Hello, I want to spread the word on something. Many newer players build giant, ugly, and space-taking mob grinders. However, on kreatious mob grinders simply do not work. Here's maxmmm's explanation of why (thanks max)
They do not work simply because of the multiplayer world-wide entity cap, when the server tries spawning mobs its has a much greater chance of spawning them in the large area around 30 players, then in a tiny 20x20 area by one player. Also, most mob grinders wouldn't work in singleplayer anyway, because you need to light up caves/surface before that's the only place mobs can spawn.
They work in the nether/end because they have different mobcaps, but if you see someone loading the main end island you will notice that there become very few enderman in the enderman farm. This is because there are more spawning places on the island than the farm and the chances of spawning on the island are larger, plus once enough spawn the mobcap is reached and no more will spawn until one is killed or unloaded.
I'm sure most experienced players know about this, however, I feel many new players need to know, so they don't waste their time and others' time building giant mob grinders that don't work. If you want to build a grinder, you'll have to find a spawner. I don't think this applies to other dimensions though, because enderman and wither skeleton grinders are pretty successful. So, to summarize, don't build mob grinders, they're ugly and they don't work. Thanks for your time.