The inverse skill relative to casting votes is the ability of a player to avoid receiving elimination votes. As the main mechanism for eliminating players is to vote them out, a player’s ability to avoid elimination votes is an essential skill in the game. As with vote accuracy, this is accomplished by calculating the marginal change (increase or decrease) between the actual votes received and the probable votes anticipated (if votes were cast randomly). The probable vote avoidance rate is calculated by taking the number of probable votes anticipated divided by the number of potential votes that can be received. The underlying assumption is that the probable vote avoidance rate is equal to the likelihood of a player avoiding votes if each vote cast was completely random. By calculating the marginal difference between the probable vote avoidance rate and the actual vote avoidance rate, a player’s ability to avoid receiving votes can determined.
Each specific tribal council vote has a unique set of circumstances that must be accounted for to properly contextualize the vote avoidance calculation. The probable vote avoidance rate decreases as the size of the tribal council decreases (less voters). This demonstrates that as the number of voters decreases, it is increasingly difficult to avoid probable votes, assuming votes are cast randomly.
Below are eight different tribal councils where vote avoidance is calculated for each of the players. The eight examples were selected because they are of similar size, but constitute different vote mechanics. This demonstrates how the vote mechanics affect the context of each particular tribal council and individual player.
Example #1 – Season 1, Cycle 1:
# of players attending tribal council = 8
# of votes cast = 8 (one vote per player)
# of players immune from receiving votes = 0
As each player at the tribal council were in the same position (one vote each, not immune), their probable vote avoidance rate for this tribal council was 85.71%. For example, Richard's probable vote avoidance rate was calculated by taking the random probability that Richard could receive a vote from each of the other players (1 / 7 = .1429) and multiplying it by the number of players who voted (.1429 x 7 = 1.0000). Then the probable random votes to receive is subtracted from the maximum vote against (7 - 1 = 6) to calculate the probable random votes to avoid. The probable avoidance rate is the result of dividing the probable votes to avoid by the maximum votes against (6 / 7 = .8571).
A player who successfully avoided all votes had a 100% vote avoidance rate for the tribal council vote. For example, Richard’s marginal vote difference was .1429 for this tribal council vote (1.0000 vote avoidance rate - .8751 probable vote avoidance rate). Sonja, as the player voted out, had a negative marginal vote difference of -.4286 for this tribal council vote (.4286 vote avoidance rate - .8571 probable vote avoidance rate).
Example #2 – Season 2, Cycle 9:
# of players attending tribal council = 8
# of votes cast = 8 (one vote per player)
# of players immune from receiving votes = 1
As the only immune player, Nick was not eligible to receive votes. As the other players at the tribal council were in the same position (one vote each, not immune), their probable vote avoidance rate for this tribal council was 83.67%. For example, Tina's probable vote avoidance rate was calculated by taking the random probability that Tina could receive a vote from Nick (1 / 7 = .1429) in addition to the random probability that Tina could receive a vote from each of the other players (1 / 6 = .1667 x 6 votes = 1.0000). Then the probable random votes to receive is subtracted from the maximum vote against (7 - 1.1429 = 5.8571) to calculate the probable random votes to avoid. The probable avoidance rate is the result of dividing the probable votes to avoid by the maximum votes against (5.8571 / 7 = .8367).
A player who successfully avoided all votes had a 100% vote avoidance rate for the tribal council vote. For example, Tina's marginal vote difference was .1633 for this tribal council vote (1.0000 vote avoidance rate - .8367 probable vote avoidance rate). Jerri, as the player voted out, had a negative marginal vote difference of -.6939 for this tribal council vote (.1429 vote avoidance rate - .8367 probable vote avoidance rate).
Example #3 – Season 3, Cycle 3 (re-vote):
# of players attending tribal council = 8
# of votes cast = 6 (one vote per immune player)
# of players immune from receiving votes = 6
This second vote of tribal council took place after the initial vote, due to the initial vote being tied. The two players that were tied with elimination votes (Lindsey and Carl) were not allowed to vote on the re-vote. The six other players who participated in the re-vote were immune from receiving votes. The two players eligible to receive votes had a probable vote avoidance rate for this tribal council of 50%. For example, Lindsey's probable vote avoidance rate was calculated by taking the random probability that Lindsey could receive a vote from each of the other players (1 / 2 = .5000 x 6 votes = 3.0000). Then the probable random votes to receive is subtracted from the maximum vote against (6 - 3 = 3) to calculate the probable random votes to avoid. The probable avoidance rate is the result of dividing the probable votes to avoid by the maximum votes against (3 / 6 = .5000).
