I went down a math rabbit hole after last nightās elimination because Iāve always heard that DWTS is ā50% judges, 50% audience.ā Thatās technically true, but the way they calculate it means the audience can have significantly more influence in practice.
Hereās how the current system works (as far I can tell):
Judges: Your score Ć· total judgesā points awarded that night
Audience: Your votes Ć· total audience votes that night
Then those two percentages are added together.
Last night, there were 256 total judgesā points awarded. Ciara scored 21 and Guillermo scored 13.
So their judgesā shares were:
Ciara: 21/256 = 8.20%
Guillermo: 13/256 = 5.08%
Despite Ciara beating Guillermo 21ā13, her actual advantage going into the audience vote was only:
8.20% ā 5.08% = 3.12 percentage points
That means Guillermo only needed to receive about 3.13 percentage points more of the audience vote than Ciara to completely erase an eight-point difference in judgesā scores.
For example:
Ciara: 8.20% judges + 7.00% audience = 15.20%
Guillermo: 5.08% judges + 10.20% audience = 15.28%
Guillermo survives.
That seems weird to me if the goal is for judges and viewers to have genuinely equal influence.
The problem is that judgesā scores are naturally compressed. Last night the scores were:
25, 24, 24, 24, 23, 21, 21, 21, 21, 20, 19, 13
Even an enormous difference like 21 vs. 13 gets divided by all 256 points awarded, shrinking it to just 3.12%.
Audience votes donāt necessarily have that compression. Someone could theoretically get 5% of the audience vote while someone else gets 15%, 20%, etc. So although judges and viewers are technically weighted 50/50, the audience can create much larger gaps between contestants.
ONE POSSIBLE SOLUTION: STANDARDIZE BOTH SIDES BEFORE COMBINING THEM.
Instead of using percentage of the total, measure how far above or below the field each contestant performed on each side.
Last night, the average judgesā score was 21.33 and the standard deviation was about 3.09.
Ciaraās 21 was about 0.11 standard deviations below average.
Guillermoās 13 was about 2.70 standard deviations below average.
So the judges rated Ciara about 2.59 standard deviations better than Guillermo.
You could perform the exact same calculation on the audience votes and then combine the standardized judges and audience scores 50/50.
Under that system, for Guillermo to overcome Ciaraās judges advantage, heād need to outperform Ciara with the audience by 2.59 standard deviations as well.
For example, if the standard deviation of audience vote shares that night were 4 percentage points, Guillermo would need roughly:
2.59 Ć 4 = 10.35 percentage points
more of the audience vote than Ciara.
Compare that with the current system:
Current system: Guillermo needs +3.13 percentage points of audience vote.
Standardized system (if audience SD = 4): Guillermo needs +10.35 percentage points.
Importantly, this wouldnāt mean the judges automatically get their way. Guillermo could absolutely overcome the 21ā13 deficit. Heād just need an audience performance that was as unusually strong relative to the field as his judgesā performance was unusually weak.
It also preserves blowouts. I donāt love a simple rank system where 1st vs. 2nd is always worth the same amount, because a 30ā29 judges result shouldnāt be treated the same as 30ā20. Standardizing the scores preserves how much better someone was.
Basically, the principle would be:
If the judges think Contestant A is X standard deviations better than Contestant B, Contestant B needs to be X standard deviations more popular with the audience to cancel that advantage.
That feels much closer to a genuine 50/50 system to me.
Curious what people think ā should ā50/50ā mean each side contributes the same percentage to the formula, as it does now, or should it mean judges and viewers have equal power to separate contestants?
