Warning: If you do not play in sanctioned tournaments, or do not have a DCI rating, this article is entirely useless to you, except at a theoretical level.
Intro
So, what do you know about your DCI rating? Well, if you play in sanctioned tournaments and don’t even know your rating, it can be found on the DCI website (https://webapp.wizards.com/DCIMember/login.asp). If you do know your rating already, what do you know about it? Typical things you might know are that higher is good, and lower is bad. Wins make your rating go up, and losses make it go down. Draws? Well, that depends. But what is a “good” rating? What uses does your rating have? Does a high rating mean you should win all the time? This article attempts to address those questions, and shed a little more light on what your DCI rating might mean to you.
What does it mean, in general?
Let’s start with some facts. Everybody starts at with a rating of 1600. Whenever you win a match, your rating will go up by some amount. When you lose, it will go down. If you draw, your rating will go up when you have a lower rating than you opponent, and down when your rating is higher. When you play someone in a match, your ratings will change by the same amount, but in opposite directions. So, if you gain 3 points, your opponent will lose 3 points. This also means that the average rating of all DCI members will remain at 1600.
In theory, then, 1600 is a great baseline to gauge your skill. If you are below 1600, you are below average, and vice versa. In my experience, though, the following is a rough ratings breakdown. This breakdown is strictly an opinion.
Less than 1500: Terrible
1500-1600: Bad, or at least very new.
1600-1700: Average. Typical of Friday Night Magic.
1700-1800: Slightly above average.
1800-1900: Good. Able to win PTQs.
1900-2000: Very good. Potential Pro Tour caliber.
2000+: Rare Skill. Pro Tour regular.
Using these guidelines, one can tell approximately where they fall in the spectrum of tournament goers. However, as I will discuss, your rating at any one point in time does not necessarily represent your level of play skill. If you play in a lot of events, though, and your rating is fairly consistent, then probably it is a fair match.
What Good is a Rating?
Other than knowing where you stand compared to other players, rating has a couple of very tangible uses. First, if your rating is high enough, you will be invited to play on the Pro Tour. Typically, for this to happen, your rating must be very high. In the high 1900s and even above 2000 is not an unreasonable expectation. If you manage to reach such a high rating, though, you can take comfort that it will not fall unless you lose matches. Ratings will not diminish over time.
The second tangible use for your rating is when you play in a Grand Prix. Depending on your rating, you will be awarded a certain number of byes, which in terms of tie-breakers, are even better than match wins. The number of byes granted is a static value:
1800-1899: 1 bye
1900-1999: 2 byes
2000+: 3 Byes
Note: these numbers apply to the United States, but may differ in other regions.
Beyond these two examples, probably the most common way to use your rating is for bragging. Since a higher rating is better, it’s not uncommon to flaunt your higher rating at lesser-ranked players. This can be used to intimidate your opponents as well. While not very sportsman-like, this can be an effective tactic. In my area there is a single player with an enormous composite rating. Without even bringing it up, his opponents know this, and feel resigned to lose the match before it even begins. Personally, I look forward to playing opponents with higher ratings, since I view it as an opportunity, as opposed to a death sentence.
Win Expectation*
So now that we know what your rating is for, let’s look at how to calculate it. An essential component to calculating your rating change is your Win Expectation, or Expected Win Percentage (EPW). Based on the difference between yours and your opponent’s ratings, the DCI calculates how likely it is that you will beat your opponent. This is the formula they use:
Expected Win Percentage = 100 / ( 10 (opponent’s rating – your rating) / 400 + 1)
What does that formula mean? In general, the wider the rating gap, the more often you should beat your opponent. Here are some concrete numbers (Assume for all examples that you are the player with the higher rating).
Rating Difference (points) | Your Expected Win Percentage |
0 | 50% |
50 | 57% |
100 | 64% |
150 | 70% |
200 | 76% |
250 | 81% |
300 | 85% |
350 | 88% |
400 | 91% |
You can see that when playing someone at the same rating as you, you are expected to win exactly half of the time. Ignoring outside factors like deck matchups or the amount of sleep you got, this makes sense. One important thing to note is that while as the rating gap widens, your percentage goes up, but it goes up less and less as the gap grows bigger. In fact, in order to have a 99% chance of beating a given person, you need to have almost 800 more points than them, which is extremely unlikely. Furthermore, your odds will never hit 100%.
Another thing to observe is that playing against a person a couple hundred points lower than you does not mean a free win. They still have a 24% chance of winning the match. Of course, this works both ways. If you have a rating of 1600 and you play against a pro with a rating of 2000, you are still expected to win 1 out of every eleven games you play.
Finally, it is important to understand that your EWP does not care what your rating is, only what it is relative to your opponent. Therefore, a 2000 player will defeat the 1800 player just as frequently as a 1800 player defeats a 1600 player. Consider that the next time an 1800 players wins a PTQ and thinks that he has a reasonable shot at a Pro Tour title.
Calculating Your Rating Change
Once you know your expected win percentage, the only other factor taken into account when calculating your rating change is the “K-value” of the event. The “K-value” of an event is tied to the competition level, so a Friday Night Magic will have the lowest K-value (8K), while higher level events can be as high as 32K. Note that the K-Value of the event represents the maximum number of points that you can potentially win or lose during each round of the event.
You can calculate your rating change using this simple formula:
New Rating = Old Rating + “K-Value” * (Win Value – Expected Win Percentage).
