I was browsing MFO and found this info, is it correct or is it outdated? If its correct it appears there is no need to get thumbring for mangudai:
"How does Ballistics and Thumb Ring work?
Each unit has a base to-hit percentage ranging from 50% (Cavalry Archers) to 100% (Mangudai). This refers to the chance that an arrow has to hit a non-moving target. If a target is moving then the arrow will aim at the spot that the unit was at when the arrow is fired. These arrows tend to miss targets, especially if the targets are moving in a lateral direction relative to the shooter. Missed arrows still have to hit somewhere, so it is possible for the missed arrow to hit another enemy unit – it just will not be the intended target.
With Ballistics, the shooter will now aim at a spot that the target is predicted to be assuming that the target continues on its current course. The base to-hit percentage is unmodified, so the shooter can still miss the target. The shooter will also miss if the target changes its vector.
With Thumb Ring, the base to-hit percentage is now 100%. Stationary targets are always hit, and targets on a constant vector are also always hit. Units that change vector are missed."
from http://www.mrfixitonline.com/viewtopic.php?t=3669
"How does Ballistics and Thumb Ring work?
Each unit has a base to-hit percentage ranging from 50% (Cavalry Archers) to 100% (Mangudai). This refers to the chance that an arrow has to hit a non-moving target. If a target is moving then the arrow will aim at the spot that the unit was at when the arrow is fired. These arrows tend to miss targets, especially if the targets are moving in a lateral direction relative to the shooter. Missed arrows still have to hit somewhere, so it is possible for the missed arrow to hit another enemy unit – it just will not be the intended target.
With Ballistics, the shooter will now aim at a spot that the target is predicted to be assuming that the target continues on its current course. The base to-hit percentage is unmodified, so the shooter can still miss the target. The shooter will also miss if the target changes its vector.
With Thumb Ring, the base to-hit percentage is now 100%. Stationary targets are always hit, and targets on a constant vector are also always hit. Units that change vector are missed."
from http://www.mrfixitonline.com/viewtopic.php?t=3669