OTOH, you can take my suggestions.
Braeden & Collin's favorite baseball game is Sure Shot Baseball... which isn't so much a board game as an excercise in manual dexterity. The board is a molded plastic and has a scoop-shaped back wall. The pitching team drops a ball down the chute (which can be aimed a little bit) toward the bat, which the hitting teams "swings" using a knob. Hits only count if they go over the wall - and depending on where they cross the wall, they count as a single, double, triple or home run. The defense can get an out, however, by catching the ball in mid-air! A swing & a miss is an out, so innings are quick.
And that's it. Not a great game, but fun to play with the kids.
Harry's Grand Slam Baseball is a quick-playing card game that manages to "feel" like a baseball game without having the tempo of the average baseball game. If you don't go into extra innings, a game is easily over in 15 minutes.
Interestingly, even with such a short playing time, the game includes stealing bases, balks, double plays, pinch hitting, relief pitching, and even the sacrifice fly. That's a lot to pack into a simple card game - and yet Grand Slam Baseball does it with class.
I'm a big fan - it makes a great "waiting for folks to show up for game night" filler. It would also be a nice game to play while watching a baseball game on TV.
Diceball! is, I'm sad to say, long OOP (out of print) and a bit difficult to find. That said, it's a really enjoyable dice-heavy baseball game that can (but doesn't have to) generate stats for a very realistic baseball game. But whether you're into the stats or not, the gameplay itself is a lot of fun, esp. using the advanced rules which allow for some oddball offensive plays (like the suicide squeeze and the hit & run). The teams are generic (blue & yellow, if my memory serves me correctly) but that doesn't stop the game from creating a story each time.
A short note about baseball & statistics: most of you are probably aware that many baseball junkies are obsessed with statistics. (All you need to do to figure this out is to listen to the color commentary on your average baseball game, where they drop stuff like "this is his second single on his first at bat in the last 12 games facing left-handed starting pitchers here at Wrigley Field." Sigh.) Baseball boardgamers tend toward this as well, which is why APBA & Dynasty League Baseball are the most beloved of baseball "simulations."
My aside about stats brings us right to the best of the games I've listed: Dynasty League Baseball. This is truly the Holy Grail for those of you who want to replay seasons with truckloads of statistical accuracy & loads of "color" - the system goes so far as to take weather & time of year into account (as they affect, ever so slightly, the distance a ball carries after being hit.)
I was introduced to Dynasty League through the good graces of Warren Madden, who is a fan & did a spectacular job of keeping the game moving. I haven't been able to justify the price tag of the game (yet!) - but if my eldest son continues to enjoy baseball, it may find a place in my collection.
Pinch HitterI haven't yet played Pizza Box Baseball... but reports from folks who've seen a copy/played the game (including the Fresno Gamers own Hobiecat, Mike) have lots of nice things to say about it. I'll be giving it a try in the next couple of weeks & I'll let you know what I think. Two Games Into the Season... Well, not actually any season... but on Opening Day, I actually managed to play two of these games. Braeden & Collin beat me at Sure Shot Baseball (sigh) and I managed 11-10 bottom of the 9th win over Mike in Harry's Grand Slam.