You can tell a bit about the health of a franchise by looking at the rate of change in their Opening Day lineups. If you see the same names over and over, that generally means a stable (good) ballclub with a productive one through nine. If you see names changing from year to year, that tends to reflect injuries, trades, youth movements, and teams in a bit of flux.
I decided to take a look at the gross and average number of Opening Day players by position for each current franchise. Baseball Reference has Opening Day starters going back to 1918, so we’ve got up to 94 years of data at our disposal. (“DH Years” should be self-explanatory.)
You can tell that certain clubs have had long histories with a few legendary players at certain positions. The Red Sox have had 56 different Opening Day right fielders, but thanks to the likes of Williams, Yaz and Rice have only had 36 different left fielders. The Royals have plowed through 33 left fielders in their 39 Opening Days, including a different one in each of the last 12 years, but having Frank White for 15 consecutive Opening Days helps keep their second basemen turnover low. On a macro level, catchers and third basemen seem to be the most stable positions for Opening Day assignments.
The next chart shows the average number of Opening Day years by franchise/position. They are color-coded to show low turnover (bluer tints) and high turnover (redder tints). The Rockies have had only two Opening Day first basemen in their 19 years of existence (Todd Helton and Andres Galarraga), hence the very blue 9.5 figure. The totals at the bottom of the chart give you the average, median, minimum and maximum values for each position.
It shouldn’t be THAT surprising that the newest expansion teams (Miami nee Florida, Tampa Bay) have the lower averages, as they needed time to separate the haves from the have-nots in their systems. The Yankees, as a counterpoint, don’t have time for turnover, and thanks in part to many Hall-of-Fame talents who stay with the club, have the highest Opening Day averages in the majors.