I recently posted a ranking of all of the teams from Season 13-24 based on their average signature dish scores. Someone commented that it would be interesting to see signature dish score vs rank, and to see if there was any correlation between those. I did just that! So, this is signature dish score vs rank for all 12 seasons with the 1-5 rating system. 

Each graph has a trendline, an equation, and an R\^2 value. The x axis for each value is order eliminated, so to find last place's predicted score, you would have to plug in 1 for x. As you can tell, each trend line predicts a general positive increase in signature dish score based on rank.

  
The most important piece of data is the R\^2 value. The R\^2 value tells you how strong the correlation between two variables is, with 1 being perfect correlation and 0 being no correlation. This tells you how well the trend line can predict the data. I put rankings of all the R\^2 values in the second imagee

The most strongly correlated season between performance and signature dish is Season 15, with an R\^2 value of 0.4006. That value doesnt indicate very strong correlation, but it is better than most. Each chef in the bottom 6 received a 2/5 or lower, with all but one of them receiving a 1/5. Each chef in the top 12 received a 3/5 or higher, with the exception of Ashley.

  
The weakest correlation came from Season 13. 0.0061 is a very, very low correlation, basically zero from a statistical lens. As you can tell from the graph, the ratings are very sporadic compared to rankings, with the winner in La Tasha getting a 1/5.

  
As you can tell, with even the highest correlation being fairly low, a chef's signature dish score is not a perfect indicator of how well they will place in a season. It's almost like a chef can improve or have an off day. Crazy, right?

Season 13-24 Signature Dishes vs Performance