An inexperienced Floorhand was assigned to obtain a measurement from the bottom of the rig floor to the Texas deck. A man-rider permit was obtained for the task, a pre-job meeting was held and the job was discussed. A man-rider JSA was on site and available. Another Floorhand was assigned to operate the man-rider winch for the Elevator Basket. The man-rider winch operator was able to see the man in the elevator basket while being lowered but there were some restrictions. A flagman was assigned, but left the work site to retrieve a measuring tape for the task. The injured person put on his safety gear, PFD and fall protection but the crew did not wait for the return of the flagman (banksman) prior to the man being lowered to the Texas deck. The injured man stated “he had to push himself away from some of the congested area an as he began to push away he apparently got his right ring finger between the lifting frame for the BOPs and the man-rider elevator basket.