Series Info...Engines of Creation #17:

Pareto Optimism

by Dave Rickey

Or: How I learned to stop worrying and love the Uberguild

Give me the fruitful error any time, full of seeds, bursting with its own corrections. You can keep your sterile truth for yourself.
--Vilfredo Pareto

One of the thorniest problems in online game design is how to deal with creating an environment where the "casual player" and the "power gamer" can co-exist. There's an implicit belief in the principle of "fairness", that what Average Joe gets for his monthly subscription is the same as everyone else, that if the powergamers are extracting more reward and playing more hours, it somehow devalues the game experience of the less obsessive.

This tempest in a teapot is the constant refrain of board warriors, with a never-ending list of reasons why those who have to work for a living (apparently with unmonitored internet access) cannot and should not be expected to compete with children and college students who can spend so much more time playing. However, this debate never goes anywhere, and the reason why is because it's all strawmen.

In any field of human endeavour, where the performance of people is ranked against each other, you quickly run into something called a "power law" relationship. The classic form of this is commonly known as the "80-20 Rule", where 20% of the participants in any activity will perform 80% of the work, and/or get 80% of the reward. The original form of this was the "Pareto Principle", the observation that 20% of the people held 80% of the wealth. Since then, it has been extended to many other areas, for example if a carpenter owns 100 tools, he probably uses only 20 of them four fifths of the time.

Unsurprisingly, similar effects turn up in online games when examining player behaviour, XP-earning rates, PvP success ratios, and so on. If the average XP per hour of play for 40th level characters is 1,000,000xp, the top half of them will be found to be earning at some multiple of that rate. What makes this significant is that pareto-optimized environments are recursive; if the top half of the playerbase is earning at 1.5 times the overall average, the top half of the half (25%) will be earning at 1.5 times *that* rate, or 2.25 times the overall average. In a "fair" environment, this process continues, the top 12.5% will be earning at 2.25 * 1.5 = 3.375 the overall rate. Carry this logic out to its logical conclusion, and in a sufficiently large population of players (tens of thousands), you should find that a small number of them are earning XP at a rate hundreds of times that of the "average" player. In fact, most players are *below* average, the high-performers at the top inflate the average to well beyond that of the performance by the majority. This would be nothing but a theoretical curiousity, if examining the performance of actual players in actual games didn't correspond strongly with the theory.

How is it possible that in a "fair" system, the majority of players will actually receive below-average results, and a minority will rake in a huge amount of the reward? It's actually fairly easy to set up a thought experiment to demonstrate this, but first I need to explain one more bit of theory: the normal distribution, also known as the "Bell Curve", which most of you should be familiar with from high-school statistics. Basically, when measuring the performance of humans against *absolute* standards, they show a characteristic pattern, with the majority of them performing at or near the average value, a handful performing well above, and a corresponding handful performing equally below the average. And individuals on multiple trials will often show this same distribution, sometimes outperforming their personal average and other times underperforming, but clustering to some degree around their average.

So, for our thought experiment, let's take 2 4-sided dice. There are 7 possible results from rolling these dice, from 2 to 8, and the chances of each result are arrayed in a bellcurve, from one chance in sixteen of a 2 or 8 to four chances in sixteen of getting a 5. To represent differing skill levels, we'll fall back on that old pencil-and-paper standby: The modifier. Our hypothetical players will be Maximum Mike with a +1 modifier, Average Joe and his twin Average Jim with no modifier, and Special Ed with a -1 modifier. So we have three bellcurves (one of them duplicated in our population so it also forms a bell curve).

For our first ruleset, we'll assume that rolling a 6 or better is a winning round, an objective standard that will represent a purely PvE contest, where players never compete directly. In this case, we'll find that Special Ed "wins" 3 times in 16 (18.75%), Average Joe and Jim "win" 6 times in 16 (37.5%), and Maximum Mike "wins" 10 times in 16 (62.5%). So in our objective measure of a game with minimal "skill", everyone but Maximum Mike is below the average "win" rate (39.0625%), and Special Ed's small (12.5%) performance penalty has resulted in a huge shortfall in results (less than 1/3 the win rate of Maximum Mike and exactly half that of the Average twins).

What we have here is essentially a mathematical proof that "Life isn't fair", something most of us figure out empirically by the time we are 12 years old. But what if the opponent is more personal? Instead of a "win" involving beating an objective score, let's pit the players against each other, one on one: The one with a higher roll wins, ties are ignored. We can predict the overall win ratios for each potential matchup by taking each potential roll of one contestant, calculating the chance that their opponent will roll higher, multiplying that by the chance of the potential roll, and summing all possible potential rolls. Each one of our players has three potential opponents.

Sparing you the math, Special Ed will win 35.8% of his rounds (assuming equal numbers against each possible opponent), 41.4% against Average Joe and Jim, 25.8% against Maximum Mike. Average Joe and Average Jim will get 50% against each other, 58.6.2% against Special Ed, and 41.4% against Maximum Mike (which becomes a wash of 50% overall). Maximum Mike wins 64.2% overall. This doesn't *seem* unfair.... But if we change our scenario slightly to include chips that transfer from loser to winner, and an overal win objective of getting all the chips, then barring a small number of chips and a bad run of luck, Maximum Mike will almost always win (if the number of chips exceeds 10, Mike will win well over 90% of the time). If all four roll simulataneously, Special Ed will win less than 10% of the time, and Maximum Mike more than 35% (and Mike's victory in the chips version becomes even more assured).

In actual games, over a significant length of time, players skill among the population stops being distributed along a bell curve. The bottom end of the curve drops out (literally, players who lose more than they win quit after shorter periods of time). As they do so, the remaining players from the bottom half the curve have increasingly poor peformance and themselves drop out, in an accelerating feedback pattern. So very small changes in overall performance can make very big differences in overall result, depending on how the contests are set up. The question becomes: How much of a factor is personal skill, how wide is the distribution in performance? The more of a factor the personal skill of the player is, the faster the dropout rate.

The conclusion we can draw from this is that there are sound psychological and mathematical reasons for the de-emphasis of personal skill in these games, and any efforts to build MMO's around personal-skill based gameplay need to account for these.

However, it is impossible to completely remove personal skill from these games, and there is an inherent risk of acclerating the dropout rate through reflexive game adjustments. Let's say, for example, that we decide that Maximum Mike's 10/16 success rate in the PvE scenario is too high, and to slow him down we change the "win" threshold to 7. Now Special Ed "wins" only 1 in 16, Average Joe and Jim 3 in 16, and Maximum Mike still wins 6 in 16. The risk of "locking out" the less effective player while trying to slow down the extreme performer is a real one.

[ <— #16: What a Difference a Year Makes | #18: Sympathetic Fallacies —> ]

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