Software piracy by users has been identified as the worst problem facing the software industry today. And the pervasiveness of software piracy throughout the world is having a profound effect on software publishing industry and the development of digital intellectual properties and technology. Because of this software shadow diffusion, a software firm loses potential profits. However, shadow diffusion the legal diffusion of the software. Software pirates may influence potential software users to adopt the software, and some of these adopters may become buyers. A diffusion modeling approach is suggested to track shadow diffusion and the legal diffusion of a software over time. The approach enables management to estimate the pirated adoptions over time and the percentage of legal adoptions due to the influence of pirates. The modeling approach is applied to study the diffusion of types of software in United Kingdom. The results suggest the diffusion that although six of every seven software users utilized pirated copies, these pirates were responsible for generation more than 75% of new software buyers significantly influencing the legal diffusion of the software. Although software piracy would decrease the profit of software firms, the protection of software is not always a good idea. Owning to network effect, sometimes the software firms should choose not to protect their software.