The end-end distances of loops in proteins are found to be distributed according to the worm-like chain model with a persistence length l(p) = 3.04 Angstrom. For a protein with a loop at a certain short end-end distance, increasing the loop length is expected to decrease the protein stability since the entropic cost increases for constraining the loop ends at the given distance. The predicted decrease in stability is tested against experimental results on the four-helix-bundle protein Rop, in which the native two-residue loop is replaced by two to ten glycinces. Without adjustable parameters, the prediction agrees with experiment with a correlation coefficient of 0.99.