In 2003, Martin and Woodcock noticed a connection between the representation theory of the blob algebra and the Kazhdan-Lusztig polynomials associated with the infinite dihedral group. However, no conceptual explanation for this coincidence has yet been provided. In this study, a possible explanation of this phenomenon is suggested by enunciating a conjecture that relates the endomorphism algebra of Bott-Samelson bimodules to certain subalgebras of the blob algebra obtained by idempotent truncation. Evidence supporting this conjecture is provided. (C) 2019 Elsevier B.V. All rights reserved.