Hi

in one of my fantasy leagues, where there are 7 of us players and the league average makes up the 8th player

the league average is worked out by adding the 7 players scores and dividing them by 7 - bit obvious but just in case

there have been 4 game weeks so far and the league average has won every game

so he's finished 4th/8, 4th/8 and 5th/8, 5th/8 and yet despite those finishing positions has beaten his opponents and won every game week

it's only 4 games i know but it just seems funny that the league average is top of the league

is there anyway to work out what the odds of this happening would be?

would it just be because it is an average 50/50 each week (because we are all new to the game, then maybe it would change vs better opponents when people get used to it)

so winning 4 50/50 in a row isn't actually that unusual and is just about a 16/1 chance so nothing that unusual it just seems if for eg you were rolling a 1-8 dice and you got 4,4,5,5 and you needed your opponent to be higher than the 4 or 5 on each roll it seems like the odds maybe longer

and the chances of winning a single game week seeing it's an average?
would it be 50/50? or slightly more as it's 4/8, 4/8, 5/8, 5/8 he's finnished.

thanks for any help

Think the chances of the average winning a tie are about 3.5/8 so 0.4375 as a percentage

so four times in a row google says is 0.03663

rounded up so maybe a 4% chance i think

The average isn't necessarily the same as the 50% mark like it is with an even-sided die. Someone might pull the average above or below the 50% line, so there isn't enough info to calculate the chance of losing to the average.

I'm also not sure what you mean. Do the 4th/4th/5th/5th refer to each week, and the avg is ahead after the 4 weeks, or do those ranks refer to 4 categories and the avg repeated those performances each week (and won each week)?

They wouldn't need to exceed 4 on each roll, just have an avg roll higher than 4.5, so for instance {8,8,2,1} would suffice.
P(lose to avg) = P(sum <18) = [1 - P(18)]/2

Yeah that the average finnishes 4th or 5th/7 each week

Ah I see thanks