Here is a great in-depth FanGraphs article that compares League and Jansen:http://www.fangraphs.com/fantasy/index. ... dominance/
Some of the most important stats/observations--in my opinion--in the article is that League flat out lost the closers job due to inefficiency in the role to Wilhelmson in Seattle (2012). Also, the only reason League was anointed the closer in the first place in Seattle (2011) was because David Aardsma got injured.
The stats show that League has a high walk rate, with a low K rate--not a good combination. Last year, he had a 2.1% HR/FB ratio--a stat that is unsustainable. Yes, he had a great 2011 season where he had 37 saves, but that successful season looks to be fueled by the 1.4 BB rate--which clearly looks like the outlier in his career stats (last year had a 4+ BB rate).
In sum, don't be fooled that just because League was given big money that he has elite skills to retain the closer's role all season. The Dodgers have very high expectations with the amount of money they have spent in the past 1/2 year, and if League starts to blow a few saves in a row--which is likely to occur as it did in Seattle--expect him to have a short leash.
Also, possibly the #1 reason I believe League will have a short leash is because of Mattingly's contract. This is Mattingly's final guaranteed year under the contract; however, the team has a team option for 2014. This offseason, Mattingly asked the Dodgers to pick up the option now so that he wouldn't be a lame duck coach, but the Dodgers refused. So Mattingly's job is on the line this year, and if his team starts blow leads in the ninth inning, a change will be made quickly.