One measure of voting effectiveness is vote clustering. The ability of a player to cluster their vote with other player's votes increases their chances to eliminate players from the game. Since a plurality of votes is required to eliminate a player, not only must votes be cast accurately, they must be clustered. This means that votes must be placed in coordination with other players to reach a plurality. Each specific tribal council vote has a unique set of circumstances that must be accounted for to properly contextualize the vote cluster calculation. This is accomplished by calculating the actual clusters as a percentage of the weighted clusters. Weighted clusters are calculated by taking the total number of clusters possible (per voter) and dividing that number by the total number of players who are eligible for elimination. The percentage of actual clusters (vs. weighted clusters) represents the portion of clusters attained. By calculating this percentage, a player’s ability to cluster votes can be measured.
Weighted Clusters vs. Max Clusters:
An important distinction is made by using weighted clusters as the denominator in this calculation instead of max clusters. For example, a tribal council where there are five players (with no one immune and each player has one vote), the most any player could cluster is three.
Player A has four opportunities to reach the max cluster of three in this theoretical vote. Player A can vote with players B, C, and D to eliminate player E. Player A can vote with players B, C, and E to eliminate player D. Player A can vote with players B, D, and E to eliminate player C. Finally, player A can vote with players C, D, and E to eliminate player B. But there is a fifth outcome where the max cluster is reached for the tribal council. If players B, C, D, and E all vote together to eliminate player A, then the max cluster of three is reached (for each of players B, C, D, and E), but player A's cluster rate is zero (because they cannot vote for themselves). For player A, there are five total outcomes where the max cluster is reached in the tribal council, but one of those outcomes results in zero clusters for player A (4 max cluster outcomes / 5 total outcomes = 80%). By taking the individual max cluster (three) and discounting it by 20% (represents the one outcome with zero clusters for player A), the weighted clusters are calculated to be 2.4 (3 x (1 - .20)). The weighted cluster is accounting for the proportional outcome between the max cluster rate being achieved (by including the one zero cluster outcome). This is why it was selected to be the denominator for this rate statistic.
Below are eight different tribal councils where vote clustering 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 max clusters for this tribal council was 42. For example, Richard's max clusters was calculated by taking the clusters he could have with each player and adding up the individual clusters from all players, which equaled 42 max clusters.
The max clusters for each player were then divided by the total number of players who could receive votes. Each player's weighted clusters equaled 5.25 (42 / 8). A total of 42 (5.25 x 8) total clusters were possible for the tribal council.
A player who clustered their vote most effectively, likely voted for the eliminated player. For example, Rudy’s cluster percentage was .5714 for this tribal council vote (3 clusters / 5.25 weighted clusters). An ineffective cluster likely resulted in a vote for a player that was not eliminated. Richard's cluster percentage was .0000 for this tribal council vote (0 clusters / 5.25 weighted clusters).
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's max clusters for this tribal council was 42. Nick's max clusters was calculated by taking the clusters he could have with each player and adding up the individual clusters from all players, which equaled 42 max clusters.
As the other seven players were in the same position (one vote each, not immune), their max clusters for this tribal council was 36. For example, Tina's max clusters was calculated by taking the clusters she could have with each player and adding up the individual max clusters from all players, which equaled 36 total max clusters.
The max clusters for each player were then divided by the total number of players who could receive votes. Nick's weighted clusters equaled 6 (42 / 7). Everyone else's weighted clusters equaled 5.1429 (36 / 7). A total of 42 (6 + (5.1429 x 7)) total clusters were possible for the tribal council.
A player who clustered their vote most effectively, likely voted for the eliminated player. For example, Tina’s cluster percentage was .9722 for this tribal council vote (5 clusters / 5.1429 weighted clusters). An ineffective cluster likely resulted in a vote for a player that was not eliminated. Amber's cluster percentage was .1944 for this tribal council vote (1 cluster / 5.1429 weighted clusters).
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 player's max clusters for this tribal council was 10. For example, Teresa's max clusters was calculated by taking the clusters she could have with each player and adding up the individual clusters from all players, which equaled 10 max clusters.
The max clusters for each player were then divided by the total number of players who could receive votes. Each player's weighted clusters equaled 5 (10 / 2). A total of 30 (5 x 6) total clusters were possible for the tribal council.
