Post by thisismyotheraccount on Jul 9, 2019 20:00:11 GMT -5
Throughout this we will look at the set of bonus puzzles after episode 2340 and the set of bonus puzzles after episode 5850.
This way we will analyze all bonus puzzles since players were given RSTLNE and then had to choose 3 consonants and 1 vowel.
(I think this is true but could be wrong on the episode number switch
And also analyze a more "modern" set of puzzles; in this case season 31 and later.
The most straight forward way to determine the best bonus letters would be to look at the (percent) frequency that each bonus letter appears in each set of puzzles:
all bonus puzzles after episode 2340
O 9.5
A 8.5
I 8.1
E 7.4
R 5.1
T 4.8
N 4.8
U 4.6
H 4.5
G 4.4
S 3.7
P 3.7
L 3.6
B 3.6
D 3.5
C 3.3
Y 3.2
F 3.1
W 2.4
K 2.3
M 2.2
V 1.7
J 0.8
Z 0.5
Q 0.4
X 0.4
NUMBER OF PUZZLES: 3414
Best letter choices: H G P O
all bonus puzzles after episode 5850
O 9.8
A 8.9
I 7.8
E 7.3
N 5.3
R 5.2
T 4.8
U 4.8
G 4.2
H 4.1
P 4.1
D 3.7
L 3.6
C 3.5
S 3.4
B 3.3
Y 3.3
F 2.7
W 2.4
M 2.2
K 1.9
V 1.7
J 0.8
Z 0.5
Q 0.5
X 0.3
NUMBER OF PUZZLES: 1122
Best letter choices: G H P O
In both sets of puzzles G H P and O are the best choices. But in the bonus round the RSTLNE gives us some more information that we can use.
A common "Wheel" word ending is "ING". And after we are given our "free" letters, if a word has this ING ending, we would see _N_ at the end of the word.
For both sets of puzzles when we see a word that's 5 letters or longer that ends in _N_ there's about a 75% chance that the ending is in fact ING. 75% is far from a guarantee, but when we take advantage of the category ("What are you doing?" and "Fun & Games" almost always have an ING ending),
and look at the structure of the puzzle (often you can diagram the types of words in the puzzle: verbs, adjectives, etc.) we can tease out if the _N_ ending is actually ING or not. For the sake of analysis, lets assume we can do this consistently.
This means that guessing G or I and revealing the G or I in the ING ending has no value to us. We already know this information. Other I's and G's are still valuable however.
So lets look at puzzles with _N_ endings and those without _N_ endings, in each of our sets of bonus puzzles this time excluding I's and G's that are a part of an ING ending.
Below are the puzzles that have a word 5 letter or longer that have an ending of _N_ after we are given our "free" letters.
puzzles with a _N_ ending in puzzle after episode 2340
O 8.6
A 7.4
I 5.3
N 4.6
E 4.3
U 4.1
R 3.8
P 3.7
D 3.5
T 3.5
H 3.5
B 3.3
S 3.2
K 3.1
L 2.9
C 2.8
Y 2.7
W 2.7
G 2.2
F 2.2
M 2.0
V 1.4
J 0.6
Z 0.4
X 0.4
Q 0.3
NUMBER OF PUZZLES: 462
Best letter choices: P D H O
puzzles with a _N_ ending in puzzle after episode 5850
O 8.9
A 7.6
I 5.3
E 4.7
R 4.5
N 4.4
D 4.2
U 4.1
P 4.0
T 3.3
B 3.2
H 3.1
S 3.0
L 2.9
C 2.9
W 2.8
Y 2.8
K 2.5
M 2.2
F 2.1
G 2.1
V 1.3
Z 0.5
J 0.4
X 0.4
Q 0.3
NUMBER OF PUZZLES: 227
Best letter choices: D P B O
puzzles without a _N_ ending in puzzle after episode 2340
O 9.6
A 8.7
E 8.0
I 7.6
R 5.3
T 5.1
H 4.7
U 4.7
G 3.8
S 3.8
L 3.7
N 3.7
P 3.7
B 3.7
D 3.5
C 3.4
F 3.3
Y 3.2
W 2.4
K 2.2
M 2.2
V 1.7
J 0.8
Z 0.5
Q 0.4
X 0.4
NUMBER OF PUZZLES: 2952
Best letter choices: H G P O
puzzles without a _N_ ending in puzzle after episode 5850
O 10.0
A 9.3
E 8.0
I 7.0
R 5.4
T 5.2
U 4.9
H 4.4
P 4.1
N 4.0
L 3.7
C 3.7
D 3.6
S 3.5
Y 3.4
B 3.4
G 3.3
F 2.8
W 2.3
M 2.1
V 1.9
K 1.7
J 0.9
Z 0.5
Q 0.5
X 0.3
NUMBER OF PUZZLES: 895
Best letter choices: H P C O
P and O remain solid choices while, B C D G and H fight for the last two consonant spots depending on which set of puzzles you use and if the puzzle contains a _N_ ending or not.
