Last I heard the exact formulas haven't been revealed. The LOTRO help system has this:
MenaceMenace is an online-only mechanic. Every shadow phase, there is a chance that
Menace will activate. This chance is zero at the beginning of the game, but increases each time that the Free Peoples player adds twilight to the twilght pool. The amount of twilight the Free Peoples player adds to the pool is tracked throughout the game, and the more twilight they add, the larger the chance of that
Menace will activate, until it is automatic. The chance of
Menace activating increases only when the Free Peoples player adds twilight to the pool; it is not affected by any twilight that the Shadow player may add. The chance of
Menace activating is tracked separately for each player in a game.
When
Menace activates, the Shadow player may play any
Menace minions still in their draw deck. When they are played from the draw deck, the
Menace abilities on these minions may be used. These abilities may not be used when the minion is played normally from hand.
Menace can only activate at the start of the Shadow phase, in which case your draw deck will highlight, and can be selected to play any
Menace minions it contains.
TriumphTriumph is an online-only mechanic. Some Free Peoples characters have a Triumph keyword on them. For each skirmish event played by the Free Peoples player during a skirmish involving a character bearing the Triumph keyword, the chance of Triumph triggering for that character increases, until it is automatic. If it triggers, the character will hint during the phase in which its Triumph ability can be used, and it may be selected normally to use its ability.
For example, Aragorn, The Dunadan, bears the game text "Triumph: At the start of the maneuver phase, you may wound a minion." Each maneuver phase the game will compare a random number against the chance that Triumph may activate, and if the check is passed, Aragorn will hint and his Triumph ability can be used. If the check does not pass, he will not hint, and his Triumph ability cannot be used that phase.