Win Value is just 0 for a loss, .5 for a draw, and 1 for a win. So let’s consider the example of the 1600 player against the 1800 player. With a 200 point gap, the 1800 player is expected to win about 76% of the time, so his rating changes would be as follows (assuming 8K):
Win: +1.92
Draw: -.32
Loss: -6.08
This looks like a pretty poor situation to be in, since you lose more than three times as many points if you lose than you would gain if you win. However, taking into account EWP, you are supposed to win 76% of the time, which balances these numbers out perfectly. That is to say, if you played a large number of games, and won 76% of them, your rating would stay exactly the same in the end.
Other points of interest include:
(1) The points you’d win minus the points you’d lose always add up to the K-value of the event. So if you’d gain 1 point, you’d lose seven.
(2) You will always lose points drawing with someone who has a lower rating than you.
(3) The number of points you win is exactly the same as the number of points your opponent loses, and vice-versa.
(4) Fractions of a point do matter. Even though the DCI reports show only your whole number of points (and rank you as such), they keep a running total of your exact rating.
Reasons Your Rating is Wrong
Since I have started playing sanctioned Magic a few years ago, I have played in exactly 100 events. After an initial spike, my rating has stayed surprisingly consistent. Therefore, my assumption was that my rating is probably accurate, and clearly says where I fit in terms of skill. But was my assumption right? Here are a few examples of why your rating might not really represent you level of skill.
(1) Your rating fluctuates a lot.
Look at your rating over the course of the last year. Has it gone up and down a lot? If it has been steadily going in one direction, it probably means that your rating still hasn’t caught up to your current level of skill. However, if it jumps up and down a lot, then your rating probably isn’t a very good indicator of skill. Good players can do horribly in tournaments and bad players can win them. This will cause ratings to fluctuate. In higher K-value events, this phenomenon is even more pronounced. For example, I rarely play limited games, and my rating sat at 1625 for 1 whole year while I did not play a single limited match. Later, I played in a 16K tournament, and went 4-0 against 1900 rated players. So my rating went up about 50 points in a single day. Is it because I am really good and should be rated much higher? No – swings this large do not well represent my actual play still. In this case I happened to play against the 4 highly rated players at the tournament, while the rest of the players had similarly poor ratings as my own. Through their drafting mistakes, I somehow wound up with a ridiculous deck they crushed my more-talented opposition.
(2) Ratings don’t take the metagame into account.
Even though the DCI says I should only win 1 out 11 games against a player with 400 more points than me, little do they know that I am running my land destruction / Cranial Extraction deck again a Tooth and Nail deck. So despite my poor DCI expected win percentage, I can probably still play poorly and win this match based on the decks we are playing. Your rating can be a measure of how good you are at selecting decks as well as your play ability. From my own experience, when I played Psychatog in Standard, my rating went up and up. When I played non tier-one decks, it came down. Of course, any other number of factors can impact whether you win or lose a match, including testing, luck, etc. So in a way, your rating captures not your level of technical play, but your overall ability to play the game of Magic.
(3) The average skill of the players in your area can dramatically affect your rating.
Consider the extreme example where all the players at your local tournaments have a 1600 rating, because they have just started playing live tournament magic. However, they are good at the game from playing Magic Online, so their play skill is typical of an 1800 player. After this group of players has played against each other for a few dozen tournaments, their ratings would all still be at 1600, despite their skill level. Remember, your rating actually represents your win expectation relative to those around you, not necessarily to the entire magic community.
Although this scenario is extreme, it happens all the time on a smaller scale. For example, in my area, there are many players with a decent amount of skill without a rating to match. Again, their rating is kept down because the overall talent of the players here is reasonably high. Whenever a PTQ comes around close to my area, people from here will typically do well, and increase their ratings. Over time, those ratings increases will be redistributed among the rest of the players here, and our overall rating will go up to the point where it will be on par with what is typically associated with that rating. Of course, there are probably areas where ratings are higher than they should be as well. For example, there are no doubt many ex-pros who still have a top rating, but haven’t been putting in the time to keep up their game. In time, their average rating will also come down to where it should be.
Rating Inflation
Another small point to consider is the concept of rating inflation. The idea behind DCI ratings is that the average remains 1600, no matter what. And since one person wins the same number of points another loses, this would be a fact. However, a person retains their DCI rating long after they have stopped playing the game, or at least playing sanctioned matches. Therefore, the average rating of active players is not necessarily 1600. If players leave the game at equal rates with high ratings and low ratings, then the average could potentially stay the same. I suspect, though, that players who quickly earn low ratings leave the game at a faster pace than those in the upper tiers. Players will either get discouraged and quit, or become better and raise their rating. In both cases, that leaves the group of active players with a minority of its constituents in the sub-1600 range. That means that the average rating is actually above 1600, and that it will continue to grow. So while an 1800 rating may mean you’re a good player today, ten years from now 1800 may be the norm. If anyone has data about the ratings cutoffs required for a Pro Tour invitation over time, that data could be used to support or refute the rating inflation hypothesis.
Parting Thoughts
By this point you should now know what good your rating it, how it’s calculated, and what it might say about you. Rating isn’t everything when it comes to your talent as a tournament player, but is can definitely be a good indicator. Some other great statistics to consider are your overall win percentage, your performance at different types of tournaments, and your success rate against your various opponents.** All of these things together help to paint the picture of where you fit in the competitive magic world.
Until next time, keep your rating high.
~jeff till
[email protected]
* Formulas obtained from http://www.wizards.com/DCI/main.asp?x=MTG_DCI_Ratings_Expl
** A friend and I put together a script that will tell you this information based on your DCI match history. (http://www.potozniak.org/mtg/upload_stats.pl). Note: the DCI authorizes the use of this script only for your own personal use (ie: you cannot look up other people’s data.)