One measure of voting effectiveness is vote accuracy. The ability of a player to vote other players out of the game demonstrates their ability to know who is being targeted by a plurality of the tribe. Since a plurality of votes is required to eliminate a player, not only must votes be clustered, they must be cast accurately. This means that votes must be placed on the person who is being eliminated and not placed on players that will remain in the game. Each specific tribal council vote has a unique set of circumstances that must be accounted for to properly contextualize the vote accuracy calculation. This is accomplished by calculating the marginal change (increase or decrease) between the actual vote and the probable vote rates. The probable vote accuracy rate is calculated by taking the number of votes a player has to cast divided by the number of people that are eligible to receive a vote. The underlying assumption is that the probable vote accuracy rate is equal to the likelihood of a player voting correctly if their vote was completely random. By calculating the marginal difference between the probable vote accuracy rate and the actual vote accuracy rate, a player’s ability to vote accurately can be measured.
Below are eight different tribal councils where vote accuracy 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 accuracy rate for this tribal council was 12.5%. For example, Richard's probable vote accuracy rate was calculated by taking the random probability that Richard could vote for any one player (1 / 7 = .1429) and multiplying it by the random probability of that same player being the player voted out (1 / 8 = .1250). .1429 x .1250 = .0179. There were seven players who could have been voted out by Richard, therefore, 7 x .0179 = .1250.
A player who voted correctly had a 100% vote accuracy rate for the tribal council vote. For example, Rudy’s marginal vote difference was .8750 for this tribal council vote (1.0000 vote accuracy rate - .1250 probable vote accuracy rate). An incorrect vote cast resulted in a 0% vote accuracy rate. Richard had a negative marginal vote difference of -.1250 for this tribal council vote (.0000 vote accuracy rate - .1250 probable vote accuracy 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 had a probable vote accuracy rate for this tribal council of 14.3%. Nick's probable vote accuracy rate was calculated by taking the random probability that Nick could vote for any one player (1 / 7 = .1429) and multiplying it by the random probability of that same player being the player voted out (1 / 7 = .1429). .1429 x .1429 = .0204. There were seven players who could have been voted out by Nick, therefore, 7 x .0204 = .1429.
As the other seven players were in the same position (one vote each, not immune), their probable vote accuracy rate for this tribal council was 14.3%. For example, Tina's probable vote accuracy rate was calculated by taking the random probability that Tina could vote for any one non-immune player (1 / 6 = .1667) and multiplying it by the random probability of that same player being the player voted out (1 / 7 = .1429). .1667 x .1429 = .0238. There were six players who could have been voted out by Tina, therefore, 6 x .0238 = .1429.
A player who voted correctly had a 100% vote accuracy rate for the tribal council vote. For example, Tina’s marginal vote difference was .8571 for this tribal council vote (1.0000 vote accuracy rate - .1429 probable vote accuracy rate). An incorrect vote cast resulted in a 0% vote accuracy rate. Amber had a negative marginal vote difference of -.1429 for this tribal council vote (.0000 vote accuracy rate - .1429 probable vote accuracy 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 the 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 six players had a probable vote accuracy rate for this vote of 25.0%. For example, Teresa's probable vote accuracy rate was calculated by taking the random probability that Teresa could vote for any one player (1 / 2 = .5000) and multiplying it by the random probability of that same player being the player voted out (1 / 2 = .5000). .5000 x .5000 = .2500. There were two players who could have been voted out by Teresa, therefore, 2 x .2500 = .5000.
A player who voted correctly had a 100% vote accuracy 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 voter had a 100% vote accuracy rate for this tribal council vote. An incorrect vote cast resulted in a 0% vote accuracy rate. Teresa had a negative marginal vote difference of -.5000 for this tribal council vote (.0000 vote accuracy rate - .5000 probable vote accuracy 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 one of the two immune players, Mike had a probable vote accuracy rate for this tribal council of 16.7%. Mike's probable vote accuracy rate was calculated by taking the random probability that Mike could vote for any one player (1 / 6 = .1667) and multiplying it by the random probability of that same player being the player voted out (1 / 6 = .1667). .1667 x .1667 = .0278. There were six players who could have been voted out by Mike, therefore, 6 x .0278 = .1667.
As the other six players were in the same position (one vote each, not immune), their probable vote accuracy rate for this tribal council was 16.7%. For example, Will's probable vote accuracy rate was calculated by taking the random probability that Will could vote for any one non-immune player (1 / 5 = .2000) and multiplying it by the random probability of that same player being the player voted out (1 / 6 = .1667). .2000 x .1667 = .0333. There were five players who could have been voted out by Will, therefore, 5 x .0333 = .1667.
