My Math Forum Help on comparing differing sets of data

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 February 26th, 2010, 06:07 PM #1 Newbie   Joined: Feb 2010 Posts: 2 Thanks: 0 Help on comparing differing sets of data Hi guys, I'm hoping you can help me figure something out. I'm running a video game website, and on this website we have a scoreboard that tracks scores that players submit, ranking them from best to worst. It currently tracks two different types of events - racing (time submissions like 2:03.22) and tricking events (score submissions like 3,227,896). The scoreboard then ranks them from best to worst accordingly - highest score on top, lowest time on top. None of this is surprising I'm sure. But now we come to my hangup, and that's why I'm asking for some advice from people who know about mathematical terminology and formulas. I'm trying to build a "ranking system" that lists who are the best players based on certain criteria. For example, who is the best racer or likewise, and who is the best overall across many different tables of scores. One of the things I'd like to do is weight the scores to an independent figure, say something like 1000. For score submissions, that's easy, you simply divide the score submitted by the highest score: say the score is 100,000, and the top score is 125,000 this makes the formula (100,000 / 125,000) * 10000 = 800. So the top score would have an integer of 1000, the scores below would all be below that. Easy, right? Now here's the kicker: how do you do this for TIMED rankings since the fastest time is the best? For example, if Bob has a time of 1:00 and Tom has a time of 1:05, what's the mathematical formula to equate these scores so that Bob's score ranks to 1000 and Tom's score is some figure below that? 1. Bob: 1:00 --- 1000 2. Tom: 1:05 --- 995 (or whatever the formula says it is) I KNOW this is not that hard, but I can't wrap my head around it, nor can I find a formula online that tells me how to do this. Can you think of anything off the top of your head?
 February 26th, 2010, 06:24 PM #2 Senior Member   Joined: May 2008 From: York, UK Posts: 1,300 Thanks: 0 Re: Help on comparing differing sets of data You could use something like $1000-k(t-t_b),$ where $t$ is the time in seconds, $t_b$ is the best time and $k$ is a scaling factor. This formula would basically take $k$ points off for each second past the best time. This has the disadvantage that if $k(t-t_b)$ is greater than 1000, you get a negative point score - you could just let it be zero in this case, or if you wanted a non-zero score for any time you could use something like $1000\alpha^{t-t_b},\ 0\,<\,\alpha\,<\,1$ which reduces the score by a factor of $\alpha$ for each second past the best time - e.g. for $\alpha=0.99,\ t_b=60,$ t --- Score 60 | 1000 65 | 951 70 | 904 75 | 860 120 | 547 180 | 299
 March 1st, 2010, 05:49 PM #3 Newbie   Joined: Feb 2010 Posts: 2 Thanks: 0 Re: Help on comparing differing sets of data Yes, that seems like it might do the trick. Thank you! The only concern I see is that there are many different levels of "time ceilings" we could use on these tracks - some tracks take 5 minutes, other tracks take 30 minutes. We would want a spread of scores on the same curve as those that the score events have, to be sure that there is an equivalent relationship between the two events.

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