The NUMA Histogram

[Nexx]

There's a debate going on at Uservoice about the user histograms on NUMA. I am bringing the debate to the forums because the uservoice limit of 400 characters is really tough to work with.

Please note that the histogram deals with the exact rating of a map, not the rounded rating that shows up.

So, on the one side, player_03 and myself suggest that the histogram intervals should be:
[0.0 - 0.5) [0.5 - 1.5) [1.5 - 2.5) [2.5 - 3.5) [3.5 - 4.5) [4.5 - 5.0]
That makes 6 bars for the 6 possible ratings a map can have (0-5). Simple, right?

Well, on the other side, Arachnid wants to keep the histogram the way it is:
[0 - 1) [1 - 2) [2 - 3) [3 - 4) [4 - 5]
The problem is that the full labels don't fit, so he just used the first # to label each interval. Arachnid mainly thinks this is better because it results in 5 intervals of equal size. He has a real problem with the two half-intervals on the ends of our suggested histogram.

Arachnid, here's the strongest case I can make for our suggestion:
What is the purpose of that histogram? I would say that it is to show how many maps of each rating a user has. I think that's a solid statement, but let me know if you disagree with this, since it's the foundation of my whole argument. With that purpose in mind, let's consider how many different ratings a map can receive. Of course, the overall rating is an average, and as such it can take on a multitude of different values. However, for display purposes, the average rating is rounded, resulting in only 6 possible ratings: 0, 1, 2, 3, 4, 5. For all intents and purposes, all those exact values simply become a set of integers. This is not an interpretation, it's a fact. From the perspective of the user, all average ratings are integers.

Therefore, given our stated purpose, the histogram should be a graphical tally for the 6 possible discrete values.

For example, let's say a user has 5 maps with the following exact ratings: 2.9, 3.2, 3.6, 4.1, 4.5. Those maps will show ratings of 3, 3, 4, 4, 5. Thus the histogram for that user should be (0,0,0,2,2,1), with labels 0, 1, 2, 3, 4, 5. Let's consider the current system, which looks at the exact average ratings. That system would result in the histogram (0,0,1,2,2), with the labels 0-1, 1-2, 2-3, 3-4, 4-5. To be sure, that histogram functions properly, but in this case it doesn't display things the way the user expects. It doesn't correlate with the way the rest of the site handles average ratings.

Of course, the fact that the site deals with the exact values for the average ratings means that the histogram is working with essentially continuous values, not discrete values. But that's not a big problem. All one has to do is handle those continuous values like the rest of the site handles them. That is, just emulate rounding, namely by using the following intervals: [0.0 - 0.5) [0.5 - 1.5) [1.5 - 2.5) [2.5 - 3.5) [3.5 - 4.5) [4.5 - 5.0]. The half-sized intervals on the end aren't wrong or misleading because the histogram is emulating the site's conversion of (essentially) continuous values into discrete values.

And that's the entirety of my argument. Please let me know if you have questions and I will do my best to clarify.

Edit: It appears that perhaps Arachnid's system is not quite what I said it is above. Perhaps Arachnid is rounding the average first, and then using the bounds [0 - 1) [1 - 2) [2 - 3) [3 - 4) [4 - 5]. But even so, that's really equivalent to this: [0.0 - 0.5) [0.5 - 1.5) [1.5 - 2.5) [2.5 - 3.5) [3.5 - 5.0], which involves unequal widths. In any case, the argument only changes a little to become: split that last interval into 2 intervals!

[Rose]

I don't understand. I know that one of my maps is an average rating of 3, but that its exact rating is somewhere around a 2.7 or so. According to what you're saying about how the current system works, then my histogram would show it as a 2. It doesn't; my histogram correlates with every average rating that I have. It's not inaccurate for me.

[chume14]

Ok very good point well made just a couple of questions. Would column width be consistent or represent interval size and would height represent number (frequency) or frequency density. I do agree this should be done though

[Nexx]

I don't understand. I know that one of my maps is an average rating of 3, but that its exact rating is somewhere around a 2.7 or so. According to what you're saying about how the current system works, then my histogram would show it as a 2. It doesn't; my histogram correlates with every average rating that I have. It's not inaccurate for me.

Well, I just tallied your rated maps and compared against your histogram and they're spot on, as you say. (The exact value used in the histogram can be found in the page source code) The same is true for me as well. Hmm. Either we're wrong about what we think our map averages are or Arachnid is using a different system than what he suggested on the Uservoice page.

Ok very good point well made just a couple of questions. Would column width be consistent or represent interval size and would height represent number (frequency) or frequency density. I do agree this should be done though

To clarify for everyone else, the first question is asking if the bars on the ends would be half the width of the bars in the middle. The answer to that is no, because again, this is emulating a histogram of discrete values. As for bar height, is represents frequency, of course. Look at the example I gave. If it was frequency density, I would've explicitly said so because that can get quite confusing.

[otters~1]

The NUMA histograms need fixing, that I'll agree with. The main problem is that they don't even have a space for five-rated maps.

[Nexx]

The NUMA histograms need fixing, that I'll agree with. The main problem is that they don't even have a space for five-rated maps.

Actually, if you had read the first post, you would see that there is a space for them: mixed in with the 4's. Obviously that doesn't work so well.

[otters~1]

The NUMA histograms need fixing, that I'll agree with. The main problem is that they don't even have a space for five-rated maps.

Actually, if you had read the first post, you would see that there is a space for them: mixed in with the 4's. Obviously that doesn't work so well.

I know, but there is still no way to distinguish between four-rated and five-rated maps.

[Destiny]

I agree 100% with you, nexx. I think the current system does not accurately correlate with what people expect to see. My main dissapointment with the current system is that my 4's are mixed in with my (albeit few) 5's. I'd really like to see your value fields incorperated into numa. Even if it's just for the sake of checking which kind of authors get the most 5's without scrolling through their possibly massive archives.

[Exüberance]

Ooohhhh, so 4 means (4-5]? I thought he just screwed up the code (i<5 instead of i<=5 or something similar) and it wasn't displaying 5/5s.

Maybe it could do some kind of scatter plot? That way, it can plot the exact rating of a map. And you could use simple algorithms to fit the points to a curve and make a nice-looking graph.



hhhmmm, that gives me an idea.... what if instead of selecting integers from a list (which I notice lacks 'average' for some reason. Unintentional?), so used a slider bar thing, to show about how good the map is.

[===|===|===|===|=O=]

meh, maybe that's not such a good idea. The histogram really should be made better. Ratings on NUMA are kind of dead right now. So many 5/5s on average maps, no average rating option, messed up ambiguous histogram, very restricted ratings....


One more thing that migth be cool is if your comments on maps that you favourited showed up starred or something, and a map would show a number of stars under it's rating for the number of people who favourited it. That way the people who seem to think the lesser options you give people, the better the ratings work, will be happy. (I still can't believe we had a number of people who wanted a binary rating system..... that's what bitesized maps were for!!)