.7 seconds to complete an attack.

No. That's not the same.

an attack each .7 second means that in 7 seconds, you have 10 attacks.

.7 attack each second means that in 10 seconds, you have 7 attacks.

So, 10 attacks in 7 seconds is much better than 7 attacks in 10 seconds.

i fail

My life coach says that there is *always* room to improve.

What is being described here is not attack rate but attack time.

Rate is units per unit time: seconds^-1

Time is, well, units time: seconds

The unit of the value on the character sheet in demigod is time. 0.7 of what? Seconds. It's 0.7 seconds for each attack, so it's attack time, not attack rate.

Really, it would be better if the character sheet did show attack rate. It has a very simple relationship to dps, attack damage and speed modifiers. You might have noticed that: what is speed? It's an x per unit time again. How fast is something is a rate. Easy mathematical relation, easy understanding. 10% more attack speed is a 10% higher attack rate. For attack time it's the inverse of 10% (~91%) of your old attack time.

There are many more examples. Rate should be what is shown on demigod's character panel.

(covering my ass here: Rate is not just with regard to time. It can be a ratio between any kind of value)

If the base attack speed was 0.7, yes.

Looking at charts, demigods start at around 0.7 rate of fire, making attack speed on the in-game character sheet about 1.43 (1/0.7). At 20 the attack speed is about 1 though, so about the most you can get out of attack speed is a 100% increase.

Keep in mind the character panel's +% attack speed is inaccurate. It doesn't correctly compound your per-level increase with what you get from items, etc. (it understates items the more your level increases, but it's only that display)