Many of these consonants are just 1 or 2 tenths of a percent difference from each other making it hard to argue that one is a substantially better choice over another.
Up to now we've assumed that revealing any unknown letter of a puzzle has the same value as revealing any other letter. But is that true?
It would seem that revealing the first letter of a word make is more helpful than revealing the last letter of a word when it comes time to start guessing the whole puzzle.
Lets look at the distribution of only the first letter of all the words in our sets of bonus puzzles.
Only 1st letters of puzzles after episode 2340
B 10.7
A 8.2
P 7.9
H 7.1
F 6.9
W 6.1
O 5.8
G 5.5
T 5.3
C 5.0
S 3.8
M 3.8
I 3.8
D 3.2
J 3.2
V 2.8
Y 1.8
L 1.7
K 1.7
U 1.4
Q 1.3
R 1.2
E 1.0
N 0.7
Z 0.2
X 0.0
NUMBER OF PUZZLES: 3414
Best letter choices: B P H A
Only 1st letters of puzzles after episode 5850
B 11.1
A 10.0
P 9.3
O 7.3
H 7.1
W 6.5
F 6.1
G 5.0
C 4.3
T 4.1
M 3.9
I 3.7
J 3.4
D 3.3
V 2.9
Y 2.1
U 1.8
Q 1.8
S 1.8
K 1.1
E 1.0
L 0.8
R 0.7
N 0.6
Z 0.3
X 0.0
NUMBER OF PUZZLES: 1122
Best letter choices: B P H A
Surprisingly over 10% of all words in a bonus puzzle start with the letter B, with A following close behind. Many of these A words are (A, AN, AND) so we shouldn't be too tempted into changing our vowel choice,
but some of the consonants we considered appear with double the frequency as others when looking at first letters of words.
Lets look at the full puzzles again, this time doubling the value of revealing the first letter of a word while also excluding any value for revealing an I or G in a word ending in ING 5 letters long or more.
Double value of revealing 1st letter of word after episode 2340 (no value for I's or G's in ING ending)
O 8.8
A 8.4
I 6.7
E 6.3
H 5.0
T 4.9
B 4.8
R 4.4
P 4.4
U 4.1
G 3.8
F 3.7
S 3.7
C 3.6
D 3.5
N 3.3
L 3.3
W 3.1
Y 2.9
M 2.4
K 2.2
V 1.9
J 1.2
Q 0.6
Z 0.5
X 0.3
NUMBER OF PUZZLES: 3414
Best letter choices: H B P O
Double value of revealing 1st letter of word after episode 5850 (no value for I's or G's in ING ending)
O 9.4
A 9.1
E 6.3
I 6.2
P 4.9
T 4.7
B 4.6
H 4.6
R 4.5
U 4.3
C 3.7
D 3.7
N 3.5
G 3.3
F 3.2
L 3.1
S 3.1
Y 3.1
W 3.1
M 2.4
V 1.9
K 1.8
J 1.2
Q 0.7
Z 0.5
X 0.3
NUMBER OF PUZZLES: 1122
Best letter choices: P B H O
Valuing the reveal of the first letter more, and giving no value to reveals of I's and G's in ING endings, we find that both sets of bonus puzzles we're looking at have B H P and O as the most valuable letters to choose.
With these letters plus the RSTLNE, we should expect to reveal the first letter of 45% of bonus puzzle words, while only making a minimal sacrifice by not strictly choosing based on total letter frequency.
FINAL CONCLUSION: P B H O
I'd love to hear anyone's thoughts, something I should include or errors I overlooked.
