In the last article a case was made for calculating performance ratios as part of the normal scoring process in sailboat racing. The crux of the argument was that simply providing ordinal data, the finish places, or interval data, elapsed time deltas, deprived sailors of important information that could be used to gauge their own race performance within the scored race and across other races in the series. It was also suggested that ratio data could form the basis of a fair and equitable handicapping system. The article is available here.
Characteristics of a Fair Handicapping System
What is a fair and equitable handicapping system? A fair and equitable system will have three main characteristics: 1) At the start of each race, each boat has an equal chance of winning; 2) If all boats in a sail in a race precisely to their handicap, the race will end in a tie; and 3) The rating for any boat will be independent of all other boats in the class. These characteristics, while deeply intertwined differ subtly.
The ostensible purpose of all handicapping systems is to level the playing field so that all competitors have an equal opportunity to win. That a fair handicapping system should do this is tautological. The problem with the dominant performance handicapping system is that it is not fair because it is class based. Any particular boat in a class may not be representative of the class; it may be much faster or much slower than the class rating. This puts some boats at and advantage and others at a disadvantage. I have discussed this issue here. It is my position that for club level and perhaps regional level racing an individual handicap is the fairest handicap and best for the sport.
The second characteristic, all boats sailing precisely to their handicap results in a tie, is simply a mathematical equivalent of the fairness characteristic. The logic is simple, if all boats sail to their handicap the corrected times will be equal and thus a tie. The reality of course, is that it is highly unlikely that in any race all of the competing boats will sail precisely to their handicap. Any small variation will cause different elapsed times, though perhaps in the fractions of seconds.
Third, the handicap should be independent of other boat boats in the class, but this is not the case in most classes. The greater the number of boats in the class, the less each boat contributes to the class rating. If all classes have the same or similar numbers of boats, the effect of class size is negated to some extent. However, if a boat is unique, then the class rating is functionally an individual rating. This is an inherent inequity in a class based rating system.
Sailed To Ratings
Let’s pick up where we left off. A race has been sailed and the ratios will have been calculated. To refresh our memory, the ratio score is calculated by dividing the median elapsed time of the fleet by the boat’s median elapsed time. The ratio can be considered a “Sailed To” rating, an indicator of how fast the boat sailed in relation to other boats in the fleet. In a fleet with an odd number of boats competing the median boat will be the middle boat when rank ordered by uncorrected elapsed times. In an even numbered fleet the median boat will be half way between the two middle boats. If then we multiply a boat’s ratio score by it’s uncorrected elapsed time the product will be a corrected time that will equal the median uncorrected time. That will be true for all boats in the fleet and would result in a tie, meeting the second characteristic of a fair and equitable handicapping system.
Of course in the foregoing paragraph all that has been demonstrated is the multiplicative inverse, a number multiplied by its inverse is equal to 1. The ratio calculated from the first race is an indicator of the relative speed of a boat/crew combination. What if it is used to correct elapsed time in a subsequent race? Is this a valid idea?
It is widely accepted that the best, though not perfect, predictor of future behavior is past behavior. In sports this is most clearly manifested in baseball’s obsession with data and statistics. And we should remember that above all else, sailboat racing is human behavior. So, yes, it is legitimate to use past performance to predict future performance in sailing and we have established that a ratio score is most representative of a boat’s performance relative to other boats.
On the following Wednesday evening our fleet races again. At the conclusion of the race ratio scores are again calculated and they differ from the prior week’s ratios. If ratio scores are a good indicator of relative performance and the scores differ from one week to another, which score is the most valid? The answer is that human behavior is variable. Even Babe Ruth, Mickey Mantle, and Hank Aaron, esteemed home run hitters, struck out a lot.
If ratio scores are collected over the course of a few weeks, it is likely that each score will differ from the others. With five, six, ten ratio scores which is the best indicator of a boat’s typical performance? For this it is necessary to look at the nexus of human behavior, the normal distribution, and measures of central tendency.
From Sailed To Ratings to a Fair Handicap
A key assumption is that Sailed To ratings will be normally distributed. The normal distribution has a number of well-established statistical properties. The relevant properties for our purposes are those associated with the measures of central tendency, mean, mode, and median. By way of quick review, the mean is the arithmetic average of all the data points in the distribution, the mode is the most frequently occurring number, and the median is the midpoint with half the values above and half below the median. In a normal distribution the value of the mean, median and mode are equal. This is a key indicator of the normal distribution.
Another assumption is that the Sailed To ratio will be likely be different from race to race and that is impossible to predict what that number will. In this sense the number will be random. This holds true because the variables that affect race performance are infinitely variable. How well a boat sails in any given race is a function of the boat and its preparation, crew skill, weather conditions, other boats in the race, other boats near or passing through the race course, and so on. Each factor is subject to greater or lesser control by the crew. Those boats that do a good job of reducing variability on the factors under their control will generate a narrower range of Sailed To ratings than those who are able to exercise less control. A measure of variability, a standard deviation, can be calculated that quantifies the amount of variance between the Sailed to ratings. This variance is important and will be discussed in a subsequent article.
Given the random nature of Sailed To ratings, which rating should be used for handicapping a race? When look for the best number to use for a boat’s rating, we are really asking a probability question, “Of the many Sailed To ratings in the boat’s distribution of Sailed To ratings is the boat most likely to sail to in this race?” Another way of asking this question is “Which Sailed To rating did the boat sail to most often?” We might be tempted to answer the average rating would be the most appropriate and in some conditions it would be correct.
Going back a few paragraphs, it was noted that in a normal distribution the mean, mode and median were the same. However, that only works when the sample size is the same as the population size. In most cases the number of results used to calculate the rating will not be large enough for the mean, mode, and median to be equal. With small numbers the median value is the best choice, as it is not influenced by the magnitude of the range.
There it is, the individual rating is simply the median value of the boat’s Sailed To ratings. But nothing is as simple as it seems. For individual ratings to work, they must be reviewed and adjusted periodically. “How often?” is the question.
Rating Reviews are Key
To establish the initial rating it is necessary to have enough races to approximate the median and to do so quickly enough to fully implement an individual rating system. Five races appears to be a good number to start with, both for a new boat entering an established fleet or for a fleet just getting started.
It is also important to periodically review and adjust the ratings to ensure their accuracy. New sails, crew training, and crew changes can affect the boat’s rating. A periodic review and rating adjust should occur. The question is how frequently should ratings be adjusted. A couple of general guidelines seem to make sense, the ratings of all boats should be reviewed and the review should happen a “natural” time, at the end of a race series or annually. It would also be prudent to limit the number of races considered during the review. Going back one season is probably enough, last season’s results determine this season’s ratings.
Any change in a handicapping system is going to have consequences, both intended and unintended. And resistance to change is inevitable. The next article will discuss some of these consequences and address common concerns that fuel resistance.