BATTING
Let me explain a few things about batting...
I'm not an expert at hitting homeruns but I can tell you a few things...
Alot of players burst out in batting power during the night or dusk time around 4th-6th inning
and you can tell this cause when you hit a ball it will fly to the back wall no matter what.
It's a little easier to hit a homerun when you swing your bat a little late as the ball goes over the plate... you want to catch the ball with the bat when your bat is angled in between \ to -
or / to - depending on what side your on.. some people can hit homeruns at will and others can't.
Theres a few players who have a longer reach then others and can direct the ball a little better.
A friend of mine included a chart on my site which has the batting and power.. look at this chart for a better understanding.
I'm not truely possitive on who hits best at night but the manual states a couple of players...
I've also noticed that the players with pale white faces seam to hit better at night as well... these players are:

Zelda, Biff, Bela, Stan, Mike, Rocky, Harry. Fuji, Johnny, Peter. Babe, Leon, Don, Bruno, Eddie, and Artie.

Leon is the only player which I can almost always hit a homerun with... He seams to be one of the best.
The manual says Gene, Johnny, Rock, Fuji, Diablo, Davy D., Artie, Lance, Larry, Leon are the top 10....
I honestly don't think they are the best.... The chart on my website is pretty much acurate to what they can hit and mind you each player hits different types of pitches better...
Some can hit a fastball off Ronnie and get a homerun every time just because of the speed of the ball... Also it's easier to hit a homerun in the sandlot since it's the smallest field and in park homeruns are easiest in the park field since the trees stop movement.

Theres 3 players with different bats in the game... these players have the longest reach and can get some balls over the plate.

Zelda - uses a broom
Artie - uses a pick axe
Diablo - uses a spiked caveman club

If I figure anything else out which will help ya then I'll include it..
Also if you hit the ball near any players who fly chances are youll get extra bases for some reason because the computer flies above the ball if it rolls and wont chase it... its a weird glitch.

For in the park homeruns players who run the fastest are your best bet!

UPDATE: EASY HOMERS AND BETTER HITTING
I just figured this out recently so let me explain...
theres alot of players who can switch hit.. use this to your advantage
If your player bats right handed you want to go up against a right handed pitcher
About 80% of your hits will have more power and can be directed alot easier
It's not full proof but this will help you out in the long run
It also cuts off the pitcher's pitching range and they will have more trouble throwin to the inside of you in some cases.
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