THE KAIROS CONJECTURE & THE BELEGWE EQUATION

Readers may remember that last week, I posted my belief that "it should be possible to come up with a reliable formula to indicate what the chances of any PUG completing a particular instance or raid will be". This Holy Grail of scientific LOTRO studies is now within the grasp of serious students and analysts thanks to the efforts of my esteemed colleague, Master Belegwe, to whom we owe the following remarkable formula and its explanation:

The symbols are as follows:

• C - the chance of success, expressed as a percentage
• R - the relevance of rewards from a given instance expressed as a percentage of the proportion of the group the reward is relevant to
• P - the number of players present
• G - the gating requirement, expressed as an integer, with each piece of required equipment equalling 1
• D - the difficulty of the instance expressed as an integer from a scale I created (The Belegwe Scale) with values ranging from 1 to 4, 1 being the easiest and 4 being the most difficult
• A - the age of the instance expressed as an integer with each month (rounding to the nearest month) equalling 1
• P(al) - the average level of all the players present expressed as an integer
• I(l) - the level of the instance expressed as an integer
• P(n) - the number of players present who have never been to the instance before expressed as an integer
• P(e) - the number of players present who have been to the instance before expressed as an integer
• K - the Kairos constant with a value of 9.0171

The equation can be expressed more simply, and I think more elegantly, as:

• C- this remains the same as above
• X - the product of the first set of curved brackets
• Y - the product of the second set of curved brackets
• Z - the age of the instance expressed as an integer
• K - the Kairos Constant
• Alpha - the product of the New Player equation
• Beta - the product of the Experienced Player equation

It should now be child's play for anybody contemplating joining a PUG to gather some basic information from his potential fellow questers and enter the numbers into the Belegwe equation before deciding whether to proceed; more importantly, his or her decision will have been taken on the basis of firm scientific evidence rather than mere prejudice and conjecture. A new age of rationalism dawns on Middle-Earth!