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Farsight Studios
The Pinball Arcade / Farsight Studios
(An attempt at) The top 40 TPA players from leaderboard scores
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<blockquote data-quote="vikingerik" data-source="post: 150951" data-attributes="member: 3745"><p>Why do you require this? Is there a mathematical basis, or just doing it that way because you have been? All sorts of functions are easier to work out with a baseline of 0 rather than 1. The difference between 0 or 1 point at the bottom of the board won't mean anything for the total rankings and makes it mathematically cleaner.</p><p></p><p>But anyway, that doesn't really matter. Yeah, what shape to make the curve is a bigger question. I think the log method is naturally emergent from mathematics, while the other non-linear methods are artificially constructed to fit what you/we already decided we wanted the curve to look like. The log method needs no magic-constant besides how deep you want to rank.</p><p></p><p>Thinking about other methods in the real-world for comparison... NASCAR ranks linearly, one point per race position. <a href="http://en.wikipedia.org/wiki/Official_World_Golf_Ranking#Calculation_of_the_rankings" target="_blank">Golf ranks on an arbitrary schedule</a>: "major winners get 100 ranking points. The second place golfer gets 60% of this amount, 40% for 3rd, 30% for 4th, 24% for 5th, down to 14% for 10th, 7% for 20th, 3.5% for 40th to 1.5% for 60th." Tennis does about the same as golf with fixed numbers per event rather than percentages.</p><p></p><p>Hey, how about we use the PAPA ranking method? <a href="http://www.ifpapinball.com/ranking-info" target="_blank">http://www.ifpapinball.com/ranking-info</a> We can treat each table as a tournament of equal value, skipping that whole complicated section about Tournament Value Adjustment. Then the ranking uses the sum of a linear method through the entire population plus a power method for the top 32 players. Interested in that at all?</p></blockquote><p></p>
[QUOTE="vikingerik, post: 150951, member: 3745"] Why do you require this? Is there a mathematical basis, or just doing it that way because you have been? All sorts of functions are easier to work out with a baseline of 0 rather than 1. The difference between 0 or 1 point at the bottom of the board won't mean anything for the total rankings and makes it mathematically cleaner. But anyway, that doesn't really matter. Yeah, what shape to make the curve is a bigger question. I think the log method is naturally emergent from mathematics, while the other non-linear methods are artificially constructed to fit what you/we already decided we wanted the curve to look like. The log method needs no magic-constant besides how deep you want to rank. Thinking about other methods in the real-world for comparison... NASCAR ranks linearly, one point per race position. [URL="http://en.wikipedia.org/wiki/Official_World_Golf_Ranking#Calculation_of_the_rankings"]Golf ranks on an arbitrary schedule[/URL]: "major winners get 100 ranking points. The second place golfer gets 60% of this amount, 40% for 3rd, 30% for 4th, 24% for 5th, down to 14% for 10th, 7% for 20th, 3.5% for 40th to 1.5% for 60th." Tennis does about the same as golf with fixed numbers per event rather than percentages. Hey, how about we use the PAPA ranking method? [url]http://www.ifpapinball.com/ranking-info[/url] We can treat each table as a tournament of equal value, skipping that whole complicated section about Tournament Value Adjustment. Then the ranking uses the sum of a linear method through the entire population plus a power method for the top 32 players. Interested in that at all? [/QUOTE]
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The Pinball Arcade / Farsight Studios
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Farsight Studios
The Pinball Arcade / Farsight Studios
(An attempt at) The top 40 TPA players from leaderboard scores
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