What is the test for determining whether a plaintiff has been successful in her claim against a third party?

Whether the two suits involve the same claim or cause of action requires us to look at four criteria, which we do not apply mechanistically: (1) whether the two suits arise out of the same transactional nucleus of facts; (2) whether rights or interests established in the prior judgment would be destroyed or impaired by prosecution of the second action; (3) whether the two suits involve infringement of the same right; and (4) whether substantially the same evidence is presented in the two actions. Chao v. A-One Med. Servs., Inc., 346 F.3d 908, 921 (9th Cir.2003).