I'm a big military enthusiast and of course love maps, so I'm giving you feedback to help present a more professional approach to your product. Please don't take my comments personal.
Just wondering who you are gearing this map toward - what audience do you want to communicate it too? Depending on the purpose and audience there are many improvements you can make. Right now this map doesn't do much for me at all and doesn't present relevant information other than a quick visual. I sort of shrug my shoulders to be honest. I guess I'm looking for a context this map is supposed to be in because it lacks so much information. For a general public audience, you are going to have to label the various countries on the map as a start simply because there are many, many people that are not literate in geography. And that's an understatement. So, you have to make it idiot proof to be blunt. On the flip side, if this map is just to be a quick visual to get a big picture sense like a slide in a presentation to those versed in military matters then the bare bones approach may be fine. If someone is standing up next to this map projected on a screen and explaining the data by narration then you might get by.
You need to give a total figure for all of the military personnel globally. Don't leave it up to the reader to add all those numbers up after deciphering the size of the dots in the legend key. I also would be curious to see how many troops are based in the U.S.! As an American, it would be great to get up to date information as to how many troops are based on home soil and compare that to how many abroad. And are you including active military "reserve" personnel in these figures too or regular U.S. Army troops and Air Force personnel? Along those lines, why have you omitted the naval presence of the U.S. military all across the globe?
In your Middle East inset (which needs a subhead) since it is the most important hotspot in the world for military matters, you definitely need to label them all of or at least the major countries besides the ones the U.S. has a presence in. Israel, Iran, Saudi Arabia are very important in today's geopolitical realm. It is surprising to find out - based on this map - that the U.S. has 2,500 troops in Pakistan. I thought we are only flying drones. So, it begs the question - what kind of troops are you presenting data on? Advisors, special forces, paramilitary forces within the CIA, FBI, DEA? I cannot make a clear conclusion based on this map data.
I, like Nick, would like to see actual numbers with each country. The dots are nice but they need to be re-enforced with numbers. I also agree that the title of "troop deployment" is a little misleading too because in a lot of countries there are just U.S. air bases or advisors or administrative or logistical personnel as opposed to combat troops. When I read "troops" I think combat boots on the ground.
I hope this helps. I just think this map has the potential to be very, very intriguing and to really present a big picture, but it needs a purpose and needs lots of improvements.