What is the best way to motivate teaching assistants?

I think the best way to motivate a person in academia is to give them a bit of job security, some funding which enables them to follow their interests, and a great team to work with. I am not sure if you can realistically give "your(sic!) TAs" any of this.

In absence of solid motivating factors, you are trying to engage the team in some form of internal competition, which may motivate some people and completely put off others. For example, I personally would be puzzled as to why should I compete for some statistics or evaluations which look rather meaningless unless it has any effect on my promotion or chances of future employment.

Most people I worked with responded well to:

• smart goals
• positive example
• cutting the crap (including crap meetings)

In my experience, teaching is rather a pleasant activity and there is a lot of gratification in the process of working with students. An excessive amount of paperwork, bureaucracy and management can only spoil the fun.

However, I have been told (by someone not involved with the class) that I am "overquantifying" things. Also, even with all of this, there are four people who I would describe as "bad TAs" (and five people who I would describe as excellent TAs, and three people who I would describe as good TAs).

I presume that your good TAs are always on top of the lists you publicly post, and your "bad" TAs are on the bottom? Why do you think this public shaming will motivate them?

Here is what I would do:

• Centrally, I would stop posting things that make some TAs feel good at the expense of making others feel bad. The shoutouts are nice, but for statistics etc. I would only post who was on top (or maybe the top-3 or something), and only if it is not always the same people. Try your best to rotate your statistics in a way that everybody gets some love.
• Assign work. It appears to me that TAs are somewhat free in choosing their own work (since you give stats on who graded how many assignments). This naturally leads to some people slacking off and others, more or less happily, picking up their tasks. A simple solution to that is to make up a schedule.
• Validate that your "bad" TAs are objectively not doing a good job, and are not just weaker in comparison to your exceptionally great other TAs.
• If you feel your bad TAs are actually objectively lacking, use the central management principle of praising in public (which you already do, to some extent) and criticising in private. Talk to the TAs that you are not satisfied with in private and explain what you think they should do to improve. Give actionable tips - "you should know more about the subject" may be objectively true, but will also not change in the duration of the course. My impression is that with your statistics you attempt to shame people into improving without having to have an awkward conversation with the underperformers. Unfortunately, this is not how management works.
• Above all, it pays to keep in mind that not everybody is the same and has the same constraints etc. No matter what you do, not everybody will go above and beyond. If 5 out of 12 people regularly go above and beyond and most others are also doing a good job, you already have a strong team. Don't downplay this, not to yourself and definitely not to the team.

I have heard beatings can work well:

There's a famous expression attributed to Captain Bligh of the stricken HMS Bounty, who was overthrown in a mutiny. While flogging sailors for small misdemeanours, he is said to have declared: "The beatings will continue until morale improves."