You could try and repair that, but it will probably rip out again. I'd get a mini post that has a machine screw end and drill the hole out to accept the new diameter post. Then put a washer and nut on the bottom or get a threaded T-nut and install that from underneath. Any post that gets nailed by a direct hit shouldn't be screwed into the wood.

It looks like the main cause of the problem is the chunk of wood missing on the inside of the hole for the targets.

Glue a a bamboo skewer or toothpicks in the screw hole, and maybe JB weld for the missing chunk of wood. Drill the new hole, and paint as necessary, wax the area, and then cover it with mylar.

What he said but id also add a washer to the top side because it looks like you have some material loss under the post.

I think it's this one:

http://www.pinballlife.com/index.php?p=product&id=324

This is the machine thread post that schudel was talking about. I replace that post with one of these on every BOP I do.

http://www.pinballlife.com/index.php?p=product&id=1435

I had similar happen on different games and this is what I've done. No more issues after. Here's the post and the Tnut. As above you want a small washer under the post and a nut on the thread beneath the Tnut.

http://www.marcospecialties.com/pinball-parts/530-5005-00

http://www.marcospecialties.com/pinball-parts/240-5204-00

http://www.pinballlife.com/index.php?p=product&id=320

http://www.pinballlife.com/index.php?p=product&id=2832 (get two #10 washers---one for the top of the playfield, one for the bottom)

http://www.pinballlife.com/index.php?p=product&id=749

It looks like the #10 post is the only one that will be long enough to go through the playfield and put a nut on--which means a larger hole in the playfield for the post. The #8 and #6 mini posts are only 3/4", and would need a t-nut installed (I would not recommend this since the post is too close to an opening in the playfield, and banging on the playfield to hammer it in probably wouldn't be a good idea either).

If you use the longer threaded post, I would recommend filling the hole first like I described above, then drill a fresh hole (rather than trying to hog out the existing damaged hole)

https://pinside.com/pinball/forum/topic/cleaning-and-waxing-pinball-machines-vids-guide/

I wish who ever had my bop before me did this.. Instead they drilled a new hole about 1/4" from old one, really messed with game play.....solved by purchasing new playfield..gonna try and restore old one when I install new playfield

It looks like the 8-32 is too short to go through the playfield and use with a nut. You would have to install a t-nut, but I wouldn't recommend that for the reasons mentioned above.

You would be using a small washer, correct? Anything smaller than 22mm in diameter wouldn't even touch the ball. You would be using a washer about 6mm in diameter, just a bit bigger than the bottom of the post.

According to this page, that post should be long enough to use with a nut:

http://www.actionpinball.com/parts.php?item=02-4660

The point where the ball strikes the rubber will be raised a little bit, but it should be fine.

However--since the post you linked to has a big, thick base, I'm not sure if that will make contact with the ball or not when it is raised by the washer.