The multiplicity of infection or MOI is the ratio of infectious agents (e.g. phage or virus) to infection targets (e.g. cell). For example, when referring to a group of cells inoculated with infectious virus particles, the multiplicity of infection or MOI is the ratio defined by the number of infectious virus particles deposited in a well divided by the number of target cells present in that well.
The actual number of phages or viruses that will enter any given cell is a statistical process: some cells may absorb more than one virus particle while others may not absorb any. The probability that a cell will absorb n virus particles when inoculated with an MOI of m can be calculated for a given population using a Poisson distribution.
where m is the multiplicity of infection or MOI, n is the number of infectious agents that enter the infection target, and P(n) is the probability that an infection target (a cell) will get infected by n infectious agents.
In fact the infectivity of the virus in question will alter this relationship. One way around this is to use a functional definition of infectious particles rather than a strict count, such as a plaque forming unit.
For example, when an MOI of 1 (1 viral particle per cell) is used to infect a population of cells, the probability that a cell will not get infected is P(0) = 36.79%, and the probability that it be infected by a single particle is P(1) = 36.79%, by two particles is P(2) = 18.39%, by three particles is P(3) = 6.13%, and so on.
The average percentage of cells that will become infected as a result of inoculation with a given MOI can be obtained by realizing that it is simply P(n > 0) = 1 − P(0). Hence, the average fraction of cells that will become infected following an inoculation with an MOI of m is given by:
which is approximately equal to m for small values of .
As the MOI increases, the percentages of cells infected with at least one viral particle also increases.
MOI  % Infected 

1.0  63.2% 
2.0  86.5% 
3.0  95.0% 
4.0  98.2% 
5.0  99.3% 
6.0  99.8% 
7.0  99.9% 
8.0  100.0% 
