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This post references the recent Dev article "Quick Gameplay Thoughts 12/3: Event Mission Points" and the most recent Worlds 2021 Event Pass and missions.
TL;DR: scroll down to results table and conclusions.
The purpose of this post is to compare the current and new progression systems only for ARAM and SR game modes. Unfortunately, I do not have any experience/data for alternative farming methods such as TFT or Co-op vs AI. I am also not very good at maths so this is fairly basic simulation and analysis.
The dev article states that the goals of the changes are to normalize the progression across game modes and to reduce the progression variance between games. To achieve these goals, the progression mechanics that until now reward games played will instead reward time played. The conversion of games to game time is 30 minutes PvP Summoner's Rift per game.
All new missions earn points at a rate of 4 per in-game minute if loss, 6 per in-game minute if win, at same rate for ARAM and SR. For minutes played, I will have numbers for both rounding nearest, e.g. 4.6 min -> 5 min, and also rounding down, e.g. 4.6 min -> 4 min.
The exact changes detailed in the dev post are:
- Weekly Missions: (Old) 40 points, 5 per win, 2 per loss -> (New) 1650 points
- Orb Missions: (Old) 30 games -> (New) 4500 points
- Token Earning Rate: (Old) SR 10 win 5 loss, ARAM 6 win 3 loss -> (New) 400 points = 20 tokens
I simulated the average amount of games required to complete the three mission types above in the old and new systems.
I am simulating win rate with a random function in [0, 1) with [0, wr) = win, [wr, 1) = loss. For this analysis, I am testing wr = 0.5 and 0.55, i.e. 50% and 55% win rates.
For game time, I am using an average game time of 30 minutes for Summoner's Rift, 20 minutes for ARAM. The game times are uniformly distributed by a random inclusive integer function in [0.5 * avg * 60, 1.5 * avg * 60] for a random game time in seconds, then converted to minutes and rounded. This means for Summoner's Rift games the game time is [15, 45] minutes 30 average, and for ARAM games the game time is [10, 30] minutes 20 average. The distribution and range of game times are both assumptions. I do not know the distribution of game times and that would factor into the average games required per mission since the points system wastes excess points. I am also not smart enough to foresee how much this limitation matters for my results.
All points based missions in League of Legends thus far do not bank excess points. For example, if you are at 39/40 points for a weekly mission, you will either waste 1 or 4 points to complete it, by getting 2 points for a loss or 5 points for a win. I am assuming that the new system works in the same way.
To simulate completing an old 40 points weekly mission, I have a function that returns the number of games it takes to reach 40 or more points, adding 2 points + 3 points for a win per game.
To simulate the new points per game-time missions, I have a function that generates a game length as described above, then multiplies that with the point rates for a randomly generated win or loss, sums the points earned, and this process loops until the total points are at least the amount required for the mission.
For the new tokens mission, it is completing a 400 points mission as above to get the average number of games required for the mission, then 20 divided by that number to get the expected value of tokens per game.
All results are averages of 25 000 000 simulations each. I guessed how many significant digits to leave. It is not mathematically perfect results due to pseudo-random noise but close.
Results
| Mission type | 50% wr, time rounded nearest | 50% wr, time rounded down | 55% wr, time rounded nearest | 55% wr, time roundeded down |
|---|---|---|---|---|
| Old Weekly | 11.8740 games | 11.8744 games | 11.4027 games | 11.4024 games |
| New Weekly SR | 11.5537 games | 11.7410 games | 11.3372 games | 11.5211 games |
| New Weekly ARAM | 17.0464 games | 17.4710 games | 16.7225 games | 17.1383 games |
| Old Orb | 30 games | 30 games | 30 games | 30 games |
| New Orb SR | 30.5485 games | 31.0584 games | 29.9595 games | 30.4583 games |
| New Orb ARAM | 45.5349 games | 46.6893 games | 44.6517 games | 45.7830 games |
| Old Token Expected SR | 7.5012 tokens | 7.5006 tokens | 7.7506 tokens | 7.7510 tokens |
| New Token Expected SR | 6.2062 tokens | 6.1176 tokens | 6.3096 tokens | 6.2201 tokens |
| Old Token Expected ARAM | 4.4998 tokens | 4.5002 tokens | 4.6504 tokens | 4.6500 tokens |
| New Token Expected ARAM | 4.3945 tokens | 4.2959 tokens | 4.4724 tokens | 4.3724 tokens |
Note that 55% win rate could be unrealistic and is here for interest only.
The main conclusions from these results are
- ARAM mission progress nerfed significantly as intended
- Token earning rates nerfed, significantly for SR, but not mentioned in dev post
- Progress could be nerfed slightly more if game time counted rounding down
- Weekly Mission will be faster for SR only players
Also, not part of my analysis, but I believe it is true that as devs stated, there will be less pain from long losses. However, also less satisfaction from quick wins.
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