Tuesday, February 16, 2010

Olympic Analytics or What Would My Sled Weigh?

Japanese Luger Aya Yasuda was disqualified from her first Olympics due to her sled being overweight. This error is apparently attributed to "accidentally miscalculating a somewhat complex formula," I was curious just how complicated this formula was.
RULES
Pre-Race Checks (Singles)
At the start of all four singles runs, each sled is weighed, each athlete is weighed, and temperatures of sled runners are compared to an official "control" runner.
  • In singles, the sled cannot weigh more than 23kg (50.6 lbs). 
  • There is no maximum weight for athletes. But men who weigh less than 90kg (198 lbs) may add up to 13kg (28.6 lbs) of additional weight to act as ballast. Women who weigh less than 75kg (165 lbs) are allowed to add up to 10kg (22 lbs) of extra weight. The formulas below determine how much weight may be added:  
MEN: ( 198 lbs - body weight ) x .75    
WOMEN: ( 165 lbs - body weight) x .75 
  • Also, officials check the temperature of the steel runners on an athlete's sled to make sure they haven't been heated. (Warm runners are not allowed because the heat would decrease the friction between the runners and the ice, making the sled faster.) A "control" runner, located by the start house and shaded from the sun, is used as a basis for the measurement. The competitor's runners must be within 5 degrees Celsius of the control runner's temperature. 

    I got it...you can add 75% of the difference in your body weight and a predetermined minimum amount in ballast, up to a predetermined maximum amount. 

    Yeah...that formula sucks. Thank goodness that formula wasn't something like this formula for a Player Efficiency Rating used by those who study basketball analytics:
    uPER = 1/MIN * (3PM + [(2/3)*AST] + [(2 – factor * (tmAST/tmFG)) * FG] + [FT * 0.5 * (1 + (1 – (tmAST/tmFG)) + (2/3)*(tmAST/tmFG))] – [VOP * TO] – [VOP * DRBP * (FGA – FG)] – [VOP * 0.44 * (0.44 + (0.56 * DRBP)) * (FTA – FT) + [VOP * (1 – DRBP) * (TRB – ORB)] + [VOP * DRBP * ORB] + [VOP * STL] + [VOP * DRBP * BLK] – [PF * ((lgFT/lgPF) – 0.44 * (lgFTA/lgPF) * VOP))])

    where

    factor = (2/3) – [(0.5 * (lgAST/lgFG))/(2 * (lgFG/lgFT))]
    VOP = lgPTS/(lgFGA – lgORB + lgTO + 0.44 * lgFTA)
    DRBP = (lgTRB – lgORB)/lgTRB

    Once uPER is calculated, it is adjusted for pace and scalar multiplied so that the league average player-minute is a 15 PER:

    PER = uPER * (lgPace/tmPace) * (15/lguPER)

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