases as the gap to channel capacity, C, diminishes, or namely 
N∝ 1/(C-R)^µ. While the ultimate scaling exponent equals 2, polar codes approach capacity rather slowly. For instance, their scaling exponent for the binary erasure channel (BEC) was numerically estimated to be about 3.627. Here we show how the universal scaling laws of percolation theory of statistical mechanics can be utilized to (re-) evaluate the scaling exponent of polar codes in BEC. Percolation theory describes the behavior of connected clusters in large random graphs. One of its evident manifestations is coffee percolation, modeling the way water filters through the ground beans to deliver the essential coffee brew. The derived scaling exponent, born from pure percolation analysis, agrees beautifully with recent numerical approximations. This work exemplifies the potential of percolation theory in analyzing modern error-correcting codes, which may lead to valuable results and new insights.