You can get the answer to your question with two links at the irreplaceable website baseball-reference.com:
First, here’s Kershaw’s career post-season game log so you can see his performance over the years:
Postseason Pitching Gamelog
Second, here’s a quick link to get to any and all post-season series, where you can cross reference the Dodger’s series with the appearances that Kershaw had.
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World Series Winners, Stats, and Results and Postseason Series.
Year by Year:
- 2016: he pitched (but did not get the W) in the NLCS elimination game 4 and then saved the deciding NLDS game on 1 day rest. Then he took the loss in deciding NLCS game.
- 2015: he won an elimination game in NLDS game 4 but did not pitch in the decider.
- 2014 he lost the NLDS decider, pitching on 3 days rest
- 2013 he pitched in (but did not get the W) in the NLDS winning game (again on 3 days rest), then took the loss in the NLCS decider.
- In 2009 he pitched a couple of relief innings in the game 5 NLCS loss
- In 2008 he did not pitch in either deciding game that LA participated in.
So to summarize, in “deciders” he has taken 3 losses, gotten a save, pitched in a decider win but didn’t get the win stat, and had some relief appearances.
Kershaw’s post-season ERA is (as others have noted) an ugly 4.55. What’s missing in that stat is the number of times he’s taken the ball on 3 days rest (or fewer), and the number of times he’s pitched well past 100 pitches/deep into games/facing the lineup a 4th time thanks to crummy past Dodger bullpens. There’s context to his numbers and one of the reasons we always warn about passing judgements on “short sample sizes.”