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Bucknell definitely has an advantage at the moment. It ranks #8 in RPI, compared to LU’s #18. BU also has a much better SOS and a better record. Additionally, BU has three wins against top 15 programs compared to LU’s two (Bucknell and PSU). Remember that the committee typically has place a lot of weight on RPI and SOS.
If Bucknell were to beat Army in the semis and then lose to LU, it looks like there is a good probability that they would get an at-large IF there aren’t upsets in the strong conferences, where a weak team grabs the AQ. With a win over Army and a loss to LU, Bucknell’s final RPI would be 8 or 9. For LU to get in if it loses in the finals, a lot of things would have to happen to allow them to pass at least four teams out of Ohio State, Penn, Johns Hopkins, Yale, and Princeton. I think whichever Ivy gets to their tournament final (presumably to play Cornell) will get a bid – which likely means LU would have to pass the other four.