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- This document explains how leaderboard points are calculated in the Metroid Prime Series Speedrun Rankings spreadsheet, which can be found here: https://docs.google.com/spreadsheets/d/18mZo_0cBX1X3Wf2zYB6g1B6wsFqISNL3UD9W9qPTwHQ
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- Maximum points for each category
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- Each category has a maximum number of points that can be achieved in it. This maximum is earned by holding the world record.
- The number of points assigned to the WR is different for each category of each game. The formula for the number of points assigned to the WR for a category is as follows:
- WR_Points = C * WF * sqrt(num_runs)
- where "num_runs" is the number of speedruns that have been done of the category, "WF" is a somewhat-arbitrarily defined, category-dependent weighting factor, and C is a constant that only exists so that the total number of points across all games and all categories is 10000. As of the writing of this document, the value of C is about 160.3.
- For example, the WR in Prime Any% single-segment is currently worth 160.3 * 1.0 * sqrt(98) = 1587 points.
- The purpose of the arbitrary weighting factors is that without them, some categories which are not quite so prestigious end up being worth too many points. This is admittedly an inelegant solution to the problem, but no better solutions came to mind.
- See the final section of this document for a list of the weighting factors and maximum points available in each category.
- For a speedrun to "count" for the purposes of adding up the number of speedruns that have been done in a category, the speedrun must be as fast or faster than 2 times the current WR, or 4 times the WR for low%. For example, the current WR in Prime Any% SS is 0:49, so a 1:30 would count as a speedrun for this purpose, but a 2:00 would not. (Players still receive points for speedruns that do not meet this criteria.)
- For a segmented speedrun to "count" in the above description, the speedrun must be faster than the player's best SS completion. For example, if a player's fastest Prime Any% time is 1:00, and that run was SS, then the segmented run would not count towards the total number of segmented runs for that category. (They would still receive leaderboard points for their segmented 1:00.) If the player's best SS time is 1:00 and their best segmented time is 0:55, then the segmented run would count.
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- Points for non-WR speedruns
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- Speedruns that are not the WR are worth fewer points than WR speedruns. (Naturally.) The number of points a speedrun is worth is an exponentially decaying function. The formula is as follows:
- Points = WR_Points * exp(-lambda * (Time/WR_Time - 1))
- where "WR_Points" is the number of points assigned to the WR, "Time" is the player's time, "WR_Time" is the WR time, and "lambda" is the decay constant. For Any% and 100% categories, lambda = 6, while for Low% categories, lambda = 3. For example, for Prime 1 Any% SS, the number of points for the WR is 1587, and the WR time is 0:49. A player with a time of 1:08 would receive 1587 * exp(-6 * (68/49 - 1)) = 155 points.
- A side effect of this formula is that if someone improves their own WR, they do not gain any points. Rather, everyone else who has completed a run of that category loses points instead, as their runs are now further away from the WR.
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- Low% completion points
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- A small number of points are assigned simply for completing various low% categories. There are 4 modes that provide points for low% completion: Prime 21%, Echoes 6%, Echoes 4%, and Corruption 15%. The total number of points available for each completion mode is equal to the average number of points available for all the regular speedrun categories for all 3 games (450 as of the writing of this document) times a weighting factor. Prime 21%, Echoes 6%, and Corruption 15% have four categories that each award 1/4 of the maximum possible points: simple completion, hard mode, SS, and hard SS (hypermode instead of hard mode for 15%). Echoes 4% only has simple completion and SS.
- For example, a player that has completed Prime 21% on hard mode and also has an SS completion and thus has completed 3 of the 4 categories for Prime 21% would receive 3/4 of the maximum possible points for the Prime 21% Completion category. This would be worth 450 * 3/4 = 338 points.
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- Miscellaneous notes
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- If a player has completed an SS run of a category but not a segmented run, they will be assigned points for the segmented category as if they had completed a segmented run with the same time as their SS run. This is because players do not gain any advantages by neglecting to split their run into segments, and there is precedent in the speedrunning community for faster SS runs superseding slower segmented runs.
- If a player has completed 100% or Low% in a game but not Any%, they will still be assigned points for Any% based on their fastest 100% or Low% time. This is because there is no restriction in the Any% category that players are not allowed to obtain the maximum or minimum possible number of items.
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- Speedrun categories
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- The number of points assigned to the WR for each category as of the writing of this document are shown here.
- +----+---------------------------+----------+--------+------------+--------------+
- | ID | Category | Num_Runs | Weight | Max_Points | World_Record |
- +----+---------------------------+----------+--------+------------+--------------+
- | 1 | Prime Any% SS | 98 | 1.0 | 1587 | 0:49 |
- | 2 | Prime Any% Segmented | 31 | 1.0 | 892 | 0:49 |
- | 3 | Prime 100% SS | 56 | 1.0 | 1199 | 1:10 |
- | 4 | Prime 100% Segmented | 18 | 1.0 | 680 | 1:10 |
- | 5 | Prime 21% SS | 9 | 1.0 | 481 | 1:43 |
- | 6 | Prime 21% Segmented | 13 | 1.0 | 578 | 1:33 |
- | 7 | Prime 21% Completion | | 1.0 | 450 | |
- | 8 | Echoes Any% SS | 25 | 1.0 | 801 | 0:53 |
- | 9 | Echoes Any% Segmented | 5 | 1.0 | 358 | 0:53 |
- | 10 | Echoes 100% SS | 11 | 1.0 | 532 | 1:49 |
- | 11 | Echoes 100% Segmented | 6 | 1.0 | 393 | 1:49 |
- | 12 | Echoes 6% SS | 5 | 0.8 | 287 | 1:16 |
- | 13 | Echoes 6% Segmented | 5 | 0.8 | 287 | 1:16 |
- | 14 | Echoes 6% Completion | | 0.6 | 270 | |
- | 15 | Echoes 4% SS | 3 | 0.4 | 111 | 4:43 |
- | 16 | Echoes 4% Segmented | 2 | 0.4 | 91 | 4:43 |
- | 17 | Echoes 4% Completion | | 0.3 | 135 | |
- | 19 | Corruption Any% SS | 8 | 0.5 | 227 | 1:46 |
- | 20 | Corruption Any% Segmented | 3 | 0.5 | 139 | 1:46 |
- | 21 | Corruption 100% SS | 7 | 0.5 | 212 | 2:42 |
- | 22 | Corruption 100% Segmented | 0 | 0.5 | 0 | 2:42 |
- | 23 | Corruption 15% SS | 1 | 0.4 | 64 | 3:15 |
- | 24 | Corruption 15% Segmented | 2 | 0.4 | 91 | 3:15 |
- | 25 | Corruption 15% Completion | | 0.3 | 135 | |
- +----+---------------------------+----------+--------+------------+--------------+
- | | Prime Total | | | 5868 | |
- | | Echoes Total | | | 3265 | |
- | | Corruption Total | | | 867 | |
- +----+---------------------------+----------+--------+------------+--------------+
- | | Total | | | 10000 | |
- +----+---------------------------+----------+--------+------------+--------------+
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