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Overview

This library is designed to rank randomizer racers. It's based on the Glicko-2 rating system with some experimental modifications. You can read about Mark Glickman's Glicko-2 system here. The multiplayer implementation was partially borrowed from ms2300's implementation.

Usage

You can install RandoRank as a python package with pip by running pip install randorank. The first thing you'll want to do is determine a period length(e.g. four weeks) and a set of constants to use for your game/category.

To use this library to rank randomizer players, you can instantiate a MultiPeriod class, set the system variables with the add_constants() method, add races with the add_races() method, then export a dictionary of players with their ranking with the rank() method. When a period has concluded, you can feed this dict into a new MultiPeriod instance with the add_players() method and continue ranking.

Setting Constants and Multiplayer Glicko Implementation

The MultiPeriod class will initialize with a default set of constants designed for the A Link to the Past Randomizer. To set your own constants, create a dict with the following keys:

example_constants = {'tau': .02,
                     'multi_slope': .008,
                     'multi_cutoff': 8,
                     'norm_factor': 1.3
                     'victory_margin': 600
                     'initial_rating': 1500,
                     'initial_deviation': 300,
                     'initial_volatility': .22}

a MultiPeriod has an attribute MultiPeriod.constants with these values as a dict. There are also set_[constant name] methods for each of these individually. tau is the Glicko system constant. For randomizer races, it should be set low, around .02. multi_slope, multi_cutoff, and norm_factor are part of the multiplayer implementation, which divides races into a series of 1v1 matches and applies a weight based on race size and how close two racers finished compared to each other and the distribution of times in the race.

The cutoff determines how many runners a race must have for the library to use the multiplayer implementation. Below that, it will use the stock Glicko formula. The normalization factor is used to determine a "floor" time for the race and is game-specific. The formula for scoring a normalized race is first_quartile + (IQR * norm_factor). Times in between are assigned a value between 0 and 1, 1 being the first place finisher. To determine a normalization factor for your game or category, you should experiment with different values for multiple races and use your best judgement to figure out which value gives the best floor time. Since this formula is less accurate with less racers, we use the cutoff to prevent it from skewing final rankings. The slope is used later as part of the formula for determining a 1v1's weight.

In races above the cutoff, we take the original weight and multiply it by the result of the following:

let normed_diff = the absolute value of the difference between the two players'
normalized scores

1 - (multi_slope * (size ** (1 - abs(normed_diff)))) * (1 / (1 - multi_slope))

This generally means that the bigger the race, and the closer the two runners' finish times, the lower the weight for their 1v1. But no matter the race size, top finishers' scores against the very bottom will remain the same.

For races below the cutoff, we use the "victory margin" in seconds to calculate a weight for each 1v1. When this value is 600 seconds, or 10 minutes, a different in times of ten minutes or more gives full weight to the 1v1. Below that, the difference is scaled for a weight between 100 and 85%. The closer the finish, the less weight is given to the 1v1.

To determine the best variables for your game or category, you'll want to look at the sorted results over several periods as well as the distribution of final ratings. Make sure the final rankings look reasonably accurate that. The distribution of scores should be somewhere between normal and right-skewed. Experiment using different values for the same data set.

Adding Races

Races are passed to the add_races() method as a list of dictionaries with names as keys and times (in seconds) as values. If a runner does not finish a race, their value should be NaN. You can set NaN values in python by importing the type from the math module(from math import nan). Suppose you want to add a race with three runners, one of whom forfeited. You would pass this dictionary:

from math import nan

example_period = MultiPeriod()
example_race = {'runner 1': 1563,
                'runner 2': 1620,
                'runner 3': nan}
example_period.add_races([example_race])

It's important that you convert all non-finishers to NaN and don't use a number like 0. NaN is a special numerical type indicating that the value is "not a number." One way to do this is applying a dictionary comprehension:

filtered_example_race = {k: math.nan if v is None else v for k, v in race.items()}

End of Period Rankings

Using the rank() method of the MultiPeriod instance will export a dictionary of dictionaries containing each runner's rating, deviation, volatility, inactive periods, variance, and delta for the end of the period. The latter three values can be discarded if you're done ranking players. If you want to continue ranking over multiple periods, you can pass this to the add_players() method of a new MultiPeriod instance.

(Experimental) If you want to calculate new mid-period with a dict of mid- period rankings and some races you'd like to add to that period you can:

  1. Pass end=False to the rank() method to get mid-period data including each player's variance and delta.
  2. Instantiate a new MultiPeriod.
  3. Take the runners who have participated only in the race(s) you want to add.
  4. Combine their pre-period rating, deviation and volatility with their mid-period variance and delta values in a dictionary.
  5. Pass this dict with only the new runners to the add_players() method of the new period.
  6. Add the new races with add_races() then rank(end=True) (the default argument to end is True.)

This will produce a rankings dict containing values for the runners in the added races. You can add them back to the first ranking dict, but make sure to zero out the delta and variance values any time you are calculating from the beginning of the period as these numbers contain information about races which was already calculated, so you will end up counting some races more than once if you don't.

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