Sectorization gain can be somewhat of a misleading term. One could think of the sectorization gain as more of a reduction factor. For an omni site, the sectorization gain is one. With a sector site, one could initially try to multiply the resulting capacity of an omni site (or single sector) by the number of sectors for the sector site (i.e. a three sector site would support three times the number of users at an omni site and a six sector site would support six times the number of users at an omni site).
This is not the case though. One can think of the additional sectors as being other locations generating interference to the desired sector. The other cell interference factor accounts for just that, interference generated by other sites. The sectorization gain is the adjustment for the other sectors at the local site causing increased levels of interference. The reason it is referred to as a sectorization gain is that for a given physical site location, this site location is able to support many more users when it is sectorized than if it stayed omni.
The sectorization gain can be improved by selecting antennas which have a good front to back ratio and which also exhibit a quick rolloff past the half power points (3 dB down from main lobe). For instance, using a 90 degree antenna in place of a 120 degree antenna for a three sector site would decrease the amount of energy (interference) going into adjacent sectors, thus increasing the sectorization gain and thereby improving upon the number of users which could be supported.
Though one can not decrease the horizontal beamwidth too far so as coverage (signal strength) is not sufficient. As the sectorization gain increases, one can see from the following graph that the number of users will increases. The sectorization gain value which is commonly used is 0.8 per sector or 2.4 for a three sector site (0.8 time 3). This 0.8 sectorization gain can be thought of as a 1 dB impact to the capacity of the site due to other sectors interference.
The above figure would apply only to a three sector site. The sectorization gain shown is for an entire site. For instance, a sectorization gain of 2.4 corresponds to 0.8 per each sector (= 2.4/3). For an omni site the sectorization gain would be 1. If one considered the sectorization per sector for a six sector site to be similar to a three sector site then the sectorization gain for the site would be 6 times the per sector value (for instance, 6 * 0.8 = 4.8).