How to validate that Traffic Manager is distributing traffic as per the policy?

This blog mainly talks about the Traffic Manager's Round Robin Policy

In my day to day job I have seen the following question come up:
Traffic manager does not seem to distribute traffic as per the policy. How can we validate this?

The following article explains how traffic manager distributes the traffic:
http://msdn.microsoft.com/en-us/library/azure/dn339010.aspx

There is one more important factor to consider:
Each client machine uses a DNS server. The clients DNS server caches the endpoint entries for the timeframe specified in Traffic Managers TTL(default value is 300sec). Hence all the machines that use the same DNS server will go to the same endpoint for the 300sec(TTL timeframe).

Example:
I have defined Round Robin load balancing and have TTL as 300sec for traffic manager. I have 2 cloud services in my traffic manager.
When I tested from 10 different client machines that use the same DNS server, all the 10 client machines went to the same endpoint for 300sec(DNS TTL) and it appeared that traffic manager was not distributing the traffic.

To check if traffic manager is distributing the traffic as per the policy I used the following site: http://cloudmonitor.ca.com/en/ping.php

This site uses machines at different locations in the world and hence different DNS. I saw that resulting IP ping was almost 50% for each IP.
(We can ignore the  packet lost Result because the cloud services will not respond to Pings.)

Thanks to Kevin for explaining this concept and sharing the method to validate the traffic manager load distribution.