A player who successfully avoided all votes had a 100% vote avoidance rate for the tribal council vote. Since no one was eliminated as a result of this re-vote (Lindsey and Carl again tied, each received 3 elimination votes), no player had a 100% vote avoidance rate for this tribal council vote. Lindsey and Carl's marginal vote difference was 0.0000 for this tribal council vote (.5000 vote avoidance rate - .5000 probable vote avoidance rate).
Example #4 – Season 30, Cycle 11:
# of players attending tribal council = 8
# of votes cast = 8 (one vote per player)
# of players immune from receiving votes = 2
As the two immune players, Mike and Carolyn were not eligible to receive votes. As the other players at the tribal council were in the same position (one vote each, not immune), their probable vote avoidance rate for this tribal council was 80.95%. For example, Will's probable vote avoidance rate was calculated by taking the random probability that Will could receive a vote from Mike and Carolyn (1 / 6 = .1667 x 2 votes = .3333) in addition to the random probability that Will could receive a vote from each of the other players (1 / 5 = .2000 x 5 votes = 1.0000). Then the probable random votes to receive is subtracted from the maximum vote against (7 - 1.3333 = 5.6667) to calculate the probable random votes to avoid. The probable avoidance rate is the result of dividing the probable votes to avoid by the maximum votes against (5.6667 / 7 = .8095).
A player who successfully avoided all votes had a 100% vote avoidance rate for the tribal council vote. For example, Will's marginal vote difference was .1905 for this tribal council vote (1.0000 vote avoidance rate - .8095 probable vote avoidance rate). Shirin, as the player voted out, had a negative marginal vote difference of -.3810 for this tribal council vote (.4286 vote avoidance rate - .8095 probable vote avoidance rate).
Example #5 – Season 34, Cycle 14:
# of players attending tribal council = 7
# of votes cast = 7 (one vote per player, except one player stole a vote)
# of players immune from receiving votes = 1
As the only immune player, Brad was not eligible to receive votes. Sarah, by virtue of stealing Tai's vote, had a probable vote avoidance rate for this tribal council of 80.67%. Sarah's probable vote avoidance rate was calculated by taking the random probability that Sarah could receive a vote from Brad (1 / 6 = .1667) in addition to the random probability that Sarah could receive a vote from each of the other players (1 / 5 = .2000 x 4 votes = .8000). Then the probable votes to receive is subtracted from the maximum vote against (5 - .9667 = 4.0333) to calculate the probable random votes to avoid. The probable avoidance rate is the result of dividing the probable votes to avoid by the maximum votes against (4.0333 / 5 = .8067).
As a result of having his vote stolen by Sarah, Tai had a probable vote avoidance rate for this tribal council of 80.48%. Tai's probable vote avoidance rate was calculated by taking the random probability that Tai could receive a vote from Brad (1 / 6 = .1667) in addition to the random probability that Tai could receive a vote from each of the other players (1 / 5 = .2000 x 6 votes = 1.2000). Then the probable votes to receive is subtracted from the maximum vote against (7 - 1.3667 = 5.6333) to calculate the probable random votes to avoid. The probable avoidance rate is the result of dividing the probable votes to avoid by the maximum votes against (5.6333 / 7 = .8048).
As the other players at the tribal council were in the same position (one vote each, not immune), their probable vote avoidance rate for this tribal council was 80.56%. For example, Troy's probable vote avoidance rate was calculated by taking the random probability that Troy could receive a vote from Brad (1 / 6 = .1667) in addition to the random probability that Troy could receive a vote from each of the other players (1 / 5 = .2000 x 5 votes = 1.0000). Then the probable random votes to receive is subtracted from the maximum vote against (6 - 1.1167 = 4.8333) to calculate the probable random votes to avoid. The probable avoidance rate is the result of dividing the probable votes to avoid by the maximum votes against (4.8333 / 6 = .8056).
A player who successfully avoided all votes had a 100% vote avoidance rate for the tribal council vote. For example, Sarah's marginal vote difference was .1933 for this tribal council vote (1.0000 vote avoidance rate - .8067 probable vote avoidance rate). Michaela, as the player voted out, had a negative marginal vote difference of -.4722 for this tribal council vote (.3333 vote avoidance rate - .8056 probable vote avoidance rate).
