pethian said: "I had forgotten that the show had two runs at the Public, the second. one, when I saw it, being open-ended and it ran for 10 months. With that, its arrival on Broadway is still considered a new musical and not a revival? Wasn't Hedwig deemed a revival?"
It will be considered a New Musical. Hedwig was considered a revival under the classics rule, "[for a production] to be a “classic” or in the historical or popular repertoire shall not be eligible for an Award in the Best Play or Best Musical category". Hedwig and the Angry Inch fell under the "popular repertoire" clause as between the closure of its original off-Broadway production in 2000 and 2014 Broadway premiere the rights were made available regionally, with countless productions. Here Lies Love never released its regional rights, with all subsequent productions after the original 2013 Off-Broadway run being some incarnation of that original production with nearly all of the original creative team intact.
I know it may sound confusing, but I think a simply rule you can use to determine if a musical will be considered a New musical or revival is whether the show's regional rights were made easily available prior to its first Broadway production, as this is the case for Little Shop of Horrors, Assassins, Roger's and Hammerstein's Cinderella, and Hedwig and the Angry Inch.
Plays on the other hand, I have no idea, what the line in the sand is as to what qualifies as ""popular repertoire".