Answer Scoring in Plates Across America®

The main premise of Plates Across America® is to complete a route in as few puzzles as possible. The general rule is:

The longer the answer, the further you travel. 

If you play the game in our "Race Mode", at the end of the race it will show all the puzzles with your and your opponent's answers side-by-side (see image at right). If you compare the scores, you might see something that does not match the "longer is better" rule. That is because there are some exceptions to that rule. This article explains the nuances of how we calculate the scores to help explain when the rule does and does not apply.  

Lemmas

The word "lemma" has multiple meanings, but here we mean it to be the "root" of word. For example: "wanders", "wandered" and "wandering" are related words and share the same lemma word "wander".  This concept is important in the scoring because we reward a good vocabulary more than someone's ability to creatively add extra letters (also known as "stemming" words). For example, someone should not get a higher score than you just because they to added a trailing "s" to pluralize the word.

Plurals

The important part of understanding how plurals are scored is awareness that there are two different cases.

• Case (1) Both the plural form and that word's lemma both match. In this case, pluralizing the word is somewhat superfluous and is only really serving to increase the letter count.
• Case (2) The lemma of the word does not match and the pluralized form is required to be a valid answer. i.e., the ending "s" is required to make the word match.

For Case (1), the plural answer will be scored the same as the singular.  There is no penalty for using the plural form, but also there is no credit for the extra letters.

For Case (2), the plural answer will be ranked below all the other non-plural answers whose lemmas match the puzzle. For example, if the puzzle is "BDS", then "bedside" would score higher than "bedazzles" even though "bedside" has fewer letters. It is far easier to find a word with "B" and "D" and to pluralize it then it is to find a non-plural word with "B", "D" and "S".

Word Frequency

Once all the possible solution words are sorted out by whether they or not they are lemmas and their lengths, the next thing we consider is the word's frequency.  All other things being equal, the less frequently occurring words will score higher than more common, everyday words.

For example, for the puzzle "ADT", the word "audit" would score higher than "adult" even though they both have 5 letters. The word "audit" is not used as frequently as the word "adult" in normal usage. Note that the score advantage based on word frequency is not as dramatic as it is for the lemma vs. non-lemma case: it provides some advantage, but the word length scoring is more important.

Summary

Though word length is the prime element in determining the quality of the answer, it is not the only factor. Understanding the nuances of scoring will help you finish routes faster and score better in the game.

If you have not tried the game, and are interest, here's a link:

Game Demo

Happy Travels!

Interesting Puzzle Stats

If you have played Plates Across America™ and understand how the game's word puzzles work, you might have asked yourself questions, like "How many puzzles are there?".  In this post, we try to provide some interesting facts about the underlying puzzle data. In case you have not yet played the game, we'll first briefly go over how the puzzles work, however you could also familiarize yourself with the game by trying the free demo here:

https://platesacrossamerica.com/demo

 

Puzzle Rules

A "puzzle" is three letters, where the order matters. A valid answer to the puzzle is a dictionary word in which those three puzzle letters appear and are in that same order. The letters do not have to be consecutive within the word and can appear anywhere as long as the ordering is not violated. Some examples:

Puzzle	Valid Answers
ABT	about, tabletop, bicarbonate
IOL	idol, airfoil, antisocial

Most important to the game is that (generally) the longer answers are worth more than shorter answers. The longer the answer, the further you travel with each puzzle. The goal is to try to cover the distance in a route with the fewest possible puzzles.

There are a few nuances to the scores assigned to the answers so that it is not always strictly that longer ones score higher. For instance, if you just add an "s" to the end of a word to pluralize it, that would have the same value as the non-pluralized word even though it has one more letter. The full run-down of all the scoring rules will be covered in a future blog post.

The Dictionary

The puzzles are derived from the words in the game's dictionary. We built this dictionary trying to cover the most common word usages. For example, though the dictionary does include a lot of medical terminology, it is not trying to be comprehensive to cover all the more esoteric words. 

Our dictionary is not perfect, which is why we provide an in-game feature to allow players to tell us when they find something we are missing. Here's a picture of the "Report Word" link we show in the game:

So, how big is our dictionary? As of this writing, it has 98,614 words. Every week, we add more as our players report words that should be added to the dictionary.

The Puzzles

All the puzzles we show in the game have at least one valid dictionary word as its answer. In theory, there are 26 * 26 * 26 = 17,576 different 3 letter combinations. However, not all these combinations have a matching word, e.g., "WZX". In the end, there are only a total of 14,863 puzzles in our game. 

Some other facts:

• For the two example puzzles given above, ABT has 1,045 matching words and and IOL has 2,075.
• The puzzle with the most matches is IES with 18,080 different matching words.

The Answers

If you add up all the valid answers across all of the 14,863 puzzles, you would get that there are 8,071,767 total answers.  That means that the average puzzle has 543 valid answers.

Other facts:

• With a dictionary of 96,614 words, this means that the average word matches 82 puzzles.
• Since a valid answer must contain at least 4 characters, the fewest puzzles a word can match turns out to be 3. e.g., The word "pool" only matches POO, POL, and OOL.

Parting Thoughts

We hope you found this small sample of game statistics interesting.  If you have questions or think of anything related to the game's data that you are interested in, please let us know.

Happy Travels!