The crux of this entire discussion seems to be that the current XP requirements, compared to the WUs required, is too low and encourages people to write bad writeups, because WUs are usually the limiting factor. I propose that this problem can be fixed using the current leveling system of requiring a certain number of XP and a certain number of WUs.
I decided to take a mathematical approach for mending the current XP system instead, because as other E2 users have noticed, Professor Pi's scheme has flaws.
Let's start off by looking at the XP needed and WUs needed for each level, plus the number of votes acquiring that level will get you.
Level XP WUs Votes 2 Novice 50 25 10 3 Acolyte 200 70 20 4 Scribe 400 150 30 5 Monk 800 250 45 6 Crafter 1350 380 60 7 Artisan 2100 515 75 8 Seer 2900 700 90 9 Archivist 4000 900 105 10 Avatar 7500 1215 125 11 Godhead 13000 1800 150 12 Pseudo_God 23000 2700 200 13 Pedant 38000 4500 300
Given that voting is impossible prior to Level 2, it is clear that a user needs to acquire two XP per writeup to reach that level. In fact, let's use it as a benchmark. Let's call it XP1.
Let's also assume that a writer can turn out one writeup at that level of quality (earning two XPs per writeup) every two days. Some writers can do better than this; others may not be able to. This is simply to establish some sort of baseline. So, then let's add another column called D2NL, days to next level.
Let's also assume that every other day you use all of your votes. This means that you should earn, on average, you earn 20% of votes in XP when you vote and 50% of your votes in XP after dumping all your votes. This totals to 70% of votes converted to XP every other day, or 35% every day. Let's call this DXPA, or Daily XP Added
On average, then, using the WU requirements, the XP numbers are far off kilter. Let's recalculate, using the formula (XP needed for Ln = XP needed for L(n-1) + XP1(of L(n-1)) + (D2NL*DXPA of L(n-1))).
Level WUs Votes XP1 D2NL DXPA D2NL*DXPA XP needed 2 Novice 25 10 50 90 3.5 315 50 3 Acolyte 70 20 140 160 7 1120 415 4 Scribe 150 30 300 200 10.5 2100 1675 5 Monk 250 45 500 260 15.75 4095 4075 6 Crafter 380 60 760 270 21 5670 8670 7 Artisan 515 75 1030 370 26.25 9712 15100 8 Seer 700 90 1400 400 31.5 12600 25842 9 Archivist 900 105 1800 730 36.75 26827 39842 10 Avatar 1215 125 2430 1170 43.75 51319 68468 11 Godhead 1800 150 3600 1800 52.5 94500 122218 12 Pseudo_God 2700 200 5400 3600 70 252000 220318 13 Pedant 4500 300 9000 n/a n/a n/a 477718
Compared to the old style XP requirements:
Level Old XP New XP 2 Novice 50 50 3 Acolyte 200 415 4 Scribe 400 1675 5 Monk 800 4075 6 Crafter 1350 8670 7 Artisan 2100 15100 8 Seer 2900 25842 9 Archivist 4000 39842 10 Avatar 7500 68468 11 Godhead 13000 122218 12 Pseudo_God 23000 220318 13 Pedant 38000 477718
It should be pointed out that a good noder who nodes more frequently than one every two days can easily level up much faster than I predict here, because of the merit of the "cooling" system, blessings, and additional XP that good writeups will incur. This is just intended to be a rough model of an average E2 user's behavior.
In this new scheme, levels are much trickier to come by. In fact, I believe that crossing the level line will often occur with writeups before XP. This means that good writeups that can continually earn XP as people discover them and vote up (as voters would on a good WU) become much more valuable, and bad writeups simply to fill a WU count will decrease in number.
The net result of this scheme is then the same result that Professor Pi wants: good writers are rewarded for good writing. Good writers, quite simply, will be able to progress through the level system faster than those who just churn stuff out to meet the WU requirement for leveling, because this system will place the emphasis on quality over quantity.
Of course, leveling up becomes much more difficult. But, on the other hand, people of a high level would deservedly have much more prestige in the system and many bad WUs would be avoided.
Some people would most definitely drop in level if this system were implemented today. Thus, if this were to be adopted, I would be in favor of "grandfathering" those people into their current level if they so wished, with the grandfather clause disappearing at their next level up.
I strongly encourage any comments you might have via /msg. Especially you, Professor Pi.
This isn't going to be a proposal for a whole new system. It's just a couple of architectural inputs, which I am sure have already been considered, but I haven't fed Klaproth in a long while.
To modify this system, there are two key properties to look at when addressing deficiencies (all I plan on addressing): Gaming the system, and attacking a noder.
First, looking at the standard system:
A noder's NFW is trivial to boost, merely by casting all their votes in a day. To level up, they merely have to generate enough nodes; hence noding for numbers. For me to reach Level 6, I merely have to sneak in another 79 nodes; their reputation does not matter.
Attacking me is hard. Likely, each downvote costs me -.2 NFW. A single noder can cost me 60 XP, which I'd notice, but I make that after two days of voting. If you are Pseudo_Intellectual, you could do this to me in a day; most noders would take a week or more.
