There's not enough information in this tread to suggest whether or not your team was just bad, or if this is a new meta, given the new Drake properties.
The game is about turret objectives more than anything. If their entire goal is to take drakes, take turrets. This will force them back to their side of the map to defend.
I'm willing to bet it went something like this:
Jungler 1 took his own jungle.
Jungler/Top 2 took half of the Blue side bot jungle.
Jungler/Mid 3 invaded with their team, and mooched the remainder of bot jungle (red) after you had to wwithdraw/gave up 1-2 kills.
Your jungler had no farm to use, so fell massively behind.
In between clears, they went back to their lanes to clear some, but didn't put an emphasis on it and kept roaming, because they didn't want to incur a lane minion gold penalty from overfarming jungle/lane.
While your laners tried to adapt to the jungle needs and failed, the jungler just got boxed out.
You established poor lane control/farm rates due to the confusion, and they managed to probably have 90% visibility around drake pits.
The general answer: The game when played correctly always expects the unexpected. Advanced play is never just linear/push/pull combat/gentlemane structure. Unpredictability that is planned and deviant is common to play psychological games with the other team. Expect it. Play with friends who appreciate that fact (eventually once you've made them). Communicate. Check their profiles and see if it's a common thing they do. Go into the game expecting it.
If they are going to invaded based on their histories, insist your team 5 man the leash and set your players up in a flank formation instead of a huddle. Let the invade happen, 2 people bait, and then the other 3 people join in to prevent escape. Show them better teamwork, and they are likely to get frazzled.
Expect 3 smites to invade the first ~8-10 minutes of jungle, so be ready to leave lanes and gank the 1-2 who are in the wrong positions, and make them regret it.
If you're successful at that, they will be forced back to lanes, starved for XP, and down a summoner in 5v5's. Make the rest of the game about 5v5s and your XP/Farm advantages will result in your correct summoners, better incomes and XP carrying you.
If you let them separate you, you will lose.