Placement in Rankings Math

[Talamare]

I want to start by apologizing if this was posted on the wrong sub forum, I tried to be as accurate as possible since I wasn't sure what category this would fall under.

I'm basically trying to design a game in which 2 players add their placement together to determine a final team score. There are 10 possible positions, and no 2 players can have the same position. 1st, 2nd, 3rd, etc.

Now the catch is, I find it important that no 2 scores can be same. So 1st + 5th, can't equal any other combination of scores like 2nd + 6th or whatever.
As well as it's also important that to truly lock the higher scores, both players must do relatively well. So a team who gets 2nd and 3rd will beat someone who gets 1st and 4th.
Of course this second rule will get blurrier and harder to determine in the lower rankings, but that's fine.

I have considered using some existing models, like the Formula 1 Racing model. Tho personally felt it really pushed towards a single racer doing well, and the 2nd one being whatever...

As far as the work I have been doing to discover my answer mainly has consisted of plugging in essentially random array of numbers into an excel sheet. Literally Trial and Error for several hours to mostly unsatisfactory results

If trial and error, is the best way to go about this. I will happily keep trying random combinations hoping to discover the grail. Tho, I was curious to know if there is some sort of improved method to the madness.

 

[Ishuda]

I want to start by apologizing if this was posted on the wrong sub forum, I tried to be as accurate as possible since I wasn't sure what category this would fall under.

I'm basically trying to design a game in which 2 players add their placement together to determine a final team score. There are 10 possible positions, and no 2 players can have the same position. 1st, 2nd, 3rd, etc.

Now the catch is, I find it important that no 2 scores can be same. So 1st + 5th, can't equal any other combination of scores like 2nd + 6th or whatever.
As well as it's also important that to truly lock the higher scores, both players must do relatively well. So a team who gets 2nd and 3rd will beat someone who gets 1st and 4th.
Of course this second rule will get blurrier and harder to determine in the lower rankings, but that's fine.

I have considered using some existing models, like the Formula 1 Racing model. Tho personally felt it really pushed towards a single racer doing well, and the 2nd one being whatever...

As far as the work I have been doing to discover my answer mainly has consisted of plugging in essentially random array of numbers into an excel sheet. Literally Trial and Error for several hours to mostly unsatisfactory results

If trial and error, is the best way to go about this. I will happily keep trying random combinations hoping to discover the grail. Tho, I was curious to know if there is some sort of improved method to the madness.

Just some rambling Is there an underlying score which might be used? Take that Team A, A1=1st & A2=3rd, and Team B, B1=2nd & B2=4th example of yours. If the event were bicycle racing, then the underlying score would be time and best combined time [of first n riders in team] would win. If you wanted the definitive Team B won in this situation, it could be modified slightly by just using a 'penalty time' of for example, 2, 4, and 8 seconds for 2nd, 3rd, and 4th.

In addition, the number of players on a team (actually the number of significant players such as (generally) the best 5 team member times in bicycling events) will affect the structure. If there are only 2, you might use the 'penalty time' idea and see how a power series does (the 2, , 4, 8, 16, ... may work but there might be a better one).

 

[Talamare]

You know what you're asking...we don't...

Can you make it clearer...like, supply a representative example...

Merci beaucoup.

I apologize, basically each ranking for individual player will have a score. Each 2 man team will add up those score to find a final team rank.
So for example, if 1st place gave 6 points, and 3rd place gave 4 points. The final team score is 10

I'm trying to figure out a point system tho that follows two important rules
1 - No 2 scores added together can equal any other score
2 - The numbers must be relatively close to promote that both players in team do well to insure victory. One of the most important being that if your team finishes 2nd & 3rd, you would win against a team which finished 1st and 4th.

I checked the Formula 1 point ranking system, and I found that it HEAVILY favors finishing first. To the point that as long as you finish first, it nearly doesn't even matter what the other guy does. I have been doing trial and error to find an assortment of numbers, but after trying for several hours couldn't find a satisfactory sequence which is why I was wondering if there was some math magic I'm not aware of that would help with this problem.