53 vs 54 point word rarity in 5x5

[BoggleOtaku]

Hi Naboka,

When you mentioned excitement at finding 37 point words, I was confused as to why.
Then I started thinking about how excited my daughter would be at 67 point words.
And, finally, I realized you were obviously talking about 4x4 games.

Brutally faced with my ignorance of the most basic of facts regarding 4x4 and in abject apology at any mistakenly inferred slight, I present to you in meagre recompense a dynamic heat histogram of 4x4 words shown with and at same scale as the 5x5 plot.

Enjoy!

Wordtwist 5x5 Word Point Competition trends.png

[Naboka]

Hi Naboka,

When you mentioned excitement at finding 37 point words, I was confused as to why.
Then I started thinking about how excited my daughter would be at 67 point words.
And, finally, I realized you were obviously talking about 4x4 games.

Brutally faced with my ignorance of the most basic of facts regarding 4x4 and in abject apology at any mistakenly inferred slight, I present to you in meagre recompense a dynamic heat histogram of 4x4 words shown with and at same scale as the 5x5 plot.

Enjoy!

Wordtwist 5x5 Word Point Competition trends.png

Thanks. Definitely seem to be different universes, 4X4 and 5X5--and probably 6x6.

Long ago I concluded that playing the highest-point-value best words in 4x4 would require finding the q/z combination. Those two letters immediately truncate the board, resulting in a much lower number of available words. Perhaps I'm wrong but I don't think a board exists in 4x4 where a player could reliably get 701 points, which are required to retire it. In other words, playing those boards wreak havoc on average total word scores.

Playing the lower-word-availability boards has opened a new world of possibilities. I keep finding boards with words used in chemistry that have to be the unique ones that you're interested in. Long words that it's likely no one has found before. Words probably even more rare than coelenterazines.

Your comments about your wife and daughter remind me of my life. Though my wife often finds me to be a tedious bore, (not that yours finds you as such) she's been hearing too many comments from friends about how much they or their husbands enjoy conversations with me. She's beginning to reassess the value of ideas that to her are utterly meaningless. She's a pragmatist and has little patience with the physics that belie our sensory grasp of reality. If she has no immediate practical use for it, goodbye.

Since I often have a reader's rather than listener's grasp on word pronunciation, my pronunciations can sometimes be off. English is a weirdly inconsistent language with spelling and pronunciation.

I remember a while back rolling my eyes when artistic types started pronouncing homage with a silent h. I looked through several dictionaries to see if that version of pronunciation was an option and couldn't find it. Nope. But that's the way so many people are pronouncing it now.

What's really interesting is to monitor the spelling of kindergarteners. When I first started working with my wife, a very smart kid had used chree in a written sentence. ??? Tree. Our tongues are positioned so closely to the same spots when making both sounds. Almost every 5 year old I've worked with has been shocked that tree begins with t rather than ch. Same with chrain and so many others. It's often how we speak, but not how we spell.

Because the schwa sound can be confusing, I often have the correct word on a board, but am frantically trying to spell it correctly. Mostly I'm doing educated guesses for long words from arranging word elements so I'm not visually following the letter paths on the actual board.

Do 5x5 boards follow the pattern of very high point best words existing primarily on boards with fewer words?

Time to get on the bike and enjoy beig physical.

[Naboka]

ps: I did a head slap about my comment. I meant the Fibonacci spiral not the sequence. One of those senior moments of conflation. (Not that I wasn't guilty of being prone to the same stuff in my teens, 20's, 40's etc.)

I've done a lot of painting and drawing since retiring, and the application of the Fibonacci spiral or golden spiral too artwork was a revelation.

Also, I forgot to admire your color choices for the data spread.

Also, being lazy, I only gave the spread a cursory view. One thing that strikes me is the spacing of ultrarare unique words on both graphs. It seems that the spacing on the bottom row of the 5x5 is greater than the 4x4. This suggests a higher frequency of finds in 4x4. Makes me wonder if this is partially due to commonization of words that would otherwise be unique such as z/q words or -izations words. When a player familiar with 4x4 triggers on -izations, only 8 letters need to be reconfigured to arrive at a 16/33 outcome. And that can take seconds or less. I guess such combinations exist in 5x5.

