More ruminations on Facebook Scramble Highscores

Quite a significant amount of traffic to this blog comes from people looking for information about Facebook Scramble highscores, what the highest score is.

Its a difficult one, for each grid, it actually says what the highest possible score is, if you get every word thats in the grid. It even lists how many words there are for each length up to eight letters, and when you've finished playing, it lists every word too.

This one time I was playing a game against a girl with a huge vocabulary, she got around 350, I was mighty impressed. But on the same grid, I set my own personal best score of around 250. It was a high scoring grid, worth around 2500 points in total.

There's only one way to get a score anywhere near the maximum, and that is to cheat.

Wikipedia has some details about typing speeds, it says that average for a professional is 60 WPM and super ninjas can do 120 WPM. I'm guessing average word length is 4.2 letters per word, which together means you get around 6 or 8 keystrokes per second. Thats for professional typist, maybe transcribing stuff, rather than thinking about what they're typing, but lets ignore that minor detail.

The spread of letters in a grid means that around 5% of the score comes from three-letter words, 20% from four-letters, 25% from both five- and six-letter words and then the bell curve drifts back down for longer words.

For a grid worth 1000 points, in professional keystroke terms, its going to take 260 seconds to get every single word, which is a shame cos you only have 180 seconds, three minutes. Its not physically possible to get every word, you run out of time. If you start with high-value long words and then work down to the shorter words, you run out of time in the middle of the four letterers.

The human brain doesn't even work like that. It looks for shorter words than adds -s on the end and -er and -ers, -ing, -inger, -ingers. The human brain starts simple and goes complex when its looking for words in scramble, rather than starting long and going simple.

I ran the sums.

If your grid is worth 2500 points, its going to take around 600 seconds to type every word, if you're going as fast as your nimble fingers can go, ten minutes. You're going to run out of time in the middle of doing six-letter words.

I reckon with human typing speed limitations the highest score is around 1200, thats ignoring the way the human brain works and ignoring any kind of thinking about what you're typing.

More Facebook Scramble graphs

Hi, after the other day's thrilling coverage of my successes with Facebook's Scramble game, I thought I'd play a bit more, get some more data and churn out a few more graphs.

This graph neatly shows the spread of the highest possible scores when you're playing on 5x5 grids. So usually you can get a maximum of 1400 points and very occasionally you can get 2000 or so. I'm not going to rule out a 3000 point grid, but its very unlikely.

So with all these potential points up for grabs, how do I do?

Looks like I most often get around 80 and 90 points, or less. But occasionally I'm on fire and beat 150. This is rare, but not impossible.

So how come I'm occasionally on fire? Do my neurons just click sometimes, or is it cos the board is a high scoring board, and I just do as well as usual? Lets have a look...

Its kind of a normal distribution, I get around 8% of the highest score possible. Sometimes more, sometimes up to 12% of the total available, but never like 20% or 30%, that's crazy talk. Its more of a balanced spread with the percentages than it is with the actual scores.

My high score as it stands is 167, but going by these graphs, maybe if I got a good board worth 2000 points and I was on fire and got 12%, then the highest theoretical score I got get without cheating is 240.

Hmm, warm fuzzy feelings of success. I just have to keep playing and one day, my luck will turn.

Or will it?

Take a look at this graph of acheived score against highest possible score

Look, Excel has put a trend line in for me, so I can see that for higher scoring boards I score generally higher. Thank you Excel. But really its more of just a random swarm of scores with no correlation to the highest possible. I don't generally get less than 60 points, but when I get a low score, that has little to do with the highest possible score, and likewise, my highest scores don't usually come on the highest scoring grids.

Here, this graph terrifies me:-

As the highest possible score for a grid rises, the percentage of available points I get gets lower. Sure this graph is a bit of a random swarm of killer bees, but you can see it goes downwards. The highest percentages come with the low score grids and the lowest percentages come with the high score grids.

Maybe its not just chance that's causing me to be so crap compared to wimmin with large vocabularies. There was a wee nagging thing at the back of my head, maybe I'm not typing fast enough, I'm running out of time. That would kind of explain the last graph. If I'm just finding and typing words at a constant rate then the better percentages would come on lower scoring boards.

Am I actually just typing all of this with a rod taped to my forehead? It would explain so much.

Rightio, how does any of this help?

Well, it doesn't really apart from proving that the quality of the grid has little to do with my success, and that I'm like a ninja when it comes to Excel graphs, at the expense of being a bit autistic when it comes to scribbling down numbers.

Now where?

Well, you get more points for longer words.
3 letters - 1 point
4 letters - 2 points
5 letters - 4 points
6 letters - 6 points
7 letters - 9 points
8 letters - 12 points
11 letters - 24 points

'Retirements' for gods sake, 'retirements'. Its an efficiency thing. This we already knew, its just its hard to resist. You've got some easy three letterers, so you go for them, completely ignoring the fact that 'retirements' saves you two hundred an odd keypresses.

So my new strategy to slay the competition is to never do three or four letter words. Its an efficiency thing, and those little bastards are wasting your time and my time.

Its like trying to drum up immense traffic to this website by writing popular articles in the hope that google adverts will pay out a couple of pence, when what I could really do with is more modest traffic buying my Shag Times book that's for sale at the bottom of the page for a few quid.

Its a recession, its an efficiency thing.

Facebook Scramble Statistics

I don't think I know anyone who isn't addicted to Scramble on Facebook, or judging by my Facebook thing, I know a lot of girls with large vocabularies.

Anyhoo, this is a cumulative frequency graph of my scores on Scramble. My average score is about 80, but I get around 85 and 95 most often now.

Pondering how people get huge scores without cheating, I thought about maybe its to do with how 'easy' the board is, and maybe wimmin with large vocabularies just hoover up a greater proportion of the possible words.

I mean, on average your highest possible score for a 5 x 5 grid is just over 1,200, and with my average, I get 7.8% of the highest possible, my spreadsheet says its got a standard deviation of 1.89%, that pretty constant, top whack I get 12%. So if a grid has a low highest possible value, I'll get a low score, and if the grid has a huge highest possible, then I'd get a higher score, but then so would anyone else.

Here, this graph shows a little bit of a correlation between the highest possible score and my achieved score.

So, based on the research carried out so far, if I wanted to beat the highest score in my wee Scramble circle, get to the top of my leaderboard, I'd need a grid with a highest possible score of around 4,500, or more than double the highest scoring grid I've seen.

So maybe that standard deviation is the same for everyone. If someone gets and average of 20% of the possible score. The average game for them will garner a score of 240, and if they're playing for a while, they'll get a grid worth 1,900 and if their stars are aligned, they peak at around 25% they can get their high score of 475.

See what I did there.