/*
 * Official NFL QB rating
 *
 * Copyright © 1999, 2006 Bart Massey.
 * All Rights Reserved.  See the file COPYING in this directory
 * for licensing information.
 *
 * Info from
 *   http://www.nfl.com/news/981202qbrate.html
 *   http://www.bluedonut.com/qbrating.htm
 * As per reference 1, you should get
 *   qbrating(461,324,3969,35,10) ~= 112.79
 * for Steve Young.  Reference 2 refers to the
 * formula as a "quadratic" equation; it's actually
 * a linear equation in the averages, hence the
 * Nickle exact rational implementation.
 */

/*
 * The "QB Rating" is only a rating of passing
 * effectiveness, and it's pretty marginal at that.  See the
 * references above for details.  The basic rationale is
 * that there are four categories considered: completions,
 * passing yards, passing touchdowns, and interceptions.
 * For each category, the interesting statistic is the
 * average over the number of passing attempts.
 *
 * The category scores are first scaled such that a score of
 * 1 is roughly average.  The scaling is then tweaked to
 * attempt to make a score of 0 awful and of 2 exceptional.
 * A maximum of 2.375 and minimum of 0 seem mostly to be a
 * guard against anomalies.  The sum of the categorie scores
 * is the QB score.
 *
 * The QB score is then scaled such that a score of 1
 * (average) in each category gives a scaled score of
 * 66.{6}%.  This is the QB rating.  A rating of 100 is
 * considered quite good.
 */

rational qbrating (int attempts, int completions, int yards,
		   int touchdowns, int interceptions)
{
    rational cat_max = 2.375;
    rational cat_score(rational base, rational offset,
		       rational scale) {
	rational avg = base / attempts;
	rational score = (avg * 100 + offset) * scale;
	if (score < 0)
	    return 0;
	if (score > cat_max)
	    return cat_max;
	return score;
    }
    rational total = cat_score(completions, -30, 0.05);
    total += cat_score(yards, -300, 0.0025);
    total += cat_score(touchdowns, 0, 0.2);
    total += cat_max - cat_score(interceptions, 0, 0.25);
    return total * 100 / 6;
}