While New Zealand are currently in the early stages of a golden period in seam bowling, spin has fallen behind at the tail-end of Vettori's 15-year reign. Martin, 33, seems little more than a stop-gap, while leg-spinner Sohdi has played only 14 first-class matches and appears one for the future.
The pair has shown little in this test and, while a lifeless pitch hardly helped their cause, the hosts' slow-bowling troupe combined to pick up nine of New Zealand's 10 wickets on the opening two days.
Martin and Sodhi, on the other hand, have combined for 1-172 across four sessions. Instead, Williamson was the most impressive of the spin trio, exhibiting changes in flight and finding turn to keep the Bangladesh batsmen guessing.
After Anderson picked up his maiden wicket to earn the only breakthrough of a dour first session, Williamson struck on the first over after lunch, deceiving Shakib Al Hasan with bounce and inducing a top edge.
Anderson eventually broke a 121-run stand for the fifth wicket before Doug Bracewell and Sodhi, with his first test scalp, chimed in to give their side some hope entering day four.
Williamson's progress from a part-timer to a real option will be something to monitor as the tour progresses. If neither of New Zealand's spin options puts up his hand over the weekend or in the second test, there might be an inclination to opt for four seamers when the West Indies visit for three tests in December.
Williamson could carry the majority of the slow-bowling load on flat tracks, allowing for New Zealand's strength in seam to shine through. The strategy was adopted without success away to England in May but, without a genuine spinner forcing the issue, it could become more common.