A player who voted correctly had a 100% vote accuracy rate for the tribal council vote. For example, Carolyn’s marginal vote difference was .8333 for this tribal council vote (1.0000 vote accuracy rate - .1667 probable vote accuracy rate). An incorrect vote cast resulted in a 0% vote accuracy rate. Mike had a negative marginal vote difference of -.1667 for this tribal council vote (.0000 vote accuracy rate - .1667 probable vote accuracy 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 had a probable vote accuracy rate for this tribal council of 16.7%. Brad's probable vote accuracy rate was calculated by taking the random probability that Brad could vote for any one player (1 / 6 = .1667) and multiplying it by the random probability of that same player being the player voted out (1 / 6 = .1667). .1667 x .1667 = .0278. There were six players who could have been voted out by Brad, therefore, 6 x .0278 = .1667.
As four players were in the same position (one vote each, not immune), their probable vote accuracy rate for this tribal council was 16.7%. For example, Troy's probable vote accuracy rate was calculated by taking the random probability that Troy could vote for any one non-immune player (1 / 5 = .2000) and multiplying it by the random probability of that same player being the player voted out (1 / 6 = .1667). .2000 x .1667 = .0333. There were five players who could have been voted out by Troy, therefore, 5 x .0333 = .1667.
Sarah played her steal-a-vote advantage and took Tai's vote, giving Sarah two votes and leaving Tai without the ability to cast a vote. Sarah had a probable vote accuracy rate for this tribal council of 16.7% (per vote). Sarah's probable vote accuracy rate was calculated by taking the random probability that Sarah could vote for any non-immune player (1 / 5 = .2000) and multiplying it by the random probability of that same player being the player voted out (1 / 6 = .1667). .2000 x .1667 = .0333. There were five players who could have been voted out by Sarah, therefore 5 x .0333 = .1667.
A player who voted correctly had a 100% vote accuracy rate for the tribal council vote. For example, Sarah’s marginal vote difference was .8333 for this tribal council vote (1.0000 vote accuracy rate - .1667 probable vote accuracy rate). An incorrect vote cast resulted in a 0% vote accuracy rate. Aubry had a negative marginal vote difference of -.1667 for this tribal council vote (.0000 vote accuracy rate - .1667 probable vote accuracy 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 seven players were in the same position (one vote each, not immune), their probable vote accuracy rate for this tribal council was 12.5%. For example, Dean's probable vote accuracy rate was calculated by taking the random probability that Dean could vote for any one non-immune player (1 / 7 = .1429) and multiplying it by the random probability of that same player being the player voted out (1 / 8 = .1250). .1429 x .1250 = .0179. There were seven players who could have been voted out by Dean, therefore, 7 x .0179 = .1250.
A player who voted correctly had a 100% vote accuracy rate for the tribal council vote. For example, Janet's marginal vote difference was .8750 for this tribal council vote (1.0000 vote accuracy rate - .1250 probable vote accuracy rate). An incorrect vote cast resulted in a 0% vote accuracy rate. Dean had a negative marginal vote difference of -.1250 for this tribal council vote (.0000 vote accuracy rate - .1250 probable vote accuracy 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 had a probable vote accuracy rate for this tribal council of 16.7% (per vote). Gavin's probable vote accuracy rate was calculated by taking the random probability that Gavin could vote for any one player (1 / 6 = .1667) and multiplying it by the random probability of that same player being the player voted out (1 / 6 = .1667). .1667 x .1667 = .0278. There were six players who could have been voted out by Gavin, therefore, 6 x .0278 = .1667.
As six players were in the same position (one vote each, not immune), their probable vote accuracy rate for this tribal council was 16.7%. For example, Julie's probable vote accuracy rate was calculated by taking the random probability that Julie could vote for any one non-immune player (1 / 5 = .2000) and multiplying it by the random probability of that same player being the player voted out (1 / 6 = .1667). .2000 x .1667 = .0333. There were five players who could have been voted out by Julie, therefore, 5 x .0333 = .1667.
A player who voted correctly had a 100% vote accuracy rate for the tribal council vote. For example, Gavin's marginal vote difference was .8333 for this tribal council vote (1.0000 vote accuracy rate - .1667 probable vote accuracy rate). An incorrect vote cast resulted in a 0% vote accuracy rate. Julie had a negative marginal vote difference of -.1667 for this tribal council vote (.0000 vote accuracy rate - .1667 probable vote accuracy 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 had a probable vote accuracy rate for this tribal council of 16.7% (per vote). Danny's probable vote accuracy rate was calculated by taking the random probability that Danny could vote for any one player (1 / 6 = .1667) and multiplying it by the random probability of that same player being the player voted out (1 / 6 = .1667). .1667 x .1667 = .0278. There were six players who could have been voted out by Danny, therefore, 6 x .0278 = .1667.
