A detailed description of the MY4PAX DIPA rating method is given below:
The DIPA rating method is not too dissimilar from that adopted by other established websites such as BeerConnoisseur, in the sense that the final rating represents a weighted average of a given set of graded taste parameters over sampler. However, it is different in one important respect; i.e. the MY4PAX rating method utilizes the same four graders each time it rates a new DIPA beer. This way our ratings don’t get watered down by thousands of other samplers, many of whom do not fully appreciate the unique character and flavor of a good DIPA.
INTRODUCTION
The my4pax rating algorithm calculates the weighted average of the four graded taste parameters over sampler – the taste parameters that contribute most to the overall quality of the beer are weighted the heaviest.
To illustrate how the weighted average is calculated, observe the following example in which the three grading parameters – quizzes, exam, term paper – are weighted differently to determine a student’s final grade. Those grading parameters deemed most important in determining the student’s final grade are weighted the heaviest; i.e. term paper, followed by exams, and then quizzes.
Similarly, when determining the ‘Tasteability’ of a given DIPA, those taste parameters deemed most important in crafting the overall taste of the DIPA beer are weighted the heaviest, followed in order by the least important parameters.
The DIPA rating scores form a distribution ranging in value from 0 to 5. The ratings’ distribution is illustrated below in the form of a histogram (see Background Statistics below), whose bin totals are numerically integrated to generate a cumulative distribution function (CDF), from which the my4pax, DIPA beer ‘Tasteability’ is determined.
The four ‘Tasteability’ categories, corresponding probability thresholds and associated rating breakpoints for the my4pax data distribution is tabulated below:
The Cumulative Probability Thresholds ( left column ) represent the associated thresholds for the cumulative probability distribution breakpoints. For example, a DIPA rating in the interval [ 4.04 – 5.00 ] represents a sample in the upper 38 percent of the cumulative distribution, with a ‘Tasteability’ classification of “You Must Try Before You Die”.
As new DIPAs are added to the data base, the CDF will naturally change, so expect the rating interval breakpoints to change as well.
BACKGROUND STATISTICS
As noted above, the complete set of rating scores for a sample data set constitute a ratings’ distribution ranging in value from 0 to 5. This ratings’ distribution can be displayed in the form of a histogram ( see figure below ). A histogram is a graphical display of data using bars of different heights, where the height of each bar represents the number of rating samples falling within a given rating interval.
If the number of samples in each histogram bin are summed from the low end of the histogram to the upper end, and the cumulative sum per bin interval is divided by the total number of rating samples in the distribution, 398, we get the Cumulative Distribution Function (CDF) shown below. ( Since the CDF deals in percentages, its range extent is zero to one. )
Shown in the plot are the arbitrary percentile breakpoints – [ 0.00, 0.10, 0.50, 0.62, 1.00 ] – along with the corresponding rating values that serve as demarcation points for the four DIPA ‘Tasteability’ categories: “MUST TRY BEFORE YOU DIE“, “TRY IT, YOU’LL LIKE IT“, “TAKE IT, OR LEAVE IT“, and “DON’T BOTHER, SAVE YOUR MONEY“.
The complete CDF is tabulated below:
Approximately 90% of the cumulative distribution lies below the rating interval, [ 4.28 –5.00 ].
SUMMARY
In summary, the methodology used to determine the DIPA beer ‘Tasteability’ is:
- select the arbitrary CDF percentile points, i.e. [ 0.0, 0.10, 0.50, 0.62, 1.0 ], and,
- the corresponding DIPA rating values, i.e. [ 0.00, 3.52, 3.97, 4.04, 5.00 ], to define,
- the four my4pax ‘Tasteability‘ categories.
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