Lessons from the Ladder: On Rank Decay

At present, the rewards for climbing the Arena ladder to mythic are not very significant. However, the prize for staying within the top 1000 of mythic-ranked players is: a shot at one of 16 spots to play at a Mythic Championship (formerly known as the Pro Tour). Perhaps correspondingly so, reaching mythic rank is also not as difficult as trying to remain in the top 1000. It is very doable to climb to mythic playing just until one finishes the daily quests a day, and it gets easier after you’ve hit mythic the first time since then you start on platinum 4. However, staying in the top 1000 is quite a challenge. For one, the level of competition on the mythic rank ladder is higher than that in any other event on Arena. A player who consistently does 4 wins on average in constructed events, for example, cannot expect to stay in the top 1000 at the same level of performance. Another important aspect, which is the focus of this article, is rank decay. After you reach a rank on the ladder, your rank will change as time passes while you are not playing. Rank may increase (improve) within this timeframe but will inevitably decrease (worsen). The topic of this article is a presentation of anecdotal analysis of my rank decay in season 2 of WAR which I started monitoring 20 days before the end of the season.


Why do this?

As we all know, one of the biggest aspects of MTG: Arena is time. WotC has generously shared a FTP version of the greatest game ever and all we need to do to get ahead in it in terms of building our collection is to play. However, we also all know that time is a precious commodity (perhaps the most precious commodity). We all have better things to do than spend hours a day trying to stay on the top 1000 of the ladder. In fact, even playing constructed events instead is a better use of one’s time since you can at least farm gold and cards there.


Ranks on the ladder: Brief Explanation

Thus, the question is, how high up the ladder should one be X days before the end of the season for one to be able to safely sit out the remainder of the season? The short answer to this question is that it varies. Rank on the ladder follows a Glicko system. This means that ranks are computed for everyone in the system at a regular time interval. At the end of each interval, everyone in the system is reranked based on a formula, which explains why sometimes your rank can go up without you playing. 


For simplicity, imagine that there are only 4 players on the ladder. If none of them play, then their ranks will remain as they are. If the 4^th guy plays the 1^st guy and wins, then the 4^th guy moves up a rank (maybe becoming 3^rd) and the 1^st guy moves down (maybe becoming 2^nd). This impacts the other two players who did not play as the previously 3^rd ranked player can now be bumped down to 4^th while the 2^nd ranked player may now be 1^st ranked. In the actual MTGA setting, there are thousands of players on the mythic ladder. The distribution of these players can be nominally represented by the following figure.

 
The numbers on the figure are just approximations but the general idea is the lower down the pyramid your current rank is, the more sensitive you are to changes brought about by everyone else’s games (those at the bottom of the pyramid). Thus, rank decay can be expected to accelerate with time.



The Setup

I started recording rank decay after hitting rank 78. This was 20 days before the end of WAR Season 2. I initially took measurements once a day. I recorded number of hours since last measurement and rank at measurement. From these inputs, I computed (A) my current rank decay rate (in ranks/hour), (B) the critical rank decay rate (the rate at which I would get knocked out of the top 1000), (C) the average acceleration between the current and previous recorded measurements, and (D) the time it would take for my current rate to reach the critical rate at the measured acceleration. Each of these quantities provide insight on whether or not I can still make top 1000 without playing another game. Specifically:


If A becomes greater than or equal to B consistently, then I will not make top 1000 without playing.


If D is considerably less than the remaining time before the season ends, then I may not make top 1000 without playing.


I then made my decision to play based on these inputs. Every time I played and got my rank back down, everything is reset.


Results

The following chart shows the results of my run. Each time the line is broken, it means I played until I got to a better rank than my previous one.

As shown from the chart, the decay from day 0 to day 11 is about linear. That is, my rank was dropping at a constant rate of about 1.5 ranks per hour. At this constant rate, I was well within target and can expect to finish at rank 700. However, decay started accelerating after day 11, reaching well over critical rate by day 14. I was already at rank 704 by this time. I decided to play and stopped after getting to 559. However, observation of decay from this point showed that I will still not make it, and so I played again. This pattern continued, leading me to play again on days 15, 16, and 18, each time just playing enough to get back to 400+ rank. At the end of the 18^th day, with 48 hours left, I felt safe at rank 458. The data showed that I was well within the goal (I was taking measurements more frequently now). It was not until around 2 hours before the end of the season when I saw that the decay was going to accelerate so much that my position was not secured. I decided to play and luckily won the match (I piloted Gruul and got matched against a Mono U tempo deck that splashed black for some reason). That win got me from 894 to 642. My last measurement was taken 45 minutes before the end of the season, at which point I was at rank 707 and confident that I would make the goal.

What can be learned from this anecdote?
As expected, rank decay was much faster as one entered the 800+ levels. I started at rank 78 but at 20 days before end of season. I think that if this was at 7 days before the end of the season, rank 78 would be more than enough to carry one to top 1000.

Rank decay also accelerates considerably on the last 24 hours of the season compared to any other time period in my observation. My rank was decaying at less than 10 ranks an hour 48 hours before end but this shifted to about 30 ranks per hour on the last 24 hours, with measurements taken from roughly the same (400+) starting rank. This makes sense since a lot of players are trying to get into top 1000 in this timeframe.

Overall, it is definitely possible to play ranked constructed in MTGA efficiently. That is, playing the minimum number of games to make it to top 1000. If my experience of rank decay this season will remain constant for the next season, then reaching top 100 within the last 7 or so days ought to be enough. There are many factors that can change this though, like a significant influx of competitive players on the ladder this season.

May the shuffler be with you.

P.S. Below is a link to the spreadsheet that I used in case anyone wants to use it themselves. Enter data only in the yellow colored cells. I'd appreciate it if you can send me a copy of the file with the data on your experience so that I can aggregate the data and present a better analysis of what rank decay looks like for players in general.

https://drive.google.com/open?id=1k9iPav68uutVjJLjjSOSL6PL5hjUov9F