Whilst I accept Tiger Woods is the world's best tournament player, his record in matchplay of any form is very disappointing.
Ticking him off, just as happened before the past two Ryder Cups, made no difference, if anything he played worse.
IMO Tiger's performances improve with the $$ at stake.
There is no $$ at stake in the Ryder Cup, it is the great 'leveller'.
Considering the likely weather conditions also, I would back the matchplay of Montgomerie, Garcia & Olazabal over Woods.