Many people are surprised that Giants star Tim Lincecum only asked for $13 million in his first year of arbitration eligibility. Given his "special accomplishments", it was possible that he could win more than $15M in arbitration. However, there are a couple of reasons that his more modest request is the right decision.
If Lincecum were to lose, he would be awarded $8M, meaning that in future years, he would be building off a base of $8M rather than a number in the low to mid teens. It would set a very low precedent for future years, and it would be difficult for him to move into the high teens in his future arbitration years, which is where the real money is. Essentially, he is potentially sacrificing $1-2M this year in order to enhance his chance of making more in future years. It is an intelligent calculation by Lincecum and his representatives.
If he set the bar too high and lost, the Players Association would be very angry. This would cost future players millions of dollars, as the precedent set for a superstar pitcher would only be $8M, significantly less than star slugger Ryan Howard was awarded, and even less than Jonathan Papelbon, a reliever, will make in his second year of arbitration eligibility.
However, the real moral of this story is to not let star players become Super Two's. If the Giants had called him up only a few weeks later in 2007 he most likely would not have been arbitration eligible for another year. Lincecum had 2.148 years of service time, and the player with the least amount of service time who qualified for Super Two status was Mike Fontenat at 2.139. Ouch.