Who directed the Ben Hur Chariot race scene?

No, it was not William Wyler, the credited director of the film. The most famous scene by which the film is remembered was shot by Andrew Marton & Yakima Canutt, the second unit directors.

Any large project, including films, is divided into various UNITS, whose work can go on independently of each other, so as to save TIME. This is known in management parlance as the "Critical Path Method."

The CPM is an algorithm for planning a set of activities, so as to identify the longest stretch of DEPENDENT activities & measuring their duration. It is used in conjunction with PERT, (Programme Evaluation & Review Technique), another management tool.

These are used to get the project done in the shortest time, as time is money. This can be illustrated by another film "Cleopatra", which despite being the highest grossing film of its time, did not recoup its cost for a long time, because too much time was wasted during its making.

To end on a lighter note, when Barbara Streisand was approached for "Funny Girl", she asked who would direct. When told it was Wyler, she reportedly said "Oh, the Chariot guy! What does he know about girls?"