Final answer:
The procedure index would be the best index to determine the average length of time a surgeon takes to perform surgery.
Step-by-step explanation:
The best index to use for determining the average length of time it takes a particular surgeon to perform surgery would be the procedure index. The procedure index specifically focuses on the performance and efficiency of surgical procedures, including the time taken. It provides information on the duration of surgeries performed by a surgeon, which is crucial for determining the average length of time.