No surprise to see the Green Monkeys to be the best overall team. They had the most wins on the show and a lot of them were good quality wins. Lawrence of Arabia, Emiliano Zapata, Lost Hornpipe, Chandragupta, and Mussel-Shell Armor were all solid wins. They also had some strong non-winning teams too like Good-Luck Watch, Discarded Seal, and Belle Boyd. They didn't really have many bad teams either outside Dried Apple Half and Xerxes. And they had a good artifact retrieval percentage in all three seasons.
I'm surprised Red Jaguars ranked in third place. They are almost a bottom of the barrel team to me. Despite having double the temple appearances of the Purple Parrots, they only had 1 extra win than PP. And one of those wins is the tainted Shaka Zulu win. 3/4 of their wins came from easy temple layouts too. The only good Red Jaguars teams were Genghis Khan, Two-Cornered Hat, Royal Torque, and Catherine the Great. Other than that, it felt like half of the temple runs featured bad teams. Alhambra, Blackbeard, Nzinga, Missing Weather Maps, Smashed Printing Plate, and Silver Saddle Horn just to name a few. If it wasn't for the Purple Parrots lack of temple appearances, I would personally rank them as the worst team.
Orange Iguanas are no prize either. They also had twice as many temple appearances as the Purple Parrots, but only have one extra win. They had some pretty strong teams like Blue Pearl, Sir Gawain, Mush Pot Hat, Dolley Madison, Lucky Medallion, and Levitating Dog Leash. But they also had many bad and average teams. Just like the Red Jaguars, the number of temple appearances keep them from the bottom.
I think the Blue Barracudas are the most rounded team in the first 2 seasons. They didn't really have any bad teams except for Lucky Pig and Lost Logbooks. Unfortunately, their lack of appearances in Season 3 and no temple wins during that season doesn't help them. I would rank them higher than Red Jaguars at least.
My personal ranking would be:
1.) Green Monkeys
2.) Silver Snakes
3.) Orange Iguanas
4.) Blue Barracudas
5.) Red Jaguars
6.) Purple Parrots