Thinking along the same lines, I found myself wondering what is the team record for all 30 franchises for most PA from the starting four infielders? I've done the research, so it's easy to look up. (Note: for PA, I used AB+BB+HBP+SH+SF for every year from 1876-2008, so it's technically a little off, but close enough. I have actual PA for 2009, though).
Based on that, here are the records, going from most to least recently set team record:
IF PA Year Team
2740 2009 Phillies
2407 2009 Rays
2343 2008 D-backs
2458 2007 Nationals
2583 2006 Mariners
2579 2006 Marlins
2849 2005 Rangers
2746 2004 Orioles
2448 2004 Padres
2584 2003 Red Sox
2708 1999 Mets
2642 1998 Rockies
2462 1990 Blue Jays
2469 1988 Angels
2417 1988 Royals
2716 1983 Brewers
2581 1982 Pirates
2693 1978 Dodgers
2614 1977 Reds
2587 1969 Astros
2669 1968 Cubs
2777 1963 Cardinals
2605 1963 A's
2641 1962 Twins
2606 1952 Giants
2758 1936 Indians
2743 1936 Yankees
2701 1936 Tigers
2597 1921 White Sox
2616 1899 Braves
Some fun things - first, there are a lot of recent years becuase: 1) expansion means some teams have less history to draw on, 2) there's more offense nowadays than most of thenadays, and 3) the 162-game schedule comes into play.
When you look at pre-current records, they often pile up in high offensive eras. The best example came in the 1936 AL, where three of the eight pre-expansion AL squads set records that still stand for PA from starting infielders. Not-so-coincidentally, that year also set an AL record that still stands for runs per game, at 5.67. It's still incredible they had 3 teams set records that still stand, though.
Given the preponderous of high-offensive era, perhaps the most amazing team listed is the 1968 Cubs. Sure, the AL had the really low offense that year (with the entire league batting .230 and scoring an all-time AL low 3.41 runs per game, but NL teams scored only 3.43 runs per game, it's lowest mark since 1908.
What's more, the Cubs didn't just set a franchise record in 1968. Their second most PA by starting infielders came in 1969. Third place came in 1970. Fifth place was 1967. (The 2008 Cubs broke it up by coming in fourth). Leo Durocher loved filling out Ernie Banks, Glen Beckert, Don Kessinger, and Ron Santo in the lineup card everyday. In fact, the 1969 Cubs also saw an all-time MLB record when catcher Randy Hundley appeared in 160 games. No other catcher has done that before or since.
The Pirates, with only 2,581 PA in their top season (1982), are lowest of all pre-expansion squad, and the 22nd highest mark of all teams listed. Overall, it's the 62nd highest mark ever, just behind the 1939 Reds.
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