can't figure out baseball. basic principle of hitting and running is clear, but everything that goes beyond that is a complete mystery to me (esp the scoring system and who has to pass to whom). and that is after I watched a complete baseball anime!
only us sport that isn't total nonsense in my opinion. (can't take handegg or hoopball or iced hokey serious at all)
It's not really that complicated.
I assume you know baseball game is composed of 9 innings (could go to extra innings if the game is tied after 9 innings), at least in MLB (there are 6 or 7 inning games in some minor and other leagues).
Further every inning consists of top and bottom inning. In top inning it's always home team pitching (and fielding/playing defense) and away team batting - trying to score runs. In the bottom inning it's reversed.
Every team has 9 players/starters -a pitcher, a catcher, 4 infielders (1st, 2nd and 3rd baseman and a shortstop that is usually positioned between 2nd and 3rd base) and 3 outfielders. When it comes to hitting a pitcher is replaced in the lineup by Designated hitter in the American League. In the National League pitchers are hitting too so this is the biggest difference between both leagues.
You probably also know that offense gets credited with a run every time a runner gets to the "home plate". If there is one runner already on base and his team-mate hits a home-run they get two runs. If bases are loaded you get a grand slam (4 runs) with a home-run. Won't go into more details here because I think this is already clear to you but if you have other questions you can ask.
On the other hand every pitcher needs to eliminate/retire three batters (get 3 outs) to end the inning and there are different ways to do that.
1. with a strike-out (3 strikes) - when it happens it's denoted by K or a backwards K.
2. with a ground-out - the ball is put on the ground in infield and one of the defensive players (could also be a pitcher) needs to throw it to the first base before a batter/runner gets there to get an out. If there is already a runner on base a fielder can try to throw him out before he advances to 2nd (with throwing to 2nd baseman), 3rd base or even prevent him to score a run. His decision where to throw can depend on a lot of factors (game score/situation, how good fielder he is, how fast is a runner,...). Fielders can also make double plays (eliminate two runners at once), for example when the ball is hit close to the shortstop or 3rd baseman and he throws it to the 2nd baseman (before a runner gets there) and then he throws it to the 1st base before a hitter gets there. There are also triple plays when defense can retire 3 players at once but those are very rare (in average around 5 in a season) and usually attractive to see when they actually happen.
3. with a fly-ball to the outfield when one of the outfielders catch the ball without touching the ground. Now if a team already has one or more players on base he/they can try to advance (if they have less than 2 outs otherwise it's the end of the inning) but he risks getting thrown out if outfielder has a strong arm and and throws the ball to whichever base a runner is going to first. In this case defense can get 2 outs - one "automatic" for a hitter and second for a runner. When there is a runner on 3rd base and a team (offense in this case) has less than 2 outs they can also make a sac fly - they give up one out but a runner score if the ball is hit deep enough in outfield. Important thing here is that a base runner can only start to run to the home base when outfielder catches the ball.
4. pop-out - when the ball is hit very high in the air but stays in infield so it's usually very easy for fielders to catch for an out.
Now to the "count" (balls-strikes)
As mentioned above if there is no hit or an out a pitcher needs to throw 3
strikes (pitches in a strike-zone or "swing and miss"- when a hitter tries to hit but miss the ball, even if it's outside the zone) to get a strike-out
On the other hand, if he doesn't get a hit or an out a batter needs to have 4
balls (bad pitches outside the zone) to get a
walk (usually denoted by BB - base on balls) and he goes to the 1st base.
Numbers of balls are always written first (on the left) and number of strikes on the right.
3-2 count is also known as a full count.
Here is a good picture where you can see basically all that's important.
And a simplified score-board on the stadium with number of runs scored in each inning, number of total runs (R), total hits (H) and errors (E) for both teams. Number of runs is the most (and well, I would say the only) important stat.
Where it could get a bit complicated when you start to watch the baseball (it was for me at least) are foul-balls which are batted balls in a foul-territory (outside of the playing field, could also go into the stands). Foul ball is a dead ball unless it was a bunt into the foul ground.
Here is a description from wiki what happens to the count with foul balls.
A strike is issued for the batter if he had fewer than two strikes. If the batter already has two strikes against him when he hits a foul ball, a strike is not issued unless the ball was bunted to become a foul ball, in which case a third strike is issued and a strikeout recorded for the batter and pitcher.
In other words, there could be 5, 10 or even more foul-balls in one at bat and the count won't change if there are already two strikes on the count.
Hopefully I helped you to understand the game a bit better but feel free to ask if you have more questions.