A new chain on a new 22th sprocket. The chain's rollers sit low in the valleys between the sprocket's teeth. With the chain under tension it engages the sprocket smoothly, but which teeth are taking the load. Crying up the chain with a screwdriver will give us some answers. As the screwdriver moves back from the top of the sprocket it is pulling rollers at the top downward as well as backward. Then as the screwdriver approaches the bottom it is pulling rollers below it forward. The effect on the rollers at the top decreases. After a quarter turn the rollers appear to bottom out between the sprocket teeth. Pulling the chain away from the sprocket shows that only a few teeth at the top are carrying almost all of the load. Taking this further shows that the chain remains in stable contact with the sprocket if only four teeth are engaged. A worn, elongated chain sits high on the teeth at the top and bottom of a new sprocket. As each roller comes around to the top it is carrying almost the entire load and then it pops off a sprocket tooth. Look at the back of the sprocket to see how the rollers jump forward without reaching the teeth as the roller at the top pops off. Clearly efficiency is reduced due to friction, to vibration and to the impact of the roller at the top with the tooth. Crying up the chain shows that it is still quite stable in its engagement with the sprocket. Although the worn chain has much more slack than a new one, the back of each sprocket tooth is at nearly a right angle to the direction of chain tension. This other sprocket has sloping backs on the teeth from being used with a chain that was wearing. We switched the worn chain to the worn sprocket. The worn chain runs much more smoothly on the worn sprocket than it did on the new one. The chain sits high on the teeth at the top and bottom of the sprocket. With the slanted backs of the teeth, the chain is carrying tension much farther around and if fried up it jumps forward. Now the new chain on the old sprocket was slanted teeth. This chain sits low in the valleys between the teeth, but because of the slant of the teeth the chain is pushing teeth down as well as forward at the top. Crying with the screwdriver shows that the chain is carrying tension much farther around than with the new sprocket. And if lifted, this chain also jumps forward. More details at sheldonbrown.com