Now a look at the (unlikely to occur) Median Node-Fu Product) system:
Gaming the system: My NFW (not counting the +1 bonus in that node) is 1204. Since my median node is only 5 into my set of rep 4 nodes, I could delete 56 writeups below it - leaving me with an NFW of 1225. Probably not worth it. But as I manage to add more high rep nodes, the step effect to shift my median node becomes more tempting.
Attacking the system: With 5 strategic downvotes (easy to figure out where), an attacker could shift my median node down by one, costing me 301 NFW (ouch!). However, they can't shift me down again, although each attacker could, in fact, drop me by another 301 NFW. At most, they'd have to spend 151 votes (The first spends 5, the second 47, the third 105, the fourth 146, and the fifth and beyond 151). So here, one vote can cost at least -2 NFW, but only en masse, and it is hard to defend against.
Interquartile system:
This is a harder one to game. Interquartile only counts my nodes between rep 2 and 7, giving me an NFW of 1143. If I delete 4 low ranking nodes, I can add 3 points to my NFW, to a whopping 1143. If I removed the 56 writeups from the MNFP proposal, my NFW drops to 1104 - I lost too many writeups to be countered by the average jump in value of the writeups. I could probably figure out the breakeven point, but I'll leave that for someone with even more time on their hands.
Attacking isn't as easy as MNFP, but easy than XP. The only interesting places to attack are right in the middle; each vote in the middle half of my writeups costs me exactly 2 NFW.
Mean Rep*nodes system (sum of reputations)
This system is gameable by catering to the soy-eating lesbian monkeys. Every upvote increase my NFW by one, every downvote hurts it by one. Getting a writeup voted on a lot helps ... a lot. Since most noders have a right-tailed distribution (I can never remember if that is left or right skew), NFWs will be higher (mine is 1734); if, however, they are consistently higher, a shift in the metric would reduce the effect. A cap on outliers (no node can contribute greater than 50 rep or less than -5 rep to your NFW) might also reduce the impact on the system (I like those numbers, since they don't affect me).
Attackability: Here, an attacker can only cost you one NFW per vote cast, no matter where.
Damp outliers. In each system, the effects of outliers - such as a toilet seat write-up - have been brought up as a justification for central area sampling. Once a wirteup's reputation has passed beyond some threshold, its effect is measured only by weighting the direction of the sampling area. Instead of doing this, the reputation used to compute NFW can be damped. One simple, and easy to plot method, is to place caps on the upper and lower ends of the distribution. No node can contribute more than 25 reputation points to NFW. Higher rep nodes contribute 25 exactly. No node can deduct more than 2 reputation points from NFW. Lower rep nodes deduct 2 exactly. (Disclaimer: under this system, my NFW is 1631)
Alternate. In an alternate system, one could use logarithms to compute NFW - for instance, each node could contribute log(rep) if rep >0, or deduct log (1-rep) of <1. This could be renormalized (multiply by 10), leading our example noder to have an NFW of 1733. However, this system is attackable. The transitions from 0 to -1 and from 1 to 2 are the most significant (changing one's NFW by 0.3), although the transition from 0 to 1 is useless (no change). However, the higher a writeup's reputation goes, the less each successive vote yields to rep.
Just some mathy questions directed at the Prof, but I'd like to hear answers from anyone who can answer this:
So I really like the idea of the proposed MNFP system of level advancement, however I am moved by some of the comments that the median node rep might not be the best measure of central tendency. While it seems that the distribution of node reputation is roughly gaussian, it does seem that some users have a larger right side tail; that is, they have many more high rep nodes than low rep nodes.
Although a noder may not have enough high rep nodes to make his distribution very skewed, the traditional measures of central tendency for gaussian distributions may not be able to tell the whole story.
What I'm getting at is this: is there any way to meaningfully quantitify the right-side skewness of a noder's rep distribution and thus be able to reward noders that have many more high rep writups than low rep writeups?
Thanks for reading, Yours Truly Qeyser
Professor Pi's Comments: Actually, the distribution of node reputation only resembles a normal (Gaussian) distribution. The real distribution is most likely closer to a Binomial Distribution. But other factors such as writeup nuking and C!ing (more "air-time") have influence on the shape of the distribution as well. It would be very impractical to use models such as the Binomial Distribution or the Poisson Distribution (which is the limiting case of the former and would work out for larger rep-sums) because (1) there is far too much computation work required; lots of slow factorial calculations, and (2) the whole procedure of calculating an "average" node reputation would become far too complex, for the average noder to make sense of. There is actually a parameter that can be used to evaluate the degree of asymmetry of a distribution; it's called skewness. It is a 3rd order function of the node-reputations. I doubt thus parameter is practical in the evalation the "average" node distribution, and it would again make the entire procedure too complex. The median actually would be a fair measure of central tendency for the reputation-distributions we encounter, but as was already mentioned: it's easily broken by targeted downvoting on writeups with a reputation at, or slightly above the median. It is not robust enough, since it is only a single-parameter description of the distribution. In order to make it more robust, it would be better to incorporate more factors, such as the 1st and 3rd quartile values, or the reputations of all the writeups between the the 1st and 3rd quartile. Again, we don't calculate the mean of all the nodes, since that would favor the outlier points too much.
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