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OK, so you've submitted a solution to the FMC. What happens next? On results day, each FMC competitor is assigned a ranking, and rating, and a colour. But what do they all mean? On this page I attempt to clear up any confusion: |
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When you press Send it, the data in the FMC form is sent directly to me. I check the solution with Werner Randelshofer's RubikPlayer first to see that it does actually solve the scrambled cube, and second to try and identify any possible computer cheating. At the end of the week, I collect together all the entries and make a results page!
How are the FMC competitors ranked?
Solutions submitted to the FMC are judged on three "metrics". A consequence of this is that every week there are three 1st places up for grabs. A metric is a set of rules used to count the number of moves within a players solution. In the FMC, these three metrics are:
| Metric | Explanation |
| Half Turn Metric (HTM) | Half turns and Quarter turns both count as 1, and slice moves count as 2. eg R U D2 M = 1+1+1+2 = 5 moves |
| Quarter Turn Metric (QTM) | The number of quarter turns in your solution, with slice moves counting as 2. eg R U D2 M = 1+1+(2x1)+2 = 6 moves |
| Slice Turn Metric (STM) | The same as Half Turn Metric, but slice moves count as 1. eg R U D2 M = 1+1+1+1 = 4 moves |
On the FMC results pages, the order in which the competitors are placed in the ranking table is according to HTM rank. This is simply because it is the most common metric, and the metric used right at the very beginning of the FMC. So whilst a competitor may appear at the bottom of the table, it is still quite possible that he/she has achieved a first place in either STM or QTM. The other metrics, STM and QTM, were introduced later on; move counts and rankings for STM and QTM are surrounded by {} and [] respectively.
What do the different colours in each row of the results table mean?
The different colours used on the FMC results page are from an idea suggested to me by Chris Hardwick of speedcubing.com. If you take some time to browse through the FMC archives, you will see that there are quite a few "FMC Masters", and a lot of the solutions they post would be impossible to beat for someone who is taking part in the FMC for the first time, or who does not have much experience with fewest moves solving. The different colours represent the different goals that competitors can aim for when taking part in the FMC.
| Colour | Explanation |
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To achieve an expert, you need to find a solution to the scrambled cube of 27 moves or less (HTM). |
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To achieve an advanced, you need to find a solution to the scrambled cube between 28 moves and 39 moves inclusively (HTM). |
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To achieve an intermediate, you need to find a solution to the scrambled cube between 40 moves and 51 moves inclusively (HTM). |
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To achieve a beginner, you simply need to post a correct solution! (52+ moves HTM) |
So, if you've never taken part in the FMC before, or you don't submit your solutions because you feel that you have no chance of winning, say to yourself: "ok I really want to achieve an advanced solution this week", and Go For It! I love to have new participants every week :)
How do you calculate a competitors rating Dan?
The idea of a ratings system was proposed to me by Leonid Popov, a maths professor from Russia, who competes in the FMC. He likened cubing to chess, where speedcubing is the less common "blitz chess", and fewest moves solving is likened to the more classical form of the game. There are definitely distinct similarities.
A player's rating is based on the 6 previous FMC's that he/she has taken part in. It is unreasonable to expect a competitor to take part in every challenge to avoid being penalized for not entering one week, so challenges missed are not a factor in the rating calculation. But, to avoid a player not entering because they cannot find a good solution, I would urge everybody who makes an effort to find a solution, to post it that same week. Some code of honour is required here! Other factors in the calculation are the players ranking, and their move count. The formula used takes the form:
The 6 terms (kmi/Ni) represent the results for the previous 6 FMC's the competitor took part in. kmi reprsents the sports bonus awarded to each competitor each week, and is based on the HTM rank a competitor achieves for that week. kmi is calculated using the tangential law, where kmi = 1 + 0.25*tan(x) and x is related to the rank by the following table:
| HTM Rank | 1. | 2. | 3. | 4. | 5. | 6. | 7+. |
| xº | 45 | 37.5 | 30 | 22.5 | 15 | 7.5 | 0 |
| Sports Bonus (kmi) | 1.25 | 1.1918 | 1.1445 | 1.1036 | 1.067 | 1.0329 | 1 |
Ni is the move count (in HTM) for the particular FMC in which the sports bonus kmi was achieved.
n is the number of challenges for which I have data... in most cases n = 6, but in some cases where n < 6 I have to set some terms to 0, and calculate a provisional rating for that competitor.
The quantity of 16000 is calculated by the formula 1000*N0 where 1000 is the "significant coefficient" and N0 is derived from:
Leonid Popov explains all the detail behind this in a document he sent to me, this document is available here.
Notes
I hope this page clears up some of the confusion about how the FMC works! As always, it is a pleasure to organise and it is really great to have all of your solutions coming in every week!
Yahoo! Fewest Moves Challenge discussion group
- DanH -