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

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Discussion Overview

The discussion revolves around the relationship between team composition, specifically player handicaps, and the success of polo (or hockey) teams. Participants explore statistical measures, particularly standard deviation (SD) of player handicaps, to determine factors contributing to team success.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant postulates that a strongly-knit team wins on average over a less knit one, using standard deviation of handicaps as a measure of knitness.
  • Another participant suggests that a higher standard deviation may correlate with team success, indicating that teams with a wider range of player abilities (higher SD) might perform better.
  • A hypothesis is proposed that the presence of a "superstar" player could be a significant factor in a team's success, as their higher handicap could increase the team's overall SD.
  • There is a suggestion to investigate the presence of outliers in winning teams to further understand the dynamics of team success.

Areas of Agreement / Disagreement

Participants express differing views on the relationship between standard deviation of handicaps and team success, with some suggesting that higher SD correlates with better performance, while others question the initial hypothesis about team knitness. The discussion remains unresolved regarding the definitive factors contributing to team success.

Contextual Notes

Participants have not reached a consensus on the effectiveness of using standard deviation as a measure of team success, and there are unresolved assumptions about the impact of player handicaps and the definition of a "strongly-knit" team.

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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