When I was a kid, my neighborhood friends and I set up a backyard baseball league. We called it the PWABL or PABL for Perrywood Allotment Baseball League - Perrywood was the name of our "allotment" (i.e. housing development).
Unlike in the movies, we did not have dozens of kids that we could divide up into several teams. There were only four of us, not even enough for one team. But we really did run an entire league with just four kids. Each of us picked a major league team to represent. I picked the Reds, my friend Dave picked the Indians, and the two other guys picked the Red Sox and the Brewers. I remember the other two guys well, but will omit their names because I've lost track of them. Hey, if either of you guys read this, shoot me an email.
We managed to set up a schedule where each team played each opponent a set number of times - about 50 total matchups for a season that lasted many weeks. The games went like this. You turned to the sports page and from the previous day's box scores, you read off the batting order for your team. That was the batting order you had to use. We would announce each batter: "Now up for the Red Sox, Carl Yastrzemski..." (This was during the 1978 season.) The hook was that if your guy was a righty, you batted righty, but if your guy was a lefty, you had to hit lefty. If your guy was a switch hitter (I had Pete Rose on my team), then you had to bat righty the first at-bat, lefty the second, and so on. I have no idea how we kept track of all this, but by the end of the season we had the batting orders memorized. I can still remember that Rick Burleson was hitting leadoff for the Red Sox most of that season.
With only four players, we had to use everyone for every game. The two players actually matched up batted and pitched against each other, but one extra guy was an all-time fielder and the other one was an all-time catcher/umpire.
Because there was only one person per team to bat, we had to set up an elaborate set of "ghost-man" rules. If you hit a single, you would have to say "Ghost-man on first" before you stepped off the bag to go back and bat again, or else you could be tagged out. If you then hit another single, you would say "Ghost-men on first and second". The ghost-men always advanced only one base for each base the batter made. There was no scoring from second on a single. Your ghost-men ran at exactly the same pace as the actual runner. If you had a ghost-man running to second, he could be put out if the fielder stepped on second before the actual runner reached first.
We had three fields - my back yard, the Brewers' back yard, and a strip of land next to the Indians' house that was bordered by a real home run fence - a chain-link fence enclosing a friendly dog. I must say we did not have a lot of parity. The Red Sox was about a head taller than all the other teams and he hit many home runs. Except for him, nobody else hit one, except for one I hit late in the season. The player up at the time was Dave Concepcion. Sure, I remember it. It was only 36 years ago.
The fields varied wildly in dimensions and we had no bases, so you had to grab a certain tree branch or stand on a certain bare spot to get to base. It worked out OK because with only one fielder, there were very few close plays. Each field had its own weird grounds rules, like if a ball was hit under the big Christmas tree-like evergreen in my backyard and was unreachable, it was a ground rule single. Hedgerows provided the home run fences for the backyard fields. If you fouled one backwards and it cleared the hedgerow behind home plate, we called it a "Polish home run." The only statistic we kept was the total number of Polish home runs. I think the Brewers won that one. At one point, the Brewers asked the Red Sox for a nickname, and the name "K-King" was bestowed: K meaning strikeout.
We only had a few balls, so these had to be taken good care of. One of the balls was not a real baseball, but was made of some sort of rubber that if you really whacked it, it would take on an oval shape that would persist until you whacked it back into roundness.
We actually played the whole schedule as it was originally set up. I don't remember a lot of arguments about umpire calls or the very complicated set of rules. The only game I really remember ending prematurely was when the Brewers fouled off a bunt into their own teeth and had to go home for an ice-pack.
It sounds like I'm making up all these complications, but we really did play a whole season with these crazy rules. We tried to do it again the next summer, but it didn't really work out for reasons I don't remember. I think the Brewers had moved to Pennsylvania by then.