The ADVANTAGES of the new minion system
Since it seems that at least three posts on the "front page" of Boards are complaints about the new minions and why it's bad and blah blah, I'm going to make an effort to show the good side to these changes. Know that I'm not saying there are no downsides, but the bias on the Boards at the moment is silly.
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Minions push harder (assuming your team isn't ahead around the rest of the map), resulting in easier farming: We all know what often occurs is this beautiful thing called lane freezing. It keeps the lane pushed to your side of the map and puts a lot of pressure on your opponent. Before these minion changes, if the opponent knew how to manage minions, by the time you got back to lane the wave would be pushed to his side. You would have to risk your life or a bad trade against an ahead opponent to get farm, or you'd miss a lot of CS. With this change, if you're behind, the wave will push to your tower and let you farm a bit safer while giving your jungler more opportunities to gank and help you catch up. On the other side of the equation, if you're ahead, you can no longer sit top and farm minions/champions since your wave will be pushing constantly, forcing you to rotate around the map and group (keep this in mind, you'll see it again later).
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One of the top complaints I've seen around is the issue of "The lanes that are behind will just push and push and the losing teem will either have to deal with the minions or risk losing towers to a perpetual, automatic splitpush." Although this is frustrating, it can be managed. The damage amplification is only 10%/20%, not 50%/100%. The wave will not push as fast as a late game Tryndamere to your tower. It will be gradual, enough so that there are opportunities to roam about (remember this?) and get picks against the enemy team. Also, since the minion push is gradual, the winning team's minion wave will build up constantly, leading to a huge payout to whoever (preferably the behind player[s]) goes to clear the wave.
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To tie up my previous two points, I'll bluntly state the beneficial factors I've been hitting at. For one, it helps a behind laner farm and get payouts from built-up minion waves. Second, it forces the winning team to group instead of drawing games out to get a certain victory. Before, I've seen games where the fed/ahead champion(s) will sit in their lane, farm, and keep collecting ~150g off their lane opponent(s). Now, the other team can't sit in lanes since they are constantly pushing and they must group.
tl;dr These changes encourage grouping and actually leaving your lane after ~15 minutes while giving the losing team large waves to farm.
P.S. Last bit was slightly rushed since I had to get going, will reword and add a bit more later if this doesn't get downvoted to the cesspits of Boards.