What activities do you do to measure the value of sending your team to training? 

1. Based on the appraisal feedback, we set clear training objectives ( be it technical or leadershup or boosting efficiency) for people. This is fundamental to training success. 
2. After training, we measure the immediate impact through assessments to see how well the new knowledge has been absorbed.
3. Then we track the productivity improvements / KPIs related to the skills learned ( be it issue resolution time, defect count, emotional quotient etc.,) for positive trends 
 
I strongly believe that regular training effort is central to boosting employee morale  as well as efficiency and will drive higher retention rates.

One of the best ways to monitor training results is to link them to performance measurements and individual development plans. Connect training to individual goals and, as a leader, challenge the employee to apply what they have learned through coaching and mentoring sessions.

There are many reasons for training - upskilling, personal growth, new technology being introduced.  The value is in what the person has learnt and can apply to their role, or be prepared for a future role.  If you can set KPIs that is great, but they are sometimes intangible.  Especially if they are soft skills.  From an employees point of view value is measured differently - am I growing in a direction I want to, was the training useful, engaging, or even, will it get me a raise or better job.  It may lead to increased engagement as well. 

It is important to have training tied to a very specific and documented development and performance plan so it can be tracked, measured and agreed with employee and management chain.

We start by making sure the training is aligned with the person's career goals and ability to act on what they learn. Sometimes the experience is wasted if they 1) don't have a strong enough foundation in the technology to even understand what's being taught or 2) don't have the influence at the company to advocate for improvements based on the training.

For example:
-An engineer with little or no AWS experience will get little out of going to AWS re:Invent.
-An individual contributor who isn't being given leadership opportunities at work won't be able to practice what they learn at a leadership training.
-An engineer who doesn't have good rapport and influence with teams likely won't be taken seriously when they bring back ideas from a conference.

Once you've made a good match and sent the person(s) to the training, some of the other answers on this thread apply: Have them present and share what they've learned, focusing on 1-3 improvements that can be made at the company.