Recording the score of each game seems obvious. But you need to have a well- organized system that will enable you go far beyond simply keeping scores.
Once you get rolling you will want insights into each team’s performances. Home and away? Extra-inning games? One-run games? How many shutouts has a team notched? How many times have they been shut out?
The very first stat you need to record when completing a game is writing down who won and who lost. Sounds basic, but it’s the very first thing I do when I complete a game.
Using an idea borrowed from the accounting profession, I use a black pen to note positive accomplishments (wins) and a red pen to note negative accomplishments (losses). The color coding allows you to see, at a glance, if a team is on a winning roll or falling into a losing streak. 
The attached illustrates a game-by-game scoresheet. The greyed-in area for April 18 indicates no game was played on that date, which influences pitching rotations. You can easily pick out extra inning games. At the bottom, you can get a preview of how each “month” is totaled (which we’ll explore down the road). Also, you can make notes on your scoresheet. The St. Louis Browns, as you can see, opened my 1911 A.L. replay with seven straight losses, which is easy to visualize on the game-by-game scoresheet.
Next: Keeping daily standings.
These articles by Rod are great, and appreciated. I’m starting a project with the 1950s Decade Set and using some of what I’ve learned here.