My shoes with "duosole" make a clicking noise on pavement.
The plastic nubs are very hard and feel like they slap the road. They also make the shoe feel slower.
Example of shoes with this type of sole are:
Mizuno Wave Ekiden
Asics Tarther Kainos 3
What's the relationship between grip and speed?
Are these hard carbon/rubber nubs effective?
Not a fan.
I have a pair of Adidas with similar nubs. I do not notice a difference except when running on wet roads. Some other racers I have owned got very slippy on the roads when it was rainy (Brooks).
I have the Mizunos. I find them slippery in some conditions and when wearing indoors. They also seem to fight back instead of helping my stride. Not a great choice.
I find them nice on hard dirt roads, a bit annoying on hard pavement, and really annoying on wet smooth pavement.
What I dislike about them most, though, is that the little nubs have a tendency to tear off of the shoe, and I end up with big patches with no outsole way before anything else on the shoe is worn out.