Saturday, March 16, 2013

Key to Rankings Tables

total The total strength expressed as the rate of scoring against the median (WA-OR) team*. 2^(difference in strength) is the relative rate of scoring of team A to B. If the difference in strength is 1, then team A has twice the scoring rate (meaning on average team A scores twice before team B scores once). A difference of 3 means team A score 2^3=8 times the rate of team B so (on average) team A scores 8 times before team B scores once. A very high difference, like 8, does NOT mean that team A scores 2^8=256 times in a game but that if these 2 teams played 10000 (say) games, the number of team A goals divided by the number of team B goals would be 256. So, basically team B cannot score much against team A.

attack and defense The attack and defense strength. Attack strength of team A divided by the defense strength of team B gives you the expected number goals by team A in a game between team A and B. The relative size of team A's attack and defense strengths indicates the characteristic of the team---offensive versus defensive. Across all regions, the median attack/defense ratio is about 1.25 thus the attack strength tends to be a little higher which reflects that the median score is 1.25 when equal strength youth teams play. This is a characteristic of styles of play.

div The LastPlanet division. A group of competitive teams. Within a division, the match up between the top team and bottom team has an expected GD of 1, so all matches between teams in a division would be expected to be competitive. Divisions start at strength = 0 and go up and down.

n The number of games for this team in the database. You can see a list of all team games by going to the Individual Team Reports and opening the pdf for a particular team.

Relationship between strength differences and probability of match outcome (approximate)
Top row is difference between team A total strength and team B total strength. Numbers in the cells are probabilities. The assumes 'balanced' teams whose attack strength is similar to their defense strength. If both teams are highly defensive, the probabilities would be skewed towards (0-0) ties.
0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.25 2.50 2.75 3.00
win 35 39 44 49 54 59 64 68 73 77 81 85 88
tie 31 31 30 29 27 26 23 22 19 17 14 11 9
lose 34 30 26 22 19 15 13 10 8 6 5 4 3

* Yes, CA, AZ etc teams are scaled relative to WA-OR teams. I have to scale to something and we are pretty sure we have almost all select teams in WA and OR, so the median of their strengths is fairly stable. For other states, we can't be sure we have all the lower leagues so the median select team strength might be skewed up.