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

[wirefree]

TL;DR Summary

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

 

[FactChecker]

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.