Why does Sterak's Gage's AD not show up in the player's AD stat?

If you have on your champion and then look at your AD stat in the UI, it doesn't show the increase to your AD. If you hover over the Attack Stat though, you can see that the base AD that Sterak's gives is applied to your base AD, and it also shows your total AD when you hover over the Attack stat icon but you cannot see this reflected in the general UI. Just wondering why that is. Can someone from Riot explain?

http://apollo-pbe-uploads.s3.amazonaws.com/1440092394/LeagueofLegends2015-08-2013-26-55-78.jpg

Sorry if this sounds confusing but you can see it in the image above in the link. Morde has 280 AD according to the UI, but when hovered over the AD stat icon, it shows 319 AD with 183 base AD + 137 bonus AD. I was wondering if this is going to change in a future patch or this is working as intended and why.