Liquidity Amplification Factor

A ranged position with price range from 0.8 to 1.2 in the above example provides the liquidity only in the range. Since the ranged pool does not provide the liquidity outside of the range, its liquidity is concentrated in the range. Compared to the basic position with the same capital, the ranged position with [0.8, 1.2] range provides liquidity 10 times greater than the basic position in the price range. This value of 10 is the liquidity amplification factor of the ranged position. The liquidity amplification factor depends on the price range. As it can be seen below, the liquidity amplification factor increases as the size of the range is getting smaller.

Current Pool Price	Min Price	Max Price	Liquidity Amplification Factor
1	0.8	1.2	10.38
1	0.9	1.1	20.44
1	0.98	1.02	100.49
1	0.99	1.01	200.49
1.079	1.063	1.15	51.54

For a ranged pool with Pmin, Pmax and P as the minimum price, maximum price and current pool price, the amplication factor (AMP) can be calculated as

$AMP=\frac{1}{1 - \frac{1}{2}\left(\sqrt{\frac{P_{min}}{P}} + \sqrt{\frac{P}{P_{max}}} \right)}$

Note that $P_{min}≤P≤P_{max}$