Man of match points not equal per week.

[Chipoca]

I manage a sports team and we run a man of the match award after each game. I have an issue with calculating the winner because I don’t get the same amount of responses each week.

The details.
After each game, each player is suppose to send in an award for the best player, whom gets 3 points, 2nd best player, whom gets 2 points, and third best player, whom gets 1 point. Note, players can also assign 1 point each to 6 players, or 3 players 2 points each. They just need to allocate 6 points per game. Therefore each player (total of 18 players) need to assign 6 points per game, so total of 108 points are available per game. The player at the end of the year who has accumulated the most points wins player of the season.

The problem
They are meant to, but not everyone votes per game, so a player may get an unfair advantage as they accumulated a high amount of points in a game where lots of players voted.

I need to be able to adjust the value of the points awarded by the number votes submitted each week, therefore making sure that each week can be equal to the next and that everyone has equal chance.

help please.
thanks in advance.

 

[Cubist]

Let's say you have 90 points (15 people voted, 3 abstained). You'll need to multiply each player's points by "x" to bring the match total back to 108, and therefore...

90*x=108

Can you work out what x would be?

--

Another idea, you could distribute the missing points to all the players who bothered to vote, giving enough points to bring the match total back up to 108 and at the same time encouraging people to vote!

 

[JeffM]

Here is ONE of several different ways to do it. Voting problems are HARD.

Let's start with doing the ranking for a single week. Your current weightings are arbitrary. Do you really think that if Tomas voted John was best and Peter was next best, that he meant John was exactly 50% better than Peter, which is what weightings of 3 and 2 imply? Tomas may have thought John was just slightly better or may have thought John was much, much better. So rather than make up arbitrary weights, let's allow the votes to count for themselves.

My first suggestion is that for the annual selection treat each week as equal. That avoids the problem of having different numbers of voters each week. But the more interesting question is how to do each week without arbitrary and almost certainly misleading weights. You can then use the same process for the different weeks. Describing the procedure in detail would be tedious. It would need to be programmed. Instead, let's see how it would work in an example.

So we start by recording the votes by player and ranking. Then we tally the number of votes. Say that is 17 (1 person did not vote). Compute half of that giving 8.5. In this example, the person with the most votes for best is John with 7 votes. The person (excluding John) with the second most votes for best is Tomas with 6 votes. And the person with the third most votes for best is Peter with 4.

If we award best to John, 10 out of 17 disagree; he did not achieve even close to a majority, which would be at least 9. In fact the majority voted that he was not best. What to do? I suggest we look at the votes for second best among those three players only. Suppose John got 2 votes for second best, Tomas got 5 votes for second best, and Peter got 7 votes for second best. We have now found our three winners because a majority has decided that each of the three is in the top two slots.

At this point, we have choices. We can give Tomas best, Peter second best, and John third best. The rationale for that is that though Tomas and Peter had the same number of votes for best and next best, Tomas had more votes for best. Or we can give Tomas and Peter a tie for first place, and John third place. Or we can look at votes for third place between Tomas and Peter to see if that breaks the tie. Or we could let the coach break ties.

Any choice made, however, will please many members of the team. Tomas, Peter, and John will all be recognized, and at least other 11 members of the team will view the results as reasonable (if you do not allow members to vote for themselves).

Fleshing out this kind of algorithm requires considering the different situations that may arise and what decision rules should apply to these different situations, but you are likely to get a system that will please and motivate players.