How can I translate performance review results into compensation and pay increases? Can we automate this?

In our opinion, the act of converting appraisal data into pay raises cannot be automated. You have to take into account many factors like seniority of staff, current pay status, trend, and of course other staff increases. You might even have special agreements dependent on hiring contracts, and so on. 

One way to quantify performance review results is to use a rule of thumb, for example, "anyone who is rated 3 out of 5 should on average get a raise of 2% to cover inflation, anyone who is rated 4 out of 5 should get 5% pay increase, and staff with 5 out of 5 get an 8% pay increase". However, we've seen (and heard) this model fail frequently, it can only be used if you're willing to make lots of exceptions.

• Let's assume you have a junior on your team who makes 50k, and someone with 5 years of experience who makes 80k. The junior team member performs a lot better than expected, everyone is very impressed, and after two years the junior is just as good as the senior staff member. It would still take the junior 5 years to reach 80k! 
• By that time the industry standard has changed, not to mention that this (or any other) senior staff member will have gotten pay raises as well. A junior will always need to get significantly higher (or more frequent) pay raises than the senior staff member (likely 20% or even 30%) if you want them to stay at your company and not go somewhere else after two years.

We believe a rule of thumb makes sense, but it has to be at the discretion of the department manager and the team leads to view their team as a whole and find a balance that gives everyone a pay raise they deserve. Performance review data is an important factor in this, but certainly not the only one.