In the Photoelectric effect, Why does increasing the light intensity have no effect on the energy of the electron emitted?

The equation to calculate the energy of an emitted electron is: E = hf - φ, where E is the energy of the electron emitted, h is the Planck's constant, f is the frequency of the light and φ is the work function of the metal which is the minimum energy required to emit an electron. Here you can see that nothing is dependant on light intensity because the intensity is essentially the number of photons and does not increase nor decrease the energy of a single photon, therefore has no effect on the energy of an electron emitted. 

If the light has enough energy to emit a photon i.e. has a high enough frequency, then the light intensity will increase the probability of an electron being emitted from the metal.