From the overwatch official forum:

Linear Ramp and Aim Curves

Tim Ford Lead Engineer

I’d like to clear up some confusion about the difference between Linear and Exponential Ramp as well as announce some new options you can leverage to fine tune your aim. I’ve read a few posts that assume Exponential Ramp yields a exponentially higher turn rate than Linear when the aim stick is fully deflected. This is a reasonable assumption, since an exponential curve will yield a higher result than a linear curve for values greater than 1. However, the goal of Exponential Ramp is to map a sensitive aim stick to a restrained aim value. We achieve this goal by mapping linear input to exponential values over the range from 0 to 1. The exponential ramp values we are concerned with fall into the region of the curve boxed in the following image:

http://imgur.com/fiGfLpI

Your input is constrained from 0 to 1 where 0 is the value at the tip of the dead zone (usually about 20-25% stick deflection) and 1 is fully deflected. The dead zone is computed with the scaled radial technique explained here (http://www.third-helix.com/2013/04/12/doing-thumbstick-dead-zones-right.html). Linear Ramp uses this value to compute your aim turn rate. Exponential Ramp scales this value (roughly) by a power of 2.5. So, a Linear Ramp input of 0.25 will map to an Exponential Ramp input of 0.03125. A Linear Ramp input of 0.75 will map to an Exponential Ramp input of 0.4871. Naturally, a Linear Ramp input of 1.0 will map to an Exponential Ramp input of 1.0. Incidentally, Exponential Ramp is “roughly” a power of 2.5 because it’s actually a hand drawn curve we borrowed from our generous friends on the Call of Duty team.

Today, we give you two choices for input curve mapping, Linear and Exponential Ramp (Dual-Zone is technically linear as well). Of course, there are a whole family of possible curves between linear and our current exponential (and beyond). In an upcoming patch, we will add an option called Aim Ease In. This is a slider option from 0 to 100 that corresponds to an exponent from 1 to 5 respectively. Combined with Linear Ramp, this option will allow you to select a wide range of curves to map your aim input to your taste.

http://imgur.com/MzZZKNL

Aim Ease In is compatible with Exponential Ramp and Dual Zone, although you should expect a fairly compressed aim curve if you crank this option with Exponential Ramp.

Link: https://us.battle.net/forums/en/overwatch/topic/20758657839?page=1

This is all very strange to me. It's clear that Blizzard doesn't really have a grasp about what makes a good aiming system on consoles. They do know something is wrong -- they are researching it and getting advice, but, they still don't have a good solution. So, as developers, it's an easy trap to fall in to when you don't know how to solve something you expose more settings and push the problem down to the user. It's up to them to figure out what feels "right". Another example of this (to an extreme) is Valve and the Steam controller.

They've concentrated specifically on the exponent of the curve and got feedback from COD developers. This is all very basic -- circular deadzones, stick deflection-based acceleration. That's all fine, but, notice they haven't talked about the most important thing they haven't yet addressed -- that is what "1" means on all their charts they shared.

They want gamers to be able to change the way the game aims by adding another setting their customer-base won't understand. But, why is it that COD and BF feel so good without these confusing settings? That's because they don't ignore turn speed.

This is what I don't understand. There is nothing good about adding another setting (increasing parameterization) to change the exponent on their curve. What they should have done for OW -- which COD and BF already do -- is allow the gamer to choose which *part* of the curve they operate in with a significantly higher turn speed limit. This way, with the same curve, fine aim response can be adjusted just by modifying turn speed (which people do understand).

But, COD wasn't completely forthcoming with Blizzard. There is quite a bit more going on with CODs aiming system than just the "2.5" factor they shared which makes it feel great. XIM's smart translator trainer sees it and shows us. But, just increasing maximum turn speed and removing all time-based acceleration will result in an aiming system that is at least closer to COD.