This vote remained tied on the re-vote, therefore all players had the same cluster percentage. For example, Teresa’s cluster percentage was .4000 for this tribal council vote (2 clusters / 5 weighted clusters).
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's max clusters for this tribal council was 36. Mike's max clusters was calculated by taking the clusters he could have with each player and adding up the individual clusters from all players, which equaled 36 max clusters.
As the other six players were in the same position (one vote each, not immune), their max clusters for this tribal council was 30. For example, Will's max clusters was calculated by taking the clusters he could have with each player and adding up the individual max clusters from all players, which equaled 30 total max clusters.
The max clusters for each player were then divided by the total number of players who could receive votes. Mike and Carolyn's weighted clusters equaled 6 (36 / 6). Everyone else's weighted clusters equaled 5 (30 / 6). A total of 42 ((6 x 2) + (5 x 6)) total clusters were possible for the tribal council.
A player who clustered their vote most effectively, likely voted for the eliminated player. For example, Rodney's cluster percentage was .6000 for this tribal council vote (3 clusters / 5 weighted clusters). An ineffective cluster likely resulted in a vote for a player that was not eliminated. Mike's cluster percentage was .1667 for this tribal council vote (1 cluster / 6 weighted clusters).
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's max clusters for this tribal council was 30. Brad's max clusters was calculated by taking the clusters he could have with each player and adding up the individual clusters from all players, which equaled 30 max clusters.
As four players were in the same position (one vote each, not immune), their max clusters for this tribal council was 25. For example, Troy's max clusters was calculated by taking the clusters he could have with each player and adding up the individual max clusters from all players, which equaled 25 total max clusters.
Sarah played her steal-a-vote advantage and took Tai's vote, giving Sarah tow votes and leaving Tai without the ability to cast a vote. Sarah's max clusters for this tribal council was 26. Sarah's max clusters was calculated by taking the clusters she could have with each player and adding up the individual clusters from all players, which equaled 26 max clusters.
The max clusters for each player were then divided by the total number of players who could receive votes. Brad's weighted clusters equaled 5 (30 / 6). Sarah's weighted clusters equaled 4.3333 (26 / 6). Everyone else's weighted clusters equaled 4.1667 (25 / 6). A total of 30.3334 (5 + (4.3333 x 2) + (4.1667 x 4)) total clusters were possible for the tribal council.
A player who clustered their vote most effectively, likely voted for the eliminated player. For example, Troy's cluster percentage was .7200 for this tribal council vote (3 clusters / 4.1667 weighted clusters). An ineffective cluster likely resulted in a vote for a player that was not eliminated. Cirie's cluster percentage was .0000 for this tribal council vote (0 clusters / 4.1667 weighted clusters).
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 max clusters for this tribal council was 36. For example, Dean's max clusters was calculated by taking the clusters he could have with each player and adding up the individual max clusters from all players, which equaled 36 total max clusters.
The max clusters for each player were then divided by the total number of players who could receive votes. Each player's weighted clusters equaled 4.5 (36 / 8). A total of 31.5 (4.5 x 7) total clusters were possible for the tribal council.
A player who clustered their vote most effectively, likely voted for the eliminated player. For example, Janet's cluster percentage was .8889 for this tribal council vote (4 clusters / 4.5000 weighted clusters). An ineffective cluster likely resulted in a vote for a player that was not eliminated. Dean's cluster percentage was .2222 for this tribal council vote (1 cluster / 4.5 weighted clusters).
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's max clusters for this tribal council was 36. Gavin's max clusters was calculated by taking the clusters he could have with each player and adding up the individual clusters from all players, which equaled 36 max clusters.
As six players were in the same position (one vote each, not immune), their max clusters for this tribal council was 30. For example, Julie's max clusters was calculated by taking the clusters she could have with each player and adding up the individual max clusters from all players, which equaled 30 total max clusters.
The max clusters for each player were then divided by the total number of players who could receive votes. Gavin's weighted clusters equaled 6 (36 / 6). Everyone else's weighted clusters equaled 5 (30 / 6). A total of 42 ((6 x 2) + (5 x 6)) total clusters were possible for the tribal council.