The data comes from the buyavowel compendium which has some missing episodes and I pulled the data at a time when the last episode was #6972.
This way we will analyze all bonus puzzles since players were given RSTLNE and then had to choose 3 consonants and 1 vowel.
(I think this is true but could be wrong on the episode number switch
And also analyze a more "modern" set of puzzles; in this case season 31 and later.
The most straight forward way to determine the best bonus letters would be to look at the (percent) frequency that each bonus letter appears in each set of puzzles:
all bonus puzzles after episode 2340
O 9.5
A 8.5
I 8.1
E 7.4
R 5.1
T 4.8
N 4.8
U 4.6
H 4.5
G 4.4
S 3.7
P 3.7
L 3.6
B 3.6
D 3.5
C 3.3
Y 3.2
F 3.1
W 2.4
K 2.3
M 2.2
V 1.7
J 0.8
Z 0.5
Q 0.4
X 0.4
NUMBER OF PUZZLES: 3414
Best letter choices: H G P O
all bonus puzzles after episode 5850
O 9.8
A 8.9
I 7.8
E 7.3
N 5.3
R 5.2
T 4.8
U 4.8
G 4.2
H 4.1
P 4.1
D 3.7
L 3.6
C 3.5
S 3.4
B 3.3
Y 3.3
F 2.7
W 2.4
M 2.2
K 1.9
V 1.7
J 0.8
Z 0.5
Q 0.5
X 0.3
NUMBER OF PUZZLES: 1122
Best letter choices: G H P O
In both sets of puzzles G H P and O are the best choices. But in the bonus round the RSTLNE gives us some more information that we can use.
A common "Wheel" word ending is "ING". And after we are given our "free" letters, if a word has this ING ending, we would see _N_ at the end of the word.
For both sets of puzzles when we see a word that's 5 letters or longer that ends in _N_ there's about a 75% chance that the ending is in fact ING. 75% is far from a guarantee, but when we take advantage of the category ("What are you doing?" and "Fun & Games" almost always have an ING ending),
and look at the structure of the puzzle (often you can diagram the types of words in the puzzle: verbs, adjectives, etc.) we can tease out if the _N_ ending is actually ING or not. For the sake of analysis, lets assume we can do this consistently.
This means that guessing G or I and revealing the G or I in the ING ending has no value to us. We already know this information. Other I's and G's are still valuable however.
So lets look at puzzles with _N_ endings and those without _N_ endings, in each of our sets of bonus puzzles this time excluding I's and G's that are a part of an ING ending.
Below are the puzzles that have a word 5 letter or longer that have an ending of _N_ after we are given our "free" letters.
puzzles with a _N_ ending in puzzle after episode 2340
O 8.6
A 7.4
I 5.3
N 4.6
E 4.3
U 4.1
R 3.8
P 3.7
D 3.5
T 3.5
H 3.5
B 3.3
S 3.2
K 3.1
L 2.9
C 2.8
Y 2.7
W 2.7
G 2.2
F 2.2
M 2.0
V 1.4
J 0.6
Z 0.4
X 0.4
Q 0.3
NUMBER OF PUZZLES: 462
Best letter choices: P D H O
puzzles with a _N_ ending in puzzle after episode 5850
O 8.9
A 7.6
I 5.3
E 4.7
R 4.5
N 4.4
D 4.2
U 4.1
P 4.0
T 3.3
B 3.2
H 3.1
S 3.0
L 2.9
C 2.9
W 2.8
Y 2.8
K 2.5
M 2.2
F 2.1
G 2.1
V 1.3
Z 0.5
J 0.4
X 0.4
Q 0.3
NUMBER OF PUZZLES: 227
Best letter choices: D P B O
puzzles without a _N_ ending in puzzle after episode 2340
O 9.6
A 8.7
E 8.0
I 7.6
R 5.3
T 5.1
H 4.7
U 4.7
G 3.8
S 3.8
L 3.7
N 3.7
P 3.7
B 3.7
D 3.5
C 3.4
F 3.3
Y 3.2
W 2.4
K 2.2
M 2.2
V 1.7
J 0.8
Z 0.5
Q 0.4
X 0.4
NUMBER OF PUZZLES: 2952
Best letter choices: H G P O
puzzles without a _N_ ending in puzzle after episode 5850
O 10.0
A 9.3
E 8.0
I 7.0
R 5.4
T 5.2
U 4.9
H 4.4
P 4.1
N 4.0
L 3.7
C 3.7
D 3.6
S 3.5
Y 3.4
B 3.4
G 3.3
F 2.8
W 2.3
M 2.1
V 1.9
K 1.7
J 0.9
Z 0.5
Q 0.5
X 0.3
NUMBER OF PUZZLES: 895
Best letter choices: H P C O
P and O remain solid choices while, B C D G and H fight for the last two consonant spots depending on which set of puzzles you use and if the puzzle contains a _N_ ending or not.
