One of the most powerful, but daunting tools in the game of Survivor is the immunity idol. When a player possess and plays the idol, it guarantees them safety for that elimination cycle. There are many different ways in which a player can utilize an idol. 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 idol mechanisms using a linear weights-based model, the value in which a player utilizes an idol in the game can be measured.
For purposes of this measurement, an immunity idol is considered any idol or advantage that functions similar to an immunity idol, by either cancelling votes or preventing votes from being cast against the player once it's played. Since season 11, there have been seven types of these idols or advantages that are being measured.
Secret Immunity Vote (season 11) = Must be played in secret for an exposed player before votes are cast, but revealed after votes are read
Immunity Necklace (season 11) = Must be played before votes are cast
Super Immunity Idol (season 12) = Can be played after votes are read
Standard Immunity Idol (season 14) = Must be played before votes are read
Legacy Advantage (season 33) = Must be played before votes are read and only active for designated cycles
50/50 Coin (season 40) = Must be played before votes are read and only active when played successfully (50% chance)
Shot-in-the-Dark (season 44) = Must be played during vote, in exchange for the player's vote and only active when played successfully (16.7% chance)
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 utilizing an idol and the number of players in the game (that could still affect the idol) at the time the idol is utilized. There are six game states and eighteen player states, meaning that there are 108 player/game states in total. Each idol 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 thirteen players in the game while in the post-vote 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 utilized an idol during the post-vote game state, while thirteen players were in the game (that could still utilize the idol), then it should be expected that there is a 7.8% (28 / 360) chance to win between that moment and the end of the game.
Linear Weights:
Each time an idol is utilized by a player, the cycle moves from one game state to another. For example, when there are thirteen players exposed at the beginning of the cycle, they each have an expected win rate of 7.7% (1 / 13). 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 post-vote game state, a player utilizing an idol has an expected win rate of 7.8% (28 / 360). As the change in game states moves a player from a win expectancy of .0769 (beginning state) to .0778 (post-vote game state), the safety is worth +.0009 in terms of win expectancy. Every change in game states has either a net positive or negative win expectancy value.
Idol Mechanisms:
To determine the average win value of all idol mechanisms, the total win expectancy of all played for safety (as an example) is divided by the total number of played for safety (occurrences).
This calculation is repeated for all the idol mechanisms. This gives the above/below average produced by each of the kinds of idol mechanisms (or a weighted average).
Due to the large number of idol mechanisms in the game, they have been compiled into common groups. This is also due to the fact that some of these idol mechanisms have not been used enough in the game to get significant data about their value. For example, the forfeit mechanism was only utilized by one player (Randy Bailey in season 17), so the relative value would be negative due to the low number of occurrences. Where it made relational sense, idol 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 utilizes an idol during that player/game state. The formula is:
Maryanne Oketch (winner of season 42) held an immunity idol (while being immune from receiving votes) with five players in the game. The change in win expectancy for that player/game state was:
(.1680 - .2000) + 1.0000 = .9680
Total average win expectancy for all idol mechanisms (by idol group):
Point Value Calculation:
Calculations for final point values for each idol 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
Held Because Immune example:
Weighted Average (HBI) = 58.8142 / 306 = .1922
Scale = .1922 x 100 = 19.22
Weighted Average (ELIM.ID) = -80.3878 / 797 = -.1009
Scale = -.1009 x 100 = -10.09
Adjustment = -10.09 x (-1) = 10.09
Adjusted Point Value = 19.22 + 10.09 = 29.31
Immunity Idol Score Calculation:
Tony Vlachos (winner of season 28) calculation:
Immunity idol = Did Not Possess = 11
Played Without Need = 1
Played at Expiration = 1
Held Because Immune = 9
Held for Safety = 3
Active Cycles = 25
# of Idols Active When Eliminated = 0
Idol score =
Immunity Idol Rankings:
All individual immunity idol scores were calculated and ranked against the entire population of player games. A percentile rank was calculated for the ordinal rank. Tony Vlachos's season 28 idol score of 24.31 ranks him 11th overall out of 609 total player games, which fell into the 98.3 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. Tony Vlachos's career idol score of 21.32 ranks him 22nd overall out of 517 total players, which fell into the 95.9 percentile.
Tony Vlachos career calculation:
Immunity idol = Did Not Possess = 49
Played for Safety = 1
Played Without Need = 1
Played at Expiration = 1
Held Because Immune = 11
Held for Safety = 5
Active Cycles = 68
# of Idols Active When Eliminated = 0
Idol score =
To view a full list of immunity idol rankings (both by season and career), please click button below:
*** updated through season 46 ***
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