As five players were in the same position (one vote each, not immune), their probable vote accuracy rate for this tribal council was 16.7%. For example, Erika's probable vote accuracy rate was calculated by taking the random probability that Erika could vote for any one non-immune player (1 / 5 = .2000) and multiplying it by the random probability of that same player being the player voted out (1 / 6 = .1667). .2000 x .1667 = .0333. There were five players who could have been voted out by Erika, therefore, 5 x .0333 = .1667.
As the only non-immune player with an extra vote, Xander had a probable vote accuracy rate for this tribal council of 16.7% (per vote). Xander's probable vote accuracy rate was calculated by taking the random probability that Xander could vote for any one player (1 / 5 = .2000) and multiplying it by the random probability of that same player being the player voted out (1 / 6 = .1667). .2000 x .1667 = .0333. There were five players who could have been voted out by Xander, therefore, 5 x .0333 = .1667.
A player who voted correctly had a 100% vote accuracy rate for the tribal council vote. For example, Erika's marginal vote difference was .8333 for this tribal council vote (1.0000 vote accuracy rate - .1667 probable vote accuracy rate). An incorrect vote cast resulted in a 0% vote accuracy rate. Deshawn had a negative marginal vote difference of -.1667 for this tribal council vote (.0000 vote accuracy rate - .1667 probable vote accuracy rate).
Individual Vote Accuracy per Game:
A player's total vote accuracy score for the season can be calculated by adding their individual tribal council votes together. For example, Rob Mariano (2nd place in season 8) had a probable vote accuracy rate of .1842 across his seven votes cast. He was able to vote accurately seven times, which calculates to a vote accuracy rate of 1.0000 (7 / 7). His marginal vote accuracy rate was .8158 (1.0000 - .1842).
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 voting, then their voting record would appear to be the same. However, when the marginal difference is calculated, the context of each of their respective tribal council votes is properly considered. A comparison between Stephenie LaGrossa (season 11) and Parvati Shallow (season 16) shows that both players had a perfect voting record on their respective seasons, with a 100% accurate raw voting rate. Despite the fact that Stephenie cast three more total votes over the course of her season, the marginal difference was actually slightly less than Parvati's season voting record. Therefore, Parvati finished with a higher overall accuracy score.
Adjusted Vote Accuracy Rates:
Since players are not allowed to vote for themselves for elimination, most players who are eliminated via a tribal council vote cast an incorrect vote (vote for someone who remains in the game). As such, most eliminated players do not have a perfect voting record. On occasion, there are players that are eliminated with a 100% vote accuracy rate. Some notorious examples include medical evacuations (Michael Skupin in season 2 & Russell Swan in season 19), players who quit (Osten Taylor in season 7 & Julie McGee in season 29), and players voted out without casting a vote in that tribal council due to a stolen or lost vote (Jason Linden in season 39 & Brad Reese in season 41). There was even a player that was eliminated post-merge having never cast a single vote in the game (Chris Noble in season 36).
Since marginal vote accuracy is a rate statistic, calibration is required. The reason for this is because one vote cast isn't as informative about that player's skill as eleven votes cast is. Just because a player is accurate in their first vote, doesn't mean they will continue to be. So in addition to the raw accuracy 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 votes cast for all merge line players is 3.7174. The second number required is the average marginal difference for all players, which is .4843. These two numbers can be used to calculate the adjusted marginal difference, or the final accuracy score.
If a player has four or more votes cast, their score does not get adjusted. If their total votes cast is three or less, then they get an adjustment up to 3.7174 votes. For example, Jason Linden (season 39) had cast one accurate vote in his first tribal council that he attended. His probable vote accuracy for that vote was .1000 (1 vote / 10 players who could receive votes). His marginal difference was .9000 (1.0000 - .1000). At his second tribal council, his vote was stolen and therefore he did not cast a vote. He was voted out and eliminated at that tribal council. Since he only had one vote cast when he was eliminated, his adjusted score is calculated as follows:
.9000 marginal difference x 1 vote cast = .9000
3.7174 vote baseline - 1 vote cast = 2.7174 adjusted votes
2.7174 adjusted votes x .4843 average marginal difference = 1.3160
.9000 marginal difference + 1.3160 adjusted marginal difference = 2.2160
2.2160 total marginal difference / 3.7174 vote baseline = .5961 adjusted marginal difference (otherwise referred to as accuracy score)
Vote Accuracy Rankings:
All individual vote accuracy 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. Rob Mariano's season 8 accuracy score of .8158 ranks him 16th overall out of 839 total player games, which fell into the 98.2 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. Rob Mariano's career accuracy score of .6703 ranks him 64th overall out of 697 total players, which fell into the 90.9 percentile.
To view a full list of vote accuracy rankings (both by season and career), please click button below:
*** updated through season 46 ***
Comments