Many of these consonants are just 1 or 2 tenths of a percent difference from each other making it hard to argue that one is a substantially better choice over another.
Up to now we've assumed that revealing any unknown letter of a puzzle has the same value as revealing any other letter. But is that true?
It would seem that revealing the first letter of a word make is more helpful than revealing the last letter of a word when it comes time to start guessing the whole puzzle.
Lets look at the distribution of only the first letter of all the words in our sets of bonus puzzles.
Only 1st letters of puzzles after episode 2340
B 10.7
A 8.2
P 7.9
H 7.1
F 6.9
W 6.1
O 5.8
G 5.5
T 5.3
C 5.0
S 3.8
M 3.8
I 3.8
D 3.2
J 3.2
V 2.8
Y 1.8
L 1.7
K 1.7
U 1.4
Q 1.3
R 1.2
E 1.0
N 0.7
Z 0.2
X 0.0
NUMBER OF PUZZLES: 3414
Best letter choices: B P H A
Only 1st letters of puzzles after episode 5850
B 11.1
A 10.0
P 9.3
O 7.3
H 7.1
W 6.5
F 6.1
G 5.0
C 4.3
T 4.1
M 3.9
I 3.7
J 3.4
D 3.3
V 2.9
Y 2.1
U 1.8
Q 1.8
S 1.8
K 1.1
E 1.0
L 0.8
R 0.7
N 0.6
Z 0.3
X 0.0
NUMBER OF PUZZLES: 1122
Best letter choices: B P H A
Surprisingly over 10% of all words in a bonus puzzle start with the letter B, with A following close behind. Many of these A words are (A, AN, AND) so we shouldn't be too tempted into changing our vowel choice,
but some of the consonants we considered appear with double the frequency as others when looking at first letters of words.
Lets look at the full puzzles again, this time doubling the value of revealing the first letter of a word while also excluding any value for revealing an I or G in a word ending in ING 5 letters long or more.
Double value of revealing 1st letter of word after episode 2340 (no value for I's or G's in ING ending)
O 8.8
A 8.4
I 6.7
E 6.3
H 5.0
T 4.9
B 4.8
R 4.4
P 4.4
U 4.1
G 3.8
F 3.7
S 3.7
C 3.6
D 3.5
N 3.3
L 3.3
W 3.1
Y 2.9
M 2.4
K 2.2
V 1.9
J 1.2
Q 0.6
Z 0.5
X 0.3
NUMBER OF PUZZLES: 3414
Best letter choices: H B P O
Double value of revealing 1st letter of word after episode 5850 (no value for I's or G's in ING ending)
O 9.4
A 9.1
E 6.3
I 6.2
P 4.9
T 4.7
B 4.6
H 4.6
R 4.5
U 4.3
C 3.7
D 3.7
N 3.5
G 3.3
F 3.2
L 3.1
S 3.1
Y 3.1
W 3.1
M 2.4
V 1.9
K 1.8
J 1.2
Q 0.7
Z 0.5
X 0.3
NUMBER OF PUZZLES: 1122
Best letter choices: P B H O
Valuing the reveal of the first letter more, and giving no value to reveals of I's and G's in ING endings, we find that both sets of bonus puzzles we're looking at have B H P and O as the most valuable letters to choose.
With these letters plus the RSTLNE, we should expect to reveal the first letter of 45% of bonus puzzle words, while only making a minimal sacrifice by not strictly choosing based on total letter frequency.
FINAL CONCLUSION: P B H O
I'd love to hear anyone's thoughts, something I should include or errors I overlooked.
The data comes from the buyavowel compendium which has some missing episodes and I pulled the data at a time when the last episode was #6972.
