B Here's a Statistics problem for game of Polo (or Hockey if you like)

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A hypothesis suggests that a strongly-knit team wins more often than a less-knit one, measured by the standard deviation (SD) of player handicaps. However, findings indicate that teams with a higher SD, representing less-knit compositions, tend to win more frequently. For example, a team with handicaps of -2, 0, 2, and 4 (SD = 2.2) outperforms a more balanced team with handicaps of 2, 2, 3, and 3 (SD = 0.5). This suggests that the presence of a standout player may be a critical factor in a team's success. Further analysis of outliers in winning teams could provide additional insights into success factors.
wirefree
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TL;DR
Trying to find the characteristics of the winning team in terms of stan. devi. of their team's abilities.
Namaste & G'day

Postulate: A strongly-knit team wins on average over a less knit one

Fundamentals:
- Two teams face off with 4 players each
- A polo team consists of players that each have assigned to them a measure of their ability (called a "Handicap" - 10 is highest, -2 lowest)

I attempted to measure close-knitness of a team in terms of standard deviation (SD) of handicaps of the players.

Failure: It turns out that, more often than, a team with a higher SD wins. In my language, that means a less knit team. So, it turns out that a team with handicaps -2,0,2,4 (one really good player, one very poor player; (SD = 2.2) wins more often than a team with average handicaps, say, 2,2,3,3 (SD = 0.5)

I need your help.

How would you go about determining success factors?
What other combination of SD and/or handicaps would you recommend?

Some other combinations me, a statistics novice, tried without success:
- SD*(max of team's handicaps - min of team's handicaps)
- SD/(max of team's handicaps - min of team's handicaps)
- SD*(max of team's handicaps)
- SD/(max of team's handicaps)

Regards
wirefree
 
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wirefree said:
Failure: It turns out that, more often than, a team with a higher SD wins. In my language, that means a less knit team. So, it turns out that a team with handicaps -2,0,2,4 (one really good player, one very poor player; (SD = 2.2) wins more often than a team with average handicaps, say, 2,2,3,3 (SD = 0.5)
So it seems as though your hypothesis may be wrong. Perhaps the success of a team tends to depend on having a superstar player whose handicap increases the SD.
 
FactChecker said:
Perhaps the success of a team tends to depend on having a superstar player whose handicap increases the SD.
Thanks for your thoughts. I really appreciate it.
 
You can look to see if outliers are present in the winning teams.
 

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