Image 1: Normal deviation
It is somehow difficult to introduce in such a big topic as it is with measurement about something (in our case it is the measurement about skill. Do not try to think too squeezed about skill as you do for example when you rage, rather as a variable that someone has in something).
At the right side you see an image that some of you might know, it’s the normal deviation from Carl-Friedrich Gauß which shows a distribution of subjects that are spreaded across different values (x-axis). The value that those subjects have in a specific variable could be in our case the skill. Let us call the skill variable skill-construct (we call it this way because constructing a value is what every time happens: a system constructs a variable which should describe your skill numerically).
In psychology there is a huge topic which is called diagnostic. This topic does try to find out how you could diagnose a specific “thing” in someone. In our case it’s the skill in something (a specific eSports game) that you want to diagnose. Now you could ask yourself: what has this whole thing to do with skill in eSports? Wasn’t it just the MM and MMR (match making and match making rating) that finds out and descripes how good I am? Well the answer is simple: The MMR is the skill-construct. The match making functions as a diagnostic test (a huge field in psychology which trys to find out how tests should be designed best to get a specific true value).
Excursus: You can philosophise about what the true value really is. Is it an object? What kind of object is it? Do objects exisits? Isn’t all subjective? It’s a question about epistemology. In the case of psychology there is the agreement that we should talk about a construct because we actually construct something with our measurement. So let’s stay with this.
We’ve to think a MMR system like a diagnostic test (called test further on): a test constists of tasks which someone has to do which are then valued and summed up (minus errors) to get a value that is simply called test value. || Example in a MMR system in a moba game: a player (the subject) plays games which can either be won or lost. You’ve done a simple task (the game) correctly if you won. The difficulty of the task is valued by the strengh of your teammates and the strengh of the opponents. The system calculates a value maybe with other variables that are taken into account and sums this up on your test value. || As you can see the test value updates every time you play a game. So the whole MMR system is a test which processes and gets more accurate by time.
Now let’s combine two things: The system gets more accurate by time and you want to get your true skill shown up by a number (or a system which replaces those number but is calculated upon it). To get to the true value – the skill-construct – you have to get something on comparison which can value your skill (example: when you measure the temperature, you have to have a relative thing (in this case the thermometer which values your temperature) that you can actually interpret how warm or cold it is). So what is it in the world of MMR systems? Maybe you’ve already thought it: it’s the normal distribution shown in image 1. You value your skill in comparison relative to all other players in the system. Your skill-construct therefore is relative to who competes and how great people compete and for the nature of MMR systems: how often you win valuably.
You may ask now: how does this normal distribution function? It is a statistic instrument to get done with a phaenomenon which is quite common: people are often distributed in a way, so that it is nice to have an approximation which fits often: the normal distribution. This is as well the case in MMR systems. You compete with each other and most people will surround the mean value (the µ shown in image 1) – means something like “normal good”. The values left and right like 1σ and -1σ are called standard deviation (which is just a replacement of values that are behind it to get the deviation into a standard, so 1σ is 1 standard deviation above the mean value µ). The subjects that are distributed on the 1σ-line are 84.3% above others in a specific value.
At last I will provide you an example: || You are playing a moba game with an MMR system (maybe called ELO system, maybe is devided into devisions, maybe only have ranks and so on). You play for about a month, get 80 wins and 50 losses. Those wins and losses are calculated like I explained above to get your test value. The test value is ranked amongst others in something which is approximately a normal distribution. You can now do statements like “I am better than 78.1% of all people in the game”. But a system can as well put your value on graphical interfaces like devisions: “I am ranked in division 2 out of 6 total”. A system can show you the value in a way whatever it wants. ||
That’s the whole magic how a system can judge your skill. But for the attentional reader: you can’t say that you’re this great or this bad. You can only tell how this system values your true value – your true skill in the game. It can have errors. But more it defines what is considered your true skill. The measurement is what makes your skill. If you have no fingers you won’t be good but could have a huge knowledge about a specific game. Take it into account.