Ted’s Lucky Ratios: SOQ Off The Charts Lucky

Ted finally released his famous Annual Lucky Ratio rankings this afternoon and although he left open the possibility of further tinkering with the analysis and commentary, there is enough juice here to release the findings.  Sorry Scott.

Objective:
 

To precisely quantify the effect random scheduling has on the won/loss record for each team.
 

Assumptions:

-  In the QFL 13 game schedule, 6 games (46%) are played vs. division opponents and 7 (54%) are played vs. non division opponents, thus in any given week a team will play either a div or nondiv opponent based on these weightings. 
-  The distribution of which weeks that are division vs. non-div is totally random, but that 46% will be division and 54% non-division.
-  The opponent is random within the framework of either division or non-division
-  Your score for a given week defines you.   Injuries, bad bounces, guys left on the bench, while they may indeed be bad luck, are not part of this equation. 
 

Method:

 
-  For a given week, determine the number and percentage of teams a team has beaten a) within its division (max of 3 ) and b) outside its division (max of 8 )
 
-  Apply the probabilities of a week being either a division or non div week, and determine an overall chance of winning given a team’s score. 
 

Example:

 
-  A team is the high scorer of the week.  It thus beats 100% (3) of teams in its division and 100% (8) of teams non division.  It had a 100% chance of winning. 
 
-  A team scores 65 points.  65 pts would have beaten 2 of 3 teams in its division (66%) but just 3 of 8 teams outside its division (37.5%).  Its total chances of winning that week are thus 46% x 66% + 54% x 37.5% = 51%. 
 
-  A team scores 80 pts but the rest of the division scores higher.  All 4 teams in that division outscore the other 8 teams.  Said team has a 0% chance of beating a division team (if it were a division week) but a 100% chance of beating a non-division team.  The total chance of winning is 54% (46% x 0% + 54% x 100%) .
 

General Statistical Observations of the QFL:

 
I looked at scoring from the 2008 (9 wks of data), 2009 and 2010 seasons for QFL1, a total of 396 observations . 
 
 
-  Scoring is almost exactly normally distributed around a mean of 69.90 , a median of 69.33 and a standard deviation of 17.58, with a very slight positive skew of 0.19.  Breakouts of those individual seasons produced immaterial deviations within a point or so. 
-  This distribution allows us to establish precise significance to tail events when they occur. 
 
 
    

 

Definitions:
 

 – The mean is the average
-  Standard deviation describes the variance of a distribution around its mean.  68% of all values fall within 1 standard deviation of the mean (+/- 17 pts of 69 in QFL’s case), and 95% will fall within +/- 1.96 st deviations (+/- 34 pts. of 69). 
-  The median is the midpoint of a set of observations.  In a given week, the median would lie in the middle of the 6th and 7th highest scoring teams. 
-  Distance from the median for a given week is simply how far away your score was from the midpoint. 
-  A “deserved” win is simply any week where your score gave you more than a 50% chance to win. 
-  The Lucky Ratio is Deserved wins – Actual wins
-  The Very Lucky Ratio – I thought we should have a special designation for any win/loss that was really undeserved, and I set those boundaries at a loss when >60% chance to win or a win when <40% chance to win.  This ratio is the net sum of your Very (Un)Lucky wins/losses.