No, that’s not a typo — Reds, not Red Sox. Last night Martine, Dave, and I went to the Great American Ballpark in Cincinnati to see two of the worst teams in Major League Baseball. But if nothing else, the seats were half as much as Fenway in a very similar location. And thanks to the cute kid sitting next to me, my arm got on the Jumbotron. Having lost my scorebook, I once again kept score on the second-rate scorecard provided in the program. I think I will buy another scorebook prior to the California games — it’s just so much cleaner. (And for a Boston Globe article on scoring, check this out, courtesy of Jeff.)
Last night was my first trip ever to a National League park, and thus the first time I had ever seen a major league pitcher bat in person. And Randy Keisler made a pretty strong argument against the DH. After the Reds first pitcher, Ramon “not Papi” Ortiz gave up six runs in the top of the second, Keisler came in to finish out the inning by striking out Reggie Taylor. After a 1-2-3 third (5, 6-3, and 4-3), Keisler came up to start the bottom of the inning. And what a start! With the Reds down 6-1, Keisler smashed a 373 foot homerun to right-center, just a few rows away from where we were sitting. This was the start of a five run inning for the Reds to tie the game at 6.
Another 1-2-3 inning in the top of the 4th (K, 4-3, and 3) for Keisler and he was up to bat again to start off the fourth inning, this time with a double. He scored the go ahead run later in the inning when Ken Griffey Jr. hit his 510th career homerun, a 369 foot shot to center. For a brief second, I thought I might be witnessing history — a pitcher on his way to hitting for the cycle. But coming up again in the 6th, he struck out and never got another at bat. Still, it was pretty obvious who the player of the game was.
Randy Keisler, if I was a Reds fan, this is when I’d offer to name my children after you.
Jun8
Colossus of Rhode 
Somewhere I have a piece of graph paper whereon I have the scorecard for the Catfish Hunter no-hit perfect game against the Minnesota Twins (you can look up the date). I scored that game off the radio. (It ended, as I recall, with Rich Reese striking out, he was pinch hitting for the pitcher in the bottom of the ninth.) Who needs video games when you have baseball on the radio?
By the by, I’m guessing you shortened it for space, but a strikeout is scored as K-2, and some folks like to use KL-2 as well.
Ultimately, however, there is no “right” way to score a game, the key is, as you allude, to provide enough information so that in looking later, you can remember everything about the game; whether you were in attendance or listening on the radio.