In the modern era (1903-Present), has any player other than Ted Williams and Babe Ruth had a SEASON in which he reached base over fifty percent of the time (I.e., hits plus base on balls plus hit by pitch divided by at bats)?
19 times by 11 players.
ETA: Forgot to check the year. 6 players before 1903
My question was a bit unclear. I wanted Players who have had at least one such season, not one of those players’ second, third, etc. similar seasons.
Thanks to Running Coach, I got my answer: Three Players Bonds, Mantle, and Hornesby.–
I know you said 1903 and up, but just for fun; John McGraw if you count 1900. Also in the 19th century, Billy Hamilton, Joe Kelley, Hugh Duffy, and Ed Delahanty.
A lot of those were in 1894, which was the greatest hitting year in baseball history.
Why did you pick 1903? I thought the “Modern Era” included 1901 and on, when the American League was considered a “major” league?
It’s an odd barrier (the first World Series year but that wouldn’t affect regular season accomplishments) but no one did it in 1901 or 1902, anyway.
Ruth, Mantle, Bonds… all slackers. There’s one player who had two years where he had an On-Base Percentage of 1.000 - meaning he got on every single time he came to the plate! Not only that, half of his career hits were home runs!
Bonds had a year where he got on base 376 times, with 373 at-bats.
Still only an OBP of .609 - my guy had an OBP of 1.000 twice!
Of course, my guy only came to the plate three times in his career. I was just “taking advantage” of the fact that the OP never mentioned minimum number of AB/PAs.
Well, sure; but you were taking advantage of that fact about ABs to make a claim that sounds like an impressive statement about a 100% success rate. By contrast, I was taking advantage of a fact about ABs to make a claim that sounds like an impressive statement about a Better-Than-100% success rate. 
Good point - if you (re)define OBP as hits plus walks plus HBP divided by (only) at bats, it’s possible to be over 1.000, which (amazingly) Bonds did!
The immortal John Paciorek came to bat five times: three singles and two walks in his career for a BA of 1.000, a slugging percentage of 1.000, and an OBP of 1.000. All in the same game, too. Think what he could’ve accomplished in a 162 game season!!!
There was a guy who had a 2.750 slugging percentage with 5 RBI in his first major league game. Can’t think of his name. He hit a grand slam on his very first major league pitch (you cannot top that) and later in the game had a HR and a triple, plus an out. He went on to a rather modest major league career. Interviewed after the game, he lamented that his career had probably peaked. Got that right.
The only two men who hit grand slams on the first major league pitch they ever saw were Kevin Kouzmanoff and Daniel Nava, but neither fits your description. Nava went 2-4 in his first game with a double and the HR, 4 RBI total and a SP of 1.500. Kouzmanoff just had the one HR in 4 at bats and a 1.000 SP. maybe you were thinking of someone who homered on the first pitch (no GS) or hit a grand slam (first AB but not first pitch)?
J.P. Arencibia had quite a first game, including a home run on the first pitch he ever saw, but it wasn’t a grand slam; he ended up 4 for 5 with a double, two homers, 3 RBI and a 2.200 slugging percentage. That was just in 2011 and his career is already over, so he meets the “modest career” criteria but not some of the other details.
Starlin Castro had a three run homer AND a three run triple in his first game, which might make him the only player to ever do that specific thing in his first game.
Finding players who specifically drove in 5 RBI in their first game is sadly beyond my Google-fu.
Daniel Nava hit a grand slam on his first MLB pitch. He should have stopped there and been a hero forever.
On the flip side, Ron Wright struck out, hit into a double play, and hit into a triple play in his one and only major league game. Perhaps not shockingly, he did stop there, and is a hero in an entirely different sense!