A lot of features in this game are designed around providing players with a relatively intuitive understanding of what each ability and stat does... except attack speed. Why has the display of this stat gone unaddressed for so long? With all other stats, you can look at your current stat value and the bonus an item provides and determine how strong of a bonus that item will give you. For example, looking at my stat window, I currently have 80 base AD and 20 bonus AD for a total of 100 AD. A Maw of Malmortius would give me 55 AD, or a 55% increase in my damage. Seems clear enough.
How about attack speed? Looking at my stat window, I currently have 0.800 base attack speed and 0.200 bonus attack speed for a total of 1.000 attack speed. A Phantom Dancer would give me 55% attack speed, or a 55% increase in my damage (ignoring crits for a moment)... right? Well, no, the 55% only applies to your base attack speed. Okay, so it should give me 0.800 + 0.200 + (0.800 * 55%) = 1.440, or a 44% increase in my damage... right?
No again. The displayed base attack speed, 0.800, is not actually your base attack speed. It is your base attack speed plus your innate attack speed per level. The default base attack speed is 0.625 (varies by champion), and in this case I have a 0.175 bonus gained from levels. So, how much does the Phantom Dancer actually give me? It's 0.625 + 0.175 + 0.200 + (0.625 * 55%) = 1.344, or a 34.4% increase in damage. This is quite a different number from 44% or 55%.
Why is this a problem? Players need to be able to make good decisions based on the information they have on which items they should build next. For an AD carry, you generally need to build AD, Crit, and Attack Speed in roughly equal quantities to gain the maximum dps benefit. However, it is hard to do so when your champion can have as much as 60% free attack speed built into their levels that you cannot clearly see anywhere in your stats like you can for AD. This is especially a problem for newer-to-intermediate players, who might gravitate towards building lots of attack speed without realizing why it's significantly worse than it initially seems to be.
What to do about this? Due to the percentages (e.g. Phantom Dancer = 55%) being based on your base attack speed, I would suggest representing your innate attack speed per level as bonus attack speed AND displaying your total attack speed percentage. That is, in the above example, when you hover your attack speed, instead of displaying 0.800 + 0.200, it should display 0.625 + 0.375 (160%). This gives you, at a glance, an idea of how much attack speed you already have and how much a new item would really improve it. Alternately, it could show the three stats separately: 0.625 + 0.175 + 0.200 (160%). This is a bit lengthy but more accurately conveys where your attack speed is coming from.
tl;dr Attack Speed is a confusing stat and it would help to display it in a more intuitive manner so players can make better choices. Please fix this, Riot. Thanks!
EDIT: Read this if you want to learn more: http://leagueoflegends.wikia.com/wiki/Attack_speed Thanks, DodgeOrCarryMe!
EDIT2: 50+ upvotes! Surely Nerfmaster Morello will swing by eventually and improve the clarity of this confusing stat!
EDIT3: 100+ upvotes! Zileas pls, improve the clarity instead of trolling about Iaw all the time!
EDIT4: All hail Xypherous and Brackhar, everyone's favorite champion designer and generally awesome attack speed dude
EDIT5: 200+ upvotes! Thank you for the support! I'm sure the Rioters are busy improving the clarity of attack speed as we speak.