Example #6 – Season 39, Cycle 5:
# of players attending tribal council = 8
# of votes cast = 7 (one vote per player, except one player lost their vote)
# of players immune from receiving votes = 0
As a result of having lost her vote, Noura had a probable vote avoidance rate for this tribal council of 85.71%. Noura's probable vote avoidance rate was calculated by taking the random probability that Noura could receive a vote from each of the other players (1 / 7 = .1429 x 7 votes = 1.0000). Then the probable votes to receive is subtracted from the maximum vote against (7 - 1 = 6) to calculate the probable random votes to avoid. The probable avoidance rate is the result of dividing the probable votes to avoid by the maximum votes against (6 / 7 = .8571).
As the other players at the tribal council were in the same position (one vote each, not immune), their probable vote avoidance rate for this tribal council was 85.71%. For example, Dean's probable vote avoidance rate was calculated by taking the random probability that Dean could receive a vote from each of the other players (1 / 7 = .1429 x 6 votes = .8571). Then the probable random votes to receive is subtracted from the maximum vote against (6 - .8571 = 5.1429) to calculate the probable random votes to avoid. The probable avoidance rate is the result of dividing the probable votes to avoid by the maximum votes against (5.1429 / 6 = .8571).
A player who successfully avoided all votes had a 100% vote avoidance rate for the tribal council vote. For example, Dean's marginal vote difference was .1429 for this tribal council vote (1.0000 vote avoidance rate - .8571 probable vote avoidance rate). Tom, as the player voted out, had a negative marginal vote difference of -.6905 for this tribal council vote (.1667 vote avoidance rate - .8571 probable vote avoidance rate).
Example #7 – Season 38, Cycle 14:
# of players attending tribal council = 7
# of votes cast = 8 (one vote per player, except immune player had an extra vote)
# of players immune from receiving votes = 1
As the only immune player, Gavin was not eligible to receive votes. As the other players at the tribal council were in the same position (one vote each, not immune), their probable vote avoidance rate for this tribal council was 80.95%. For example, Julie's probable vote avoidance rate was calculated by taking the random probability that Julie could receive a vote from Gavin (1 / 6 = .1667 x 2 votes = .3333) in addition to the random probability that Julie could receive a vote from each of the other players (1 / 5 = .2000 x 5 votes = 1.0000). Then the probable random votes to receive is subtracted from the maximum vote against (7 - 1.3333 = 5.6667) to calculate the probable random votes to avoid. The probable avoidance rate is the result of dividing the probable votes to avoid by the maximum votes against (5.6667 / 7 = .8095).
A player who successfully avoided all votes had a 100% vote avoidance rate for the tribal council vote. For example, Julie's marginal vote difference was .1905 for this tribal council vote (1.0000 vote avoidance rate - .8095 probable vote avoidance rate). Ron, as the player voted out, had a negative marginal vote difference of -.2381 for this tribal council vote (.5714 vote avoidance rate - .8095 probable vote avoidance rate).
Example #8 – Season 41, Cycle 12:
# of players attending tribal council = 7
# of votes cast = 8 (one vote per player, except one player had an extra vote)
# of players immune from receiving votes = 1
As the only immune player, Danny was not eligible to receive votes. Xander, by virtue of having an extra vote, had a probable vote avoidance rate for this tribal council of 80.56%. Xander's probable vote avoidance rate was calculated by taking the random probability that Xander could receive a vote from Danny (1 / 6 = .1667) in addition to the random probability that Xander could receive a vote from each of the other players (1 / 5 = .2000 x 5 votes = 1.0000). Then the probable votes to receive is subtracted from the maximum vote against (6 - 1.1667 = 4.8333) to calculate the probable random votes to avoid. The probable avoidance rate is the result of dividing the probable votes to avoid by the maximum votes against (4.8333 / 6 = .8056).
As the other players at the tribal council were in the same position (one vote each, not immune), their probable vote avoidance rate for this tribal council was 80.48%. For example, Erika's probable vote avoidance rate was calculated by taking the random probability that Erika could receive a vote from Danny (1 / 6 = .1667) in addition to the random probability that Erika could receive a vote from each of the other players (1 / 5 = .2000 x 6 votes = 1.2000). Then the probable random votes to receive is subtracted from the maximum vote against (7 - 1.3667 = 5.6333) to calculate the probable random votes to avoid. The probable avoidance rate is the result of dividing the probable votes to avoid by the maximum votes against (5.6333 / 7 = .8048).
A player who successfully avoided all votes had a 100% vote avoidance rate for the tribal council vote. For example, Erika's marginal vote difference was .1952 for this tribal council vote (1.0000 vote avoidance rate - .8048 probable vote avoidance rate). Liana, as the player voted out, had a negative marginal vote difference of -.5190 for this tribal council vote (.2857 vote avoidance rate - .8048 probable vote avoidance rate).
