From the latest Team Fortress 2 update notes:

Added a “virtual mousepad” concept to rework how bots track enemy players

• They now periodically estimate the position and velocity of the enemy they are tracking, instead of “locking on”
• After rotating beyond a maximum angle, they will pause for a fraction of a second to re-center their “virtual mouse”
• Allows for over/undershoot “slop” in aiming.Looks more natural, and allows skilled players to dodge
• Addresses the “180 spin around and fire”, “Heavy bot is OP”, “Sniper is OP”, and “I can’t fight a Heavy bot as a Scout” issues

This is fascinating to me. They recently added bots to Team Fortress 2 as an experiment, and I’ve always found the idea of programming bots for multiplayer-focused 3D games to be an interesting concept but I’ve never seen anyone go into this much detail about the things they do to make the bots seem more human. Having to re-center your mouse when looking around is a motion that I think a lot of people take for granted¹, but when you think about what that does to movement and control it makes sense that it would be helpful to try to simulate that for computer-controlled opponents.

In the next patch, I hope they’ll go the extra mile and occasionally let us hear the bots’ moms screaming at them about needing to leave for soccer practice over voice chat.

—Casey (Thanks to jrr for the link!)