Friday, January 17, 2014

Collinearity and Step Progression

The latest Late Nite With Stede (#015) was recorded last night, and I was honored to be in the audience on IRC during the recording to chat with some of the gold making gurus that listen to LNWS live. It's always a good time, and if you ever find yourself having free time Thursday at midnight EST you should swing by.

It was a great show with special guest Ben Redington who is starting up a blog called The Gold Blog Method. He mentions in the podcast that he is going for an overall feel akin to that of Wowprofitz, where he is starting out as a gold making as a novice, and going over methods that he's tried and the results he's had with them, what works, and what doesn't. Should be an interesting project to see come to fruition.

Anyway, back on topic, during the podcast Stede mentioned the following tweet, and we had a bit of debate about what he said following, and honestly I think that this tweet has been a very misinterpreted example, because Celestalon chose numbers that didn't properly illustrate his point, but here it is:

Stede's comment on this tweet was
"I got a bit of a chuckle out of that because, 100 to 120 is of course what? A 20% increase. And then 500 to 600 is what? A 20% increase. And that's, those are collinear. You know they are linear. That is a linear increase. 100 to 120 and 500 to 600, is you know, they're linear with each other."
No love lost for Stede, we were just disusing the merit of this statement in chat after he said it, and I think I was not able to eloquently state my case as I could have. Now there's math incoming, high school algebra II at most, but it's still math.

Of course let's start with a definition: Two points are collinear if they both lie on the same line. Pretty straightforward.

Now, as a mathematician, next I am going to have to define my variables. My x-axis will be "Gear Steps" and my y-axis will be "Item Level". First I'd like to point out that any line we throw into this model will have all those values mentioned in the tweet as "collinear" because a straight line with a slope that's positive  will indeed transverse all y values. For example the line y=40x+10:



As you can see, all of the item points mentioned are included here, but the same would be true of even a vertical line, so saying that y values are collinear is a tautology, and does not really bring much to the table discussion wise. You will notice though, and this what I think is important to take away from this, is that the step size between 100 and 120 is .5, and the step size between 500 and 520 is .5. So, for equal step sizes, you have equal increases in gear, so as far as collinear, yes y values will end up being collinear, true enough, but when we look at step size (which is actually the slope of the line) we see that the model suggested would look something like y=20x+20:

As you can see, I think more clearly now, there's one step from 100 to 120, and there's one step from 500 to 520. On the other hand there's 5 steps from 500 to 600. This is the model I believe Celestalon was going for in the tweet, although I do agree it is a bit of a bad example. The point being at the lower item levels a 20 point jump represents a significant % change, a 20% increase from 100 to 120, whereas at the higher ilvls, continuing with that linear growth, going from 500 to 520, it's only a 4% increase in item level, and doesn't feel as rewarding as that 20% boost you got going from 100 to 120.

I get where Celestalon is coming from with this tweet, but realistically speaking I think there's a pretty big difference between 502 gear from LFR ToT and the 522 gear found in ToT normal, which was a 20 ilvl difference, and I feel that step progression between LFR and Normal should feel rewarding. Again though I really think he was looking for a "Max level step" to be the difference between patches, not within a patch. Anyway I hope I didn't bore you to death with math, and be sure to check out the latest episode of the Late Nite With Stede Podcast.

As a side note, I will be recording Episode 7 of the Drunken Musings Podcast with GoblinRaset this Saturday at 9pm EST, so feel free to tweet or comment here asking questions for our show, anything you'd love to hear us talk about, and don't forget to watch us live at GoblinRaset's Twitch Channel Sat night at 9pm EST.

Cheers,

Phat Lewts

1 comment:

  1. I just like the statement, math aside.

    This is sort of like golf. People throw thousands of dollars at the game buying the latest and greatest, either because Tiger uses the equipment or their local pro tells them to only use Titleist. In reality, the average player isn't going to notice a damned bit of difference to their game because they have the same shitty swing, can't keep their heads down, and they won't follow through. Their short game also sucks because they won't practice that at the driving range, but they sure will hit a bucket of balls. They may notice some equipment performance, but it would only be a small amount of yardage in a sample of maybe 10-dozen balls, and we all know that's unacceptable, it has to go much further for it to be better! And all the time!

    So golf's just a game, right? You would have to be a professional who has the proper stance and thousands of hours logged swinging the club the exact same way to really notice the actual difference between equipment and get the full benefit.

    Same thing in WoW. If you can replicate the exact same rotation on your character, you will notice a difference. The item difference between 500 and 520 is actually 3/4 of a tier, depending on the slots - with weapons and trinkets making the largest difference. Depending on your ability, you should notice a difference that will be around 5-10%.

    Of course, the example given was horrible but understandable. It's perception. Unless I see a 50k dps change, it's just not a reward. Ask the people who don't re/gem-forge-enchant because it's only going to add 10k to their dps. It was far easier to notice the differential when the numbers were 1000 dps vs 1100 dps, or 4000 dps vs 5000 dps. People want to see big numbers.

    Going way off the reservation on this one, I know. I'm not a math guy!

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