Statistics help required

[Phil E]

Could do with a little help if anyone is into statistics?

We have a trophy for the club that looks after referees the best each season.
Every game is marked out of 4, under ten headings.
i.e. Welcome and post match hospitality, marked 1 to 4
Changing room and shower facilities, 1-4, etc

To work out the winner I have been adding the scores for each game (so minimum 10, maximum 40 points per game.
I have then been working out the average score based on the number of games. So total number of points divided by the number of games.

This is because some clubs have a lot of teams and others only have 1, so the number of games can differ widely, which would otherwise give the big clubs an unfair advantage.

However this method has its drawback. For instance a club might have 1 game in a season which happened to score very high, and thus their average is only based on 1 game.

Is there a better way of working this out?
Thanks in advance.

 

[didds]

have a minimum number of games for "qualification" ?

Your dilemma is the standard cricket averages one whereby one player plays one game and scores 120 and takes 8 wickets, with 6 catches.
and ends up top of all the club's tables for the season. Whereas somebody else played 20 matches ...

 

[didds]

Otherwise you are going to need to come up with some sort of "weighting" application - and that's open to a huge conjecture as to how that could work?

 

[Phil E]

So am I best sticking to the way I am doing it now and throwing out any clubs with less than a certain number of games, maybe 2?

Or do I throw out the highest and lowest scores for each club, like they do in scoring ice skating?

 

[didds]

thats basically your call

try it both ways and see if that alters the results. Or you may favour one result over another so go with that one ;-)

 

[tim White]

You would need a meaningful number of games at a club; say a minimum of ten? You would also need a spread of different referees so one individual does not distort the results by being to generous, or too mean, or too regular so they get treated differently.

Rule one; YOU make the rules! set a benchmark for each category and trial it, then adjust you benchmarks and try again to see if it drastically changes the outcome.

 

[SimonSmith]

Minimum number of games as a qualifying threshold.

Take the total number of games, and then divide by the average number of teams for that club across the season.

So, you get the total score, and then divide by the number of opportunities that the club had to 'score'.

 

[Dickie E]

Minimum number of games as a qualifying threshold.

the issue there is that you might have a club that doesn't host many games but does a bang up job of looking after the refs.

You're trying to apply an objective outcome to what is very much a subjective matter so there will always be difficulties. Like trying to objectively & arithmetically decide who the most beautiful woman in the world is.

There would be a consideration, too, in my area as some government bodies throw a lot of money at some clubs (esp. those developing female and/or multicultural programs) while others do not.

Might be just as easy to ask the refs, post-season, which was their preferred club to ref at. That way, each ref attaches their own mental ranking of what was important & valuable to them.

We do something similar in a reverse way here where the clubs are asked to vote on who is their preferred ref from the previous season. It's a gut feel & subjective ranking and doesn't ask the clubs to rate refs 1 - 4 on law knowledge, fitness, empathy, presentation, etc

 

[crossref]

discard all the scores and give the award to the club that offers the bottomless pint glass
if more than one club, rotate each season

 

[didds]

discard all the scores and give the award to the club that offers the bottomless pint glass
if more than one club, rotate each season

we have a winning solution

 

[chbg]

discard all the scores and give the award to the club that offers the bottomless pint glass
if more than one club, rotate each season

From a referee that cycles/uses public transport to matches?

 

[Volun-selected]

Possible idea - work out the median scores from last season from all teams that played say 10 matches or more.

What you then do is say teams start with 5 matches with that median score in the bank as a start point. Each real match knocks off one of these filler scores with a real score.

eg - say the average score last season was 22 points (based on teams with 10 scored matches)

One team plays say 3 matches and get 21, 28, 30 you’d then keep 2 fillers of 22 so their mean would be average of 21+28+30+22+22 = 123/5 = 24.6

A team plays one match and score 34, you’d use 34 + 4*22 = 122/5 = 24.4

Once they play more than 5 matches it’s back to just real data and sum of all scores/matches played.

I say median as sometimes mean gets distorted if you have a really good/bad club but you can use mean if you prefer, and 10 was just a number I guessed so you change that based on what seems reasonable based on the real data you have.

 

[Harry]

One very simple method is to take each club's highest and lowest scores and add them together. If a team had only one game double it's score for that match.

 

[Ciaran Trainor]

From a referee that cycles/uses public transport to matches?

Works for me, I try to do mine on the train