720p vs 1080p, Does Resolution matter? - A Utilitarian Perspective

[freedquaker]

 

First of all, this topic is not necessarily about the consoles, but a more broad one which can be applied in several areas.

The main commonly accepted principles about resolution :

a) Resolution ALWAYS matters UNTIL it hits a technical or optical limit (such as the monitor capacity or human eye's limit etc).

b) Humans recongize resolutions not as absolute changes but relative changes. For example, the jump from 640*480 to 1280*960 is a lot larger than from 320*240 to 640*480 but in relative terms, they are both equal (a 4x jump).

c) Utility received from resolution increases by a dimisnishing rate (dimishing returns). In other words, if the increases between 3 resolutions are equal, the first jump will be appreciated more (an increase from 320*240 to 640*480 is more recognizable from 640*480 to 1280*960).

d) Humans are adaptive by nature. This implies that the marginal utility is initially low but after a while this effect increases (a shift up in the dimishing returns). A simple explanation is that it would be nice to go from 640*480 to 1280*960 but not necessarily "revolutionary" at first but after getting used to the higher resolution, it would be unthinkable to go back to 640*480, which implies that the utility you got from higher resolution improved by time.

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Now a few mathematical notes.... When we talk about resolution, we usually only refer to horizontal lines. Assuming a constant aspect ratio, an "n%" increase in resolution along only the horizontal line would automatically imply "((1+n)^2-1)%" increase in total resolution. For example, a 50% (0.5) increase along the horizontal line implies a 125% increase in total resolution (1.5^2-1). This is the technical increase. However, the law of dimishing returns dictate that the human mind perceives much less of an increase (or appreciates it less than mathematically suggested).

A common way expressing this dimishing returns is to use a power less than 1 such as  (x^n), where 0<n<1

640* 480 to 1280*960 implies 100% change in both directions and 2x2 -1 = 300% change in total

Assuming utility is given by x^n (where n=0.5)

Total Resolution => 1280*960 = 640*2*480*2 = 640*480*4 (4x original)
New Utility => original utility * 2^0.5x2^0.5 = 2x Original Utility (100% increase)

So basically, assuming n=0.5 (rate of returns) will match the increase in one direction.

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Now let's come back to the modern times. The difference between 2 resolutions such as 1280*720 and 1900*1080 is technically staggering (and as much demanding); however, the perception will be lower... Simply put, it will be roughly equal to the change along the horizontal line, which is roughly 50% (1080/720 -1) although the actual pixel count increase by 125% (1900*1080/1280/720-1). That is a BIG difference even with dimishing returns in place.

How about the different between 900p and 1080p. Technically the difference is 44%, although the perception will around 20% (1080/900-1) vs (1080/900)^2-1. Even 20% is a quite large to be unnoticed. Humans usually can recognize differences above 10%. The difference between 720 and 640 (12.5% along one line) is a lot harder for example.

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There are 3 more points I'd like to add though.

a) First of all those suggest differences are usually the IDEAL numbers, and your perception may be lower unless your TV set can properly display the differences well. One extreme example is 720p TV set, for which, any resolution over 720 p will be useless (and sometimes worse). Also not all TVs are created equal. It will be much easier to recognize such difference in larger and/or higher quality TV sets.

b) Human mind and eye vision are big factors. Just like TVs, not all humans are created equal. Some can see, not only physically but also perceptually better than others.

c) The recognition and utility you'll get from higher resolution increases over time. As I said, human mind is highly adaptive, and is trained to recognize the differences after a while, and once it gets used to, there is no turning back. Those ultra clear resolutions may not be a big deal for you now, but in a few years, a brain adapted to 1080p will instantly recognize the loss of clarity in 720p and never would enjoy it as much.