Part of my wondering is the existence of words in both formats that have never ever been found. Words of unknown length that no one has discovered. It would be interesting to know which format has more.

Here are some examples of the spiral. Nature is filled with them.
OIP-1345991439.Fn8I3GuVff2OXN9yrIWWPwHaEv.jpg

OIP-2032695211.VXMk0fgIY0siUV28uLiwcAHaHa.jpg



OIP-2200272153.BCEbysFA0KcxfETj7k8U6gHaE_.jpg

OIP-2821235551.SjboxF5XFo8UYia7F47zxwHaHa.jpg

[BoggleOtaku]

Nice pictures! It's a reasonable conflation: Just like DNA encodes the sequence of the protein, Fibonacci series provide the pattern of its namesake spiral, which approximates the golden spiral. Of course you have to still correctly fold the linear amino acid sequence into the 3D protein (nontrivial) and the 1D Fibonacci pattern into the 2D (if on planar or cone surface) spiral (trivial in comparison).

There's likely only one 54-point word in 5x5, as has been discussed previously, whereas there are at least three 37-pt in 4x4 (I saw three looking through some of the monthly competition records. So that would suggest more max word length boards in 4x4 leading to high frequency of finds. That seems like at least one more reason for your observation in addition to your thought on it.

I agree with your comments in the "next next" to last post (as one might literally put it in Japanese) regarding ultra rare words in small word-number boards. Take the 54 point ultra rare QUINQUASEXAGINTILLIARDTHS: so many special letters suck the capability of the board to have huge numbers of words. That seems pretty common in 5x5--you often see boards with very few words, maybe 7 or less letters, except for one or two 9+ ultra rare words, and these can often be 15+ letters. The board was apparently handcrafted to contain that word. Once that one long word (with perhaps special letters) is forced into the board, it seems like probabilities of having lots of words decreases. (Maybe further letters are randomly chosen to populate the board instead of choosing remaining ones to maximize word count, since the purpose for that board has already been fufilled by putting in the extra long word.)

Between 2016-2021, 5x5 had higher frequency top word points relative to 4x4 then and 5x5 now. There were many high scoring words there and then that ended commonly with -izations. I think this supports your comments about why 4x4 may have higher frequency than 5x5 currently.

What I found most striking in comparison of the two plots:
1. The statics for word points pre-2015 are almost identical between 4x4 and 5x5. It made me think that not only the same dictionary was used for both boards, but also that perhaps the 4x4 boards were reused in 5x5 by embedding in a 5x5 board and adding extra letters around two edges . Now I am wondering what the commonality in the actual words in word point lists for 4x4 and 5x5. Neither goes up nearly to their potential, allowing the improved boards post 2016.

2. Where as the 5x5 has odd even word point parity almost everywhere, the post-2021 4x4 charts have a pattern that almost goes in groups of threes at high word point. At least it is not nearly as good a match to an odd/even pattern.

BTW, I liked you story about pronunciation. Our daughter when maybe 3 get really excited about cliff nests. I wondered how she even knew what a cliff nest was. Had she secretly been watching "The Swallows of Capistrano"? I helpfully told her that we don't have cliff nests around here. Light dawned when she asked about cliff nest chrees.

[BoggleOtaku]

On a whim just now I tried 4x4. On about my 6th load board click I started play and got a 37 point word.
Despite my excitement, I managed not to accidently dump the game.

Beginners luck, I guess. And the timely warning!

It wasn't one of the ones I had found in the records and put in my plot. So I know there are at least 4 now.

