Previous works on substorm triggering have shown that more than 50% of the substorms are triggered by a northward turning of the IMF <i>B</i>_z; However, recent studies have found a much lower percentage. We have examined triggering using three different onset lists: The THEMIS All Sky Image (ASI) list, substorm onsets from IMAGE-FUV, and events with large geosynchronous injections. We analyzed these onset lists with three different triggering criteria: (1) a criteria based on Lyons et al. criteria; (2) a relaxation of the Lyons et al. criteria based on the visual criteria proposed by Hsu et al.; and (3) a further relaxation of the Lyons et al. criteria, requiring the same conditions proposed in the visual criteria by Hsu et al. but without the growth phase southward IMF requirements. Appling the Lyons et al. criteria we find that only 17% and 22% of the substorms are triggered in the THEMIS ASIs and IMAGE-FUV onset lists respectively, consistent with the recent studies. However, the percentage reached nearly 50% when we applied relaxed criteria, suggesting that it is possible that the Lyons et al. criteria are too strict to identify all IMF triggered events. The triggering percentage for the events with large injections reached up to 60% applying the relaxed criteria, a result suggesting the possibility that triggers are more easily identified, or that triggering is more common for larger than for smaller substorm events. We have also found evidence that larger substorms may be more likely to be non-triggered under mostly southward IMF conditions than for other IMF conditions.