Gehrig didn't always bat 4th.

In 1929 the Yankees pioneered the regular wearing of numbers on baseball uniforms.  Numbers were assigned by position in the batting order.  In 1927 Lou Gehrig for the first time in his career had batted 4th in every game.  Babe Ruth batted 3rd in every game.  In 1928 Gehrig batted 4th in 132 games, 3rd in 22 games.  Ruth batted 3rd in 132 games, 4th in 22.  They switched for games 123-144.

It's not clear why Yankee manager Miller Huggins switched them.  Here are their numbers before and after the switch:

BA    OBP  SLG   OPS
.333 .473 .737 1.211 Ruth
.377 .468 .641 1.109 Gehrig

BA    OBP  SLG   OPS
.322 .462 .704 1.166 Ruth
.370 .464 .630 1.094 Gehrig

Both seemed to have done slightly worse during the switch.

For the 1929 season they were assigned their famous numbers: Ruth 3, Gehrig 4.  The Yankees must have assumed that those numbers would represent their positions in the batting order.  However, that plan changed quickly.  In 1929 Lou Gehrig started the lowest percentage of his games batting 4th in his career and his highest percentage batting 3rd.  Gehrig also had his second highest percentage batting 6th (14% in 1925).

3rd             4th         5th           6th
50.00% 22.73% 14.94% 12.34%

See Gehrig's batting order data.

On May 11, 1929 (Yankee game 18) Lou Gehrig was batting:

BA    OBP  SLG  OPS
.388 .481 .731  1.212

Gehrig batted 4th in Yankee games 1-27 when Gehrig's numbers were down.  For game 28 Huggins again switched Gehrig and Ruth: Gehrig batted 3rd, Ruth 4th.

BA    OBP  SLG  OPS
.333 .443 .656   1.100 Gehrig
.302 .407 .563   .970 Ruth

Again not clear why Huggins made the switch except to merely shake things up.

This continued through game 37 when Ruth stopped playing until game 55.  Gehrig remained 3rd for games 28-74 when he and Ruth switched for two games.  Games 77-106 Gehrig was 3rd, Ruth always 4th when in the lineup.  Babe played 135 games in 1929, Gehrig all 154.

Gehrig was 5th in games 107-114, 118-129, 146-148.  Gehrig batted 6th in games 115-117, 130-145.  For the final games of the season Gehrig batted 4th: 149-154.  In the 133 games that he started Ruth batted 3rd in 66, 4th in 67.

Miller Huggins died September 25, 1929 in New York, NY.  He was 51.  Art Fletcher managed the final 11 (6-5) games (144-154) of the 1929 season.

Saturday, September 21, 1929, Yankee Stadium I Fletcher managed his first Yankee game.  He had managed the Philadelphia Phillies 1923-1926, finishing 8,7,6,8.  Fletcher kept Gehrig 6th (0 for 4, RBI).  Yanks defeated the White Sox 8-5.

Sunday, September 22, 1929, Yankee Stadium I Yanks played a doubleheader against the White Sox.  In game one Fletcher batted Gehrig 6th (0 for 2, 2 BB); Yanks lost 7-4.  In game two Fletcher moved Gehrig up to 5th (0 for 3, BB); Yanks won 3-1.

Two more games batting 5th, then the final 6 games batting 4th after game 148 when Gehrig went 3 for 4, BB, 4 RBI in 11-10 win in Boston raising his BA to .298.  Gehrig had dropped as low as .294 in game 146 his first game batting higher than 6th since game 129.

Gehrig's stats 1928-1930:

BA    OBP  SLG  OPS
.374 .467 .648  1.115
.300 .431 .584  1.015
.379 .473 .721 1.194

In 1929 Huggins moved Gehrig in the Yankee batting order for the most basic of reasons: he wasn't hitting enough.

The 1929 Yankees finished second in AL, 18 games behind the Philadelphia As who defeated the Chicago Cubs in the WS 4-1.  The Cubs were managed by Joe McCarthy (1926-1930) who later managed the Yankees 1931-1946.

In 1930 the Yankees had Bob Shawkey their former pitching ace manage the team.  The Yanks finished third 16 games behind the Philadelphia As who again won WS, this time over St. Louis.  Shawkey continued Huggins policy of moving Gehrig in the batting order.  Gehrig's percent of games batting:

3rd   4th    5th
3.25% 41.56%  55.19%

When he took over in 1931 Joe McCarthy batted Gehrig 4th almost exclusively from 1931 through 1937.   In 1936 Joe DiMaggio had batted 3rd in all 138 games he played and in 1937 DiMaggio batted 3rd in 144 starts and 4th in 6.  In 1938 DiMaggio batted 4th in 116 games and 3rd in 29.  In 1938 Gehrig batted 4th in only 41 (26%) games and 5th in 103 (66%) games.  The young slugger DiMaggio had supplanted Gehrig.