In order to proceed in the game, players must avoid being eliminated each elimination cycle. There are many different ways in which a player may earn safety from elimination, but each of these different safety mechanisms have a relative value to winning the game. The relative values can be determined based on the change in win expectancy between the different player/game states. The win expectancy values are based on mapping out all of the past winner's games. As a player moves through an elimination cycle, the change in win expectancy is tracked. The progressive change in win expectancy, from game event to game event and elimination to elimination, determine the weights that a particular event is worth. By determining the relative value of all the different safety mechanisms using a linear weights-based model, the value in which a player earns safety in the game can be measured.
Measurement:
Win expectancy measures the average number of times a player wins a season of Survivor, given a particular player/game state. Player/game states are a record of players securing safety and the number of players exposed at the time safety is secured. There are nine game states and nineteen player states, meaning that there are 171 player/game states in total. Each safety mechanism is earned in a particular player/game state.
Winner Outcomes:
Below is an example of how to calculate the average win expectancy. All instances were compiled where there were four players exposed while in the challenge game phase. To
calculate the average win expectancy, take all the instances of that player/game state from the entire set of seasons and find the total number of times a player has won the game. Divide that total by the total number of instances to get the average. If all that was known about a situation was that a player secured safety during the challenge game state, while four players being exposed, then it should be expected that there is a 44% (19 / 43) chance to win between that moment and the end of the game.
Despite there having been 46 seasons, there were three seasons where individual immunity was not earned/used as a way to secure safety. In season 7, the last four players competed against the jury for immunity and the jury won the challenge, leaving all four players exposed to elimination at the tribal council vote. In both seasons 38 and 44, Chris Underwood and Heidi Lagares-Greenblatt (respectively) won the final four individual immunity challenge but transferred their immunity in order to compete in the fire making challenge.
Linear Weights:
Each time safety is secured by a player, the cycle moves from one game state to another. For example, when there are four players exposed at the beginning of the cycle, they each have an expected win rate of 25% (1 / 4). The win expectancy at the beginning game state is calculated by taking one and dividing it by the number of players still in the game. This is equivalent to the random probability of a single player winning with that number of players in the game. At the challenge game state, a player earns safety (individual immunity challenge - II.CH), which has an expected win rate of 44.2% (19 / 43). As the change in game states moves a player from a win expectancy of .2500 (beginning state) to .4419 (challenge game state), the safety is worth +.1919 in terms of win expectancy. Every change in game states has either a net positive or negative win expectancy value.
Safety Mechanisms:
To determine the average win value of all safety mechanisms, the total win expectancy of all tribal immunity challenges (as an example) is divided by the total number of tribal immunity challenges (occurrences).
This calculation is repeated for all the safety mechanisms. This gives the above/below average produced by each of the kinds of safety mechanisms (or a weighted average).
Due to the large number of safety mechanisms in the game, they have been compiled into common groups. This is also due to the fact that some of these safety mechanisms have not been used enough in the game to get significant data about their value. For example, the returning player safety mechanism was only earned by two players (Lillian Morris and Burton Roberts in season 7), so the relative value would be negative due to the low number of occurrences. Where it made relational sense, safety mechanisms with minimal usage were grouped and counted together when their weighted averages were calculated.
Average Win Expectancy:
The average win expectancy includes the change in win expectancy from one game state to another. But it also includes the number of times a winner earns safety during that player/game state. The formula is:
Erika Casupanan (winner of season 41) won an individual immunity challenge with five players exposed. The change in win expectancy for that player/game state was:
(.2727 - .2000) + 1.0000 = 1.0727
Total average win expectancy for all safety mechanisms (by safety group):
Point Value Calculation:
Calculations for final point values for each safety mechanism/group:
Weighted Average = Total Win Expectancy / Total Occurrences
Scale = Weighted Average x 100
Adjustment = Weighted Average of Eliminations x (-1)
Adjusted Point Value = Scaled Weighted Average + Adjustment
Individual Immunity Challenge example:
Weighted Average (II.CH) = 108.1736 / 409 = .2645
Scale = .2645 x 100 = 26.45
Weighted Average (ELIM) = -172.3488 / 793 = -.2173
Scale = -.2173 x 100 = -21.73
Adjustment = -21.73 x (-1) = 21.73
Adjusted Point Value = 26.45 + 21.73 = 48.18
Safety Score Calculation:
Parvati Shallow (winner of season 16) calculation:
Safety earned = Tribal Immunity = 6
Individual Immunity = 1
Miscellaneous Immunity = 3 (players leave game)
Tribal Council Vote = 8
Jury Vote = .6250 (5 / 8 jury votes)
Cycles Survived = 18
Win = 1 (by default, zero eliminations)
Safety score =
Safety Earned Rankings:
All individual safety scores were calculated and ranked against the entire population of player games. A percentile rank was calculated for the ordinal rank. Parvati Shallow's season 16 safety score of 33.21 ranks her 43rd overall out of 839 total player games, which fell into the 94.9 percentile.
Additionally, player ranking combines all the points each player has earned into a single score for their career. A percentile rank was calculated for the ordinal rank. Parvati Shallow's career safety score of 28.22 ranks her 92nd overall out of 697 total players, which fell into the 86.9 percentile.
Parvati Shallow career calculation:
Safety earned = Tribal Immunity = 17
Individual Immunity = 4
Miscellaneous Immunity = 5
(players leave game = 3 & no tribal council = 2)
Tribal Council Vote = 28
Immunity Idol = 1
Purgatory = 11
Jury Vote = .9583
(5 / 8 jury votes = .6250 + 3 / 9 jury votes = .3333)
Cycles Survived = 66
Win = 1
Elimination = 3
Safety score =
To view a full list of safety earned rankings (both by season and career), please click button below:
*** updated through season 46 ***
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