Individual Vote Avoidance per Game:
A player's total vote avoidance score for the season can be calculated by adding their individual tribal councils together. For example, Cirie Fields (3rd place in season 16) had a probable vote avoidance rate of .8155 across her thirteen tribal councils where she was eligible to receive votes. She was able to avoid 73 votes which calculates to a vote avoidance rate of .9605 (73 / 76). Her marginal vote avoidance rate was .1450 (.9605 - .8155).
Marginal Rate vs. Raw Rate:
A final consideration for why the marginal rate is calculated vs. just the raw rate. If there are two players with the same raw success rate of avoidance, then their vote avoidance record would appear to be the same. However, when the marginal difference is calculated, the context of each of their respective tribal councils is properly considered. A comparison between Sandra Diaz-Twine (season 7) and Nick Wilson (season 37) shows that both players had a perfect vote avoidance record on their respective seasons, with a 100% avoidance raw rate. Despite the fact that Nick had avoided thirteen more votes over the course of his season, the marginal difference was actually less than Sandra's vote avoidance record. Therefore, Sandra finished with a higher overall avoidance score.
Adjusted Vote Avoidance Rates:
Since players are eliminated by receiving a plurality of the votes, players who are eliminated via a tribal council vote incur votes against themselves. As such, most eliminated players do not have a perfect vote avoidance record. On occasion, there are players that are eliminated with a 100% vote avoidance rate. Some notorious examples include medical evacuations (Jonathan Penner in season 16 & Neal Gottlieb in season 32), players who quit (Susan Hawk in season 8 & Colton Cumbie in season 27), and a player who was eliminated via a duel at Redemption Island (Rupert Boneham in season 27). In season 27, players voted out of the game were sent to Redemption Island, where they could compete in a duel to return to the game. Rupert was unique because he was not voted out, but switched with his partner (his wife Laura Boneham as she was voted out to go to Redemption Island).
Since marginal vote avoidance is a rate statistic, calibration is required. The reason for this is because one vote against isn't as informative about that players skill as 50 votes against is. Just because a player is successful in avoiding a small amount of votes, doesn't mean they will continue to be. So in addition to the raw avoidance rate that is calculated, a secondary adjusted rate is calculated to bring all voters up to a baseline. The baseline that is used is the merge line. Merge line represents the collective group of players (from all seasons) that are eliminated immediately before and immediately after the merge. The average number of maximum votes avoided for all merge line players is 24.0543. The second number required is the average marginal difference for all players, which is .0000. These two numbers can be used to calculate the adjusted marginal difference, or the final avoidance score.
If a player has 25 or more votes avoided, their score does not get adjusted. If their total votes avoided is 24 or less, then they get an adjustment up to 24.0543 maximum votes against. For example, Jonathan Penner (season 16) had not received a single vote in his two tribal councils that he attended. His probable vote avoidance for those two votes was .8758 (14.8889 probable votes to avoid / 17 maximum votes to receive). His marginal difference was .1242 (1.0000 - .8758). He was subsequently removed from the game for medical reasons. Since he only had a maximum of 17 potential votes against when he was eliminated, his adjusted score is calculated as follows:
.1242 marginal difference x 17 maximum potential votes against = 2.1114
24.0543 maximum votes against baseline - 17 maximum potential votes against = 7.0543 adjusted maximum potential votes against
7.0543 adjusted maximum potential votes against x .0000 average marginal difference = 0.0000
2.1114 marginal difference + 0.0000 adjusted marginal difference = 2.1114
2.1114 total marginal difference / 24.0543 maximum votes against baseline = .0878 adjusted marginal difference (otherwise referred to as avoidance score)
Vote Avoidance Rankings:
All individual vote avoidance rates (and adjusted rates) for a player's entire game were calculated and ranked against the entire population of player games. A percentile rank was calculated for the ordinal rank. Cirie Field's season 16 avoidance score of .1450 ranks her 48th overall out of 839 total player games, which fell into the 94.3 percentile.
Additionally, player ranking combines all the games each player has played into a single rate for their career. A percentile rank was calculated for the ordinal rank. Cirie Field's career accuracy score of .1241 ranks her 48th overall out of 697 total players, which fell into the 93.2 percentile.
To view a full list of vote accuracy rankings (both by season and career), please click the button below:
*** updated through season 46 ***
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