Measuring a Big 4 Country's performance is tricky business. So what would be a good way to get a handle on whether nations like United States/Venezuela/India reliably perform at a high level? What can be the parameters?
On brainstorming we see a combination of two things: high levels of country's performance, but with low variation around that high level. For example, you want your country to be able to secure, say, a Top 3 finish, but you also want them to do that every time, rain or shine, year after year, no matter what. It doesn't take much to imagine that countries that can do these two things are likely to contend for the Crown. In contrast, countries that have too many ups and downs - a glorious Crown Win followed by an agonizing Semi Final finish - will not be able to win points every time as the Top Contending nations typically do.
Statistically speaking, what we want to do is put a number on the level of performance as well as the variation around that level of performance over some period of time. For starters, imagine a distribution of performance over a span of last 13 years, since the turn of the century.
To see if Country's performance levels were dependably in a high or low range or all over the place, we can calculate a statistic called the standard deviation.
Here's how Wikipedia explains the concept: In statistics and probability theory, standard deviation (represented by the symbol sigma, σ) shows how much variation or "dispersion" exists from the average (mean, or expected value). A low standard deviation indicates that the data points tend to be very close to the mean, whereas high standard deviation indicates that the data points are spread out over a large range of values.
By calculating the standard deviation around the mean, we can see if countries are able to exceed the mean and whether they do so consistently (or have really high performance followed by really low ones). The worst kind of performers will be countries that have a low mean (teams that, on average, perform poorly) and do so consistently (i.e., they're bad every year). In-between, you'll have good countries with a fair number of bad Miss World Years or bad Countries that occasionally outstand their counterparts. The first step is to assign a number to every placement, because Winners, Top 3 Finisher, Semi Finals finish are just Titles, and we cant perform mathematics on them. So, we assigned Winners, the highest score - 8, 1st Runner Up a score - 7, and so on. These are called nominalized placements, because we have assigned them a number (nominal) value. Read below under nomenclature to see the full nominalized key. These placement brackets, are equitable, that they for clearly defined scales, Winners, Top 5s, Runner ups, etc. hence without much error we can assign them these nominalized values.
Then we calculate the mean score over the 13 years, indivdual mean scores of every country, its standard deviation and the weighted means. Here's the plot of the final results.
X- Axis : Variability of Performance (Std. Deviation)
Standard Deviation of the placement scores of individual countries about their mean score over the period 2000-2012
Y-Axis : Mean Placement scores of an individual country from 2000-2012
*All scores represent Nominalized Placements. See below | Copyright 2012 Missosology
** Placements are from Official Miss World Data.
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The Analysis and Result
The graph reveals a couple of things. First, it shows one piece of information we've already known from analysis of the aggregate Big 4 Rankings: United States (US), India (IN), Venezuela(VZ) produced the highest average placements per year around, while Puerto Rico (PR), Philippines (PH), Australia (AU) did about half as well. Mexico (MX) though not highly ranked according to the aggregate Big 4 rankings but have been performing very well in the last decade and its performance is reflected in the Graph with the other heavy weights, US/VZ/IN. We also see that South Africa(SA) and Colombia (CB) all performed about equally with a mean score of ~1.0 ( a SEMI Final Finish) . However, the standard deviation also shows that Colombia (CB) did so with much less consistency than the other two countries. It also reveals that Germany's (GR) performance was dependably lousy: they didn't have any notable finishes much and managed to do perform bad year after year.
This graph is based on the nominalized placements and represents metric consistency.
Another subsidiary information but nonetheless intuitive observation is the mean scores. Hover around a counrty's point on the graph and check the mean score. For example, US has a mean score of 1.5, meaning, its score is between a 1 and a 2, a Semifinal finish and Top 10 finish. US on an average finished in between a Semi Finalist or Top 10. India on the other hand with a mean score of 2.1 has more likely finished a Top 10 on average. While Columbia (CB) with a score of 0.9 ~1 had only managed an average semifinalist finish.
What is nominalized placements?
Simply put, for the sake of mathematical manipulation of data we have nominalized each placement (denoted each placement) bracket with a number. a '0' on the graph means no placement or a ding, 1 represents = Semi Final Finish
Nominalized Placement Scores
0 = represents a No placement/country wasn't placed)
1=Semi Finalist Finish
2 = Top 10 Finish
3 = Top 6 Finish
4,5,6,7 = 4th, 3rd, 2nd, 1st Runner Up
8 = Crowned Winner
Software used : All computations were carried out using IBM SPSS Software V20 and Mapped on IBM Many Eyes. Raw Runtime codes, in *.sav format and outputs available on request for interested developers