Steamer projects 2.4 WAR and ZiPS projects 3.3. You can see these yourself on Fangraphs. Let's just split the difference and go with 2.9.
Samardzija has 3 years of arbitrtation, including 2013, ahead of him. He settled for $2.64 million this year and we can estimate what he'll earn based on that.
- 2013: $2.64 million
- 2014: $5 million
- 2015: $10 million
I'm being generous here. I don't expect his contract will double each of the next two seasons, but I'm nothing if not generous. Matt Garza was a better pitcher than Samardzija entering arbitration and over his first 3 years he earned $18 million. The $17.6 million total over the next few seasons is close to the most he could make.
Samardzija is already 28 years old so he's at his peak. We'd typically take -0.5 WAR each year after this to get projections several years down the road. Because I'm generous, and optimistic, I'm only going to reduce it by 0.25 each of the next 3 years and then by -0.5 after that.
- 2013: 2.9 WAR
- 2014: 2.65
- 2015: 2.4
- 2017: 1.9
- 2018: 1.4
- Total: 11.25 WAR
A first year arbitration eligible player earns about 40% of his free agent value. The next year it's 60% and then the third year is 80%. Since we already know what he's earning in 2013 there's no reason to estimate his salary this season. I'm using a $5.5 million per win rate in 2013 and increasing by $0.5 million each year.
- 2013: $2.64 million
- 2014: $9.54
- 2015: $12.48
- 2016: $13.3
- 2017: $10.5
- Total: $48.5 million
Teams generally get a 10% discount on contracts 3 years or longer so that makes it a 5-year, $43.65 million contract.
However, there is no chance he's going to see an increase of nearly $7 million between 2013 and 2014. None. There's also no chance he'll finish the third year of arbitration with $12.5 million.
Over 5 years Samardzija is probably worth between $35 and $40 million. Call it $37.5 million, but that doesn't factor in the additional risk the Cubs would be taking by extending a player already under contract for 3 more years. Teams who have done so have done it with a tremendous bonus in their favor. If they signed a 5/37.5 contract, there would be no bonus for the Cubs.
So consider a 5-year, $37.5 million contract the upper limits of what Samardzija is worth at this point. Realistically, it's probably much closer to $30 million so good for the Cubs for not offering too much.