Edit: This test is no longer valid with patch 4 since testudo has been significantly boosted.
Old text:
The testudo formation is a formation that is supposed to boost shield strength.
If you check carefully, you can see that the first roman death at 0:21 is from an arrow that pierced his shield and went into the armored shoulder that he placed against the shield.
At 2:00 the ai switch to regular arrows but the romans still die the same way.
The arrows pierce the shield after 3-5 arrows then kills the roman directly after that, no matter what part of the body it hits (armored part,leg, arm etc...)
So it seems that either each hit to the shield removes some hp from the soldiers or that after 3-5 arrows to the shield, it gets broken then the arrow directly after that always kills the soldier.
This test is an old test.
I have made an another 3 tests that shows much better the effect of testudo here.
Total War ROME 2 : egyptian slingers vs praetorian guard in testudo formation
http://youtu.be/m6Nc6bmnJGk
Total War ROME 2 : egyptian slingers vs praetorian guard simply walking
http://youtu.be/P5LRYTnMld8
Total War ROME 2 : egyptian slingers vs praetorian guard running
http://youtu.be/-wI4p1X6gJo