West is an ump in the National League and has been since 1976. Hendrick played 18 years in the majors (and was quite good), about half of which were in the NL. He played for the Padres in 1977 and part of 1978, when he was traded to the Cardinals for Eric Rasmussen. He played great for the Cardinals, with an average OPS+ of 125, which means he hit 25% better than league average. Rasmussen went 22-30 for the Padres before returning to the Cardinals to be Hendrick's teammate. I'd say the Cards won that trade handily. Especially since they traded Hendrick to the Pirates in the 1985 offseason and got John Tudor and Brian Harper, two pretty good players.
Anyway, just to see if I could do it, I wanted to see how many of Hendrick's games Joe West umped behind the plate. My pre-research guess is 35, which is basically the number of games Hendrick played, divided by four (the number of umpire positions), and divided by seven, which is the average number of NL games that were played every night. I have no idea if this makes any sense. I spent 10 seconds thinking about it.
The answer was more interesting than I thought, mostly because I was pretty close with my prediction. West was the home plate umpire 30 times when Hendrick was a hitter at some point in the game. In three of those games, Hendrick was only a pinch hitter.
Also of note:
Hendrick was traded from SD to STL on May 23, 1978, but did not report and play in a game for STL until the 29th. West was the home plate umpire for a STL game on the 25th, so they just missed having one more encounter.
There were also (11) games where West was the home plate umpire for Hendrick's team, but Hendrick did not appear in the game.
Hendrick was an outfielder, mostly, so he wouldn't have had as much contact with West in the infield. However, in 1983 he played 92 games at 1b and in 1984 he played 1 game there. West was the first base umpire in none of those games.