[bwt1213]

Regarding the pronunciation of "tree" as "chree", there was a recent conversation about that on reddit. One person, a putative linguist, claimed that "chree" is how EVERYONE pronounces "tree". I said it aloud to myself to check, and I don't. Far as I know, I never have. And then I thought about how my wife said it, and how my children pronounce it, and how various people I know well say it. NONE of them say "chree". Have I ever heard it pronounced that way? Yes, frequently; it seems to be especially common in Chicago. I wonder if it goes with "dese" and "dose" and "dem", and the famous "da" -- as in "Da Bayrz".

[Boulevardiere]

I happened to score a 53-point word (PW) today. I was under the impression that a 53PW hadn't turned up previously, so I took a look through the monthly records.
I found the last time it was scored was apparently September 2024.

Oddly, I just found the same 53-point word. To give credit where credit is due, I doubt I would have strung all of the pieces together correctly if I hadn't noticed your existing 25-letter word record before playing that board. Thanks for making me look good! I'm also learning a lot about the mechanics of the game from this thread.

[Naboka]

Naboka, first time seeing that word!

I think you are right about rarity. There are different classes of rarity, so then we can have intersectional rarity where membership in more classes increases rarity, maybe in a multiplicative effect. It is pretty fascinating to look at something complex like a plane, car, IC chip, etc. and realize to make it, every part had to have a unique name, or biology every part of a cell, every chemical, etc. Or inspection, every different kind of defect has a name. If the object itself is rare or obscure, then the names of its parts may have such intersectionality.

Quick brainstorming on classes of rareness. Rareness increases with:
1. Length of word
2. Complexity of spelling
3. Difficulty of pronunciation.
4. Obsolescence (no longer needed, e.g. descriptive term of old technology that has been replaced. I guess you could also call this historical distance. Example: damascening
5. Linguistic distance: Borrowing from other languages and not widely adopted or incoroprated. Historic borrowing and loss. Example: When trade opened up with Japan I assume a cluster of rare words was incorporated into the English language as a result and to facilitate that market.
6. Cultural distance. Examples: 32 or some odd names for precipitation in extreme northern countries. Different names for items in different dialects. (-ISE vs -IZE)
7. Specificity of profession: terms for things, phenomenae, theoretical concepts (e.g., REORTHONORMALIZATION). I guess when you get into concepts, you could have increased rarity as the distance from known reality increases. Superstring theory probably has a lot of ultrarare ultrarare terms. (#7 covers speaking precisely as needed to facilitate moving the frontier of knowledge forward as opposed to #9 below.)
8. Rareness of entity or process described.
9. A desire to obscure, hide, protect livelihood, sound sophisticated, build group identity, i.e., do something other than communicate simply and clearly. examples: Cryptology, Gang or Teen slang (skibidi bussin lowkey yeet dab), some dialects (e.g., Cockney in part to foster community identity), patent language. Even professional language in clinical settings (e.g., myocardial infarction).
10. Newness. We were recently posting about mediabuzz words like Snowapocalypse and when do they become common enough to incorporate.

One through three are related to Zipf's law of abbrevation: word frequency negatively correlated to complexity.

Seven and eight are great examples of how structure can form in rare words, with clusters of rarity formed around an uncommon entity or esoteric, recondite concept and its related functionality. Patterned clusters occur in professional textbooks (corpus linguistics yield collocation biases).

Wordtwist (especially with Naboka dare I say) is the ultimate blackhole of ultrarare word collocation bias.

Have you noticed for your categorizations that simply adding an S (in 4x4) can change a 15/14 common or 15/18 wide word into a 16/30 UR word? Adding the re prefix can have the same impact, converting common to ultrarare. This would have to apply to 5x5 in the midlength words, though would guess it's inapplicable to monster words.

A game I just played demonstrated how alternate spellings can also produce levels of rarity. The attached 4 words are alternates of presbycusis, which we seniors probably know from hearing tests. It's hearing loss related to aging. (I don't think I've ever played presbycusis so have no idea as to it's rarity.)

Not sure how you would incorporate these empirical bits into your developing theory, but the more knowledge the merrier.

At least, until it buries you in despair.

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