Testing multithreaded programs is inherently challenging, as programs can exhibit numerous thread interactions. To help engineers test these programs cost-effectively, researchers have proposed concurrency coverage metrics. These metrics are intended to be used as predictors for testing effectiveness and provide targets for test generation. The effectiveness of these metrics, however, remains largely unexamined. In this work, we explore the impact of concurrency coverage metrics on testing effectiveness and examine the relationship between coverage, fault detection, and test suite size. We study eight existing concurrency coverage metrics and six new metrics formed by combining complementary metrics. Our results indicate that the metrics are moderate to strong predictors of testing effectiveness and effective at providing test generation targets. Nevertheless, metric effectiveness varies across programs, and even combinations of complementary metrics do not consistently provide effective testing. These results highlight the need for additional work on concurrency coverage metrics.