A player who clustered their vote most effectively, likely voted for the eliminated player. For example, Julie's cluster percentage was .6000 for this tribal council vote (3 clusters / 5 weighted clusters). An ineffective cluster likely resulted in a vote for a player that was not eliminated. Rick's cluster percentage was .0000 for this tribal council vote (0 clusters / 5 weighted clusters).
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's max clusters for this tribal council was 35. Danny's max clusters was calculated by taking the clusters he could have with each player and adding up the individual clusters from all players, which equaled 35 max clusters.
As five players were in the same position (one vote each, not immune), their max clusters for this tribal council was 29. For example, Erika's max clusters was calculated by taking the clusters she could have with each player and adding up the individual max clusters from all players, which equaled 29 total max clusters.
As the only non-immune player with an extra vote, Xander's max clusters for this tribal council was 30. Xander's max clusters was calculated by taking the clusters he could have with each player and adding up the individual clusters from all players, which equaled 30 max clusters.
The max clusters for each player were then divided by the total number of players who could receive votes. Danny's weighted clusters equaled 5.8333 (35 / 6). Xander's weighted clusters equaled 5 (30 / 6). Everyone else's weighted clusters equaled 4.8333 (29 / 6). A total of 40 (5.8333 + (5 x 2) + (4.8333 x 5)) total clusters were possible for the tribal council.
A player who clustered their vote most effectively, likely voted for the eliminated player. For example, Erika's cluster percentage was .8276 for this tribal council vote (4 clusters / 4.8333 weighted clusters). An ineffective cluster likely resulted in a vote for a player that was not eliminated. Deshawn's cluster percentage was .4138 for this tribal council vote (2 clusters / 4.8333 weighted clusters).
Individual Vote Clusters per Game:
A player's total vote cluster score for the season can be calculated by adding their individual tribal council clusters together. For example, Amanda Kimmel (3rd place in season 15) had a cluster rate of .9185 across her nine votes cast. She was able to cluster her nine votes 37 times out of a combined weighted clusters of 40.2814.
Adjusted Vote Cluster Rates:
Since players are not allowed to vote for themselves for elimination, most players who are eliminated via a tribal council vote cast an ineffective vote (relative to clustering). As such, most eliminated players have at least one tribal council where they are ineffective at vote clustering. On occasion, there are players that are eliminated without voting. 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 cluster percentage is a rate statistic, calibration is required. The reason for this is because one vote cast isn't as informative about that players skill as eleven votes cast is. Just because a player is effective in clustering their first vote, doesn't mean they will continue to be. So in addition to the cluster 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 weighted clusters for all merge line players is 18.1070. The second number required is the average cluster percentage for all players, which is .6632. These two numbers can be used to calculate the adjusted vote cluster rate, or the final cluster score.
If a player has 18.1070 or more weighted clusters, their score does not get adjusted. If their total weighted clusters is 18.1070 or less, then they get an adjustment up to 18.1070 weighted clusters. For example, Russell Swan (season 19) had 7.2000 weighted clusters in his only tribal council that he attended. His cluster rate was .9722 (7 / 7.2000). He was subsequently injured at a reward challenge and was medically evacuated from the game. Since he only had one vote cast when he was eliminated, his adjusted score is calculated as follows:
.9722 cluster % x 7.2000 weighted clusters = 7 clusters
18.1070 weighted cluster baseline - 7.2000 weighted clusters = 10.9070 adjusted weighted clusters
10.9070 adjusted weighted clusters x .6632 average cluster % = 7.2335
7 clusters + 7.2335 adjusted clusters = 14.2335 total clusters
14.2335 total clusters / 18.1070 weighted cluster baseline = .7861 adjusted cluster rate (otherwise referred to as cluster score)
Vote Cluster Rankings:
All individual vote cluster 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. Amanda Kimmel's season 15 cluster score of .9185 ranks her 46th overall out of 839 total player games, which fell into the 94.6 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. Amanda Kimmel's career cluster score of .8510 ranks her 58th overall out of 697 total players, which fell into the 91.8 percentile.
To view a full list of vote cluster rankings (both by season and career), please click on the button below:
*** updated through season 46 ***
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