Baseball arbitration is both an art form and cutthroat business negotiation.
The player submits a figure of his worth through his agent, and the team submits its figure for a one year contract. The arbitrator can only decide on one or the other figure. It is winner take all after arguments from both sides.
Part of the process is that if it goes to a hearing, players hear for the first time highly negative comments about their skills from their team. Teams attempt to downgrade the player's accomplishments or stat lines in order to convince the arbitrator that a lower salary is correct.
Normally, the player and team come to an agreement (an inbetween sum) and avoid the hassles of an actual hearing. But not always. Ryan Theriot took the Cubs through the hearing process, and was later traded within that year.
Sabermetrics has filled volumes of information on how one can value a player.
But there has been a fairly standard rule of thumb in regard to arbitration figures. Normally, a first time arb player would get around 1/3 of a comparable veteran's salary. A second year player, 50 percent. A third and final year arb player would get 2/3. Each time the young player would be receiving a hefty raise. However, there are exceptions when, say, a pitcher wins the Cy Young and demands current market value.
Travis Wood signed a new deal with the Cubs to avoid his first year arbitration. The sum was $3.9 million. Wood had a break-out season in 2013, with a 4.4 WAR, leading the Cubs pitching staff.
A veteran with a 4.4 WAR could probably command around $24.2 million (based upon $5.5 million/WAR). Under that valuation, Wood would have been worth $7.99 million. However, the team would look at it more towards career performance, at 6.3 WAR over 4 seasons. The average WAR times value would equate to a current player contract value of $2.8 million.
And this is the type of argument that both sides would engage in at a hearing. So it always better to try to keep the peace and settle arbitration cases prior to the hearing. In Wood's case, it seems that the sides agreed to a contract which rewarded Wood for his fine 2014 season.