Statistical/ML models when observations have different amounts of input

Let's say we're predicting an employee's performance review score for the following year based on that emplyee's metrics from each previous year of his/her employment. We might have these training observations below. Note that "2014i" means "that employee's set of input values from 2014", which for example could be {2014 performance score, 2014 salary, 2014 hours clocked, 2014 bonus paid, and 2014 PTO days taken}.

Joe (has been with the company 9 years): 2014i, 2013i, 2012i, 2011i, 2010i, 2009i, 2008i, 2007i, 2006i
Jay (has been with the company 3 years): 2014i, 2013i, 2012i
Zoe (has been with the company 1 year ): 2014i

These types of problems come up in prediction all the time (an obvious one I'd think would be predicting an athlete's performance this year based on his statistics for each year of his/her career), and I've never seen a statistical or machine learning model that allows for different amounts of input like this. I suppose I could create one model for employees who've been there 1 year, another model for employees who've been there 2 years, etc. But with some employees having 40 years of service the available data can get thin pretty quick.

What is this type of problem called, and what are some of the best models to use in this situation?