About one and a half years ago, I published a post in which I wondered if a relatively long time series (3 complete years) of scores achieved in Classic Words solo (“CWs”, i.e. electronic Scrabble) could be used to assess my intellectual performance and intellectual decline associated with ageing (I am 75 now). Conclusions were mixed as no significant patterns emerged, except, maybe, better Classic Words scores during winter.

I now have more or less convinced myself that CWs is not a suitable tool for assessing my intellectual decline, for two reasons: (1) some inherent flaws in the way CWs stores and displays data² and, possibly linked with (1), some inconsistencies (2) in the time series of scores which I cannot explain away³.

Doubts about the way CWs records scores

The CWs scoring system follows exactly the same scheme as the original Scrabble⁴.

I have developed some doubts about the scores as reported by CWs, in particular the fact that the reported daily scores (Figure 2) are “averages” while the time profiles (Figure 3) are “moving averages”. The explanations provided say that In the line chart (i.e. Figure 3a), the average score is based on the last 10 games played before the date in the horizontal axis (moving average). Although I have contacted the game developer⁵ for details, I have never been able to reproduce the time series based on the individual average daily score.

Figure 4 provides an example of what happens when comparing individual daily scores (cf. Figure 2) with time profiles (cf. Figure 3a). The example is from one of the three devices on which I play CWs, a Samsung A9+ tablet.

It appears that the A9+ Sampled and 10-back curves initially coincide (e.g. in September 2024) but that they gradually shift apart, to the extent that the phase difference reaches about one month in February 2024.

Comparing devices

I play CWs on three devices: a Kindle Fire HD 8 (since December 2019), the above mentioned Samsung Galaxy Tab A9+ (since February 2024) and a Samsung Galaxy A32 4G phone (since July 2021). The same version of CWs is installed on all devices: CW Free v2.10.1. at the “Very hard” level⁶, in French.

The time patterns of use are very different: the Kindle Fire mostly in the morning, when I wake up, after quickly checking the news in the Guardian⁷; the Tab A9+ in the evening between 8 p.m. and midnight, and the A32 when I have to idle in a queue or wait for previous patient to be “processed” by the dentist. CWs provides no information on the number of games played but I guess the average would be 2 to 3 in the morning, 4 to 5 in the evening and once a week on the phone.

Figure 5 compares the daily scores over the same period as in Figure 4. The patterns over time are vastly different. The A32 phone can be ignored as the number of games is very different from the ones played on the other devices. As shown by the histogrammes below (Figure 6) average/median values tend to be similar (Kindle Fire: 25.0/25.9, A9+ tablet: 25.4/25.3, A32 phone: 25.2/25.1), but the time profiles are very different. The 0.05 and 0.95 percentiles are, respectively 23.5/26.3, 24.9/27.5 and 24.4/25.8. There are also marked differences between devices for standard deviation and skewness: 0.87/-0.25, 1.10/0.72 and 0.43/-0.17, respectively for Fire, A9+ and A32.

It seems very unlikely that the same CWs performance of the same individual should be completely different between the morning and the evening. The value of the coefficient of correlation between the A9+ and Fire time series is -0.033.

Conclusions

It is unlikely that any definite conclusion regarding cognitive performance variations over time can be derived from the use of Classic Words solo (CWs, solo Android Scrabble). This is because (1) the scores as recorded by CWs do not seem to have a verifiable behaviour over time and (2) the scores vary greatly across devices. Unless one accepts that the cognitive performance of the same person varies a lot during the span of one day, the observed behaviour does not allow any useful or convincing conclusions to be drawn.

Notes

1. The Po valley is renowned for it’s fog. My raingauge often records 0.4 mm of “rainfall” in the morning after a rainless but foggy night. Here is a text by d’Annunzio about fog in Venice taken from the Italian Notes blog: Usciamo. Mastichiamo la nebbia. La città è piena di fantasmi. Camminano Gli uomini senza rumore, fasciati di caligene. I canali fumigano. … Le lampadine lucono come in fuochi fatui in campo santo …. I fantasmi passano, sfiorano, si dileguano …. [qualcuno] Cammina senza Tacchi, senza Scarpe, senza sandali … Una falda di nebbia mi strischia su la Gota. frotta Una di ubriachi Urla lagiù, in fondo al traghetto. Refer to the Italian Notes in the link for the translation. ↩︎
2. It is clear that the primary aims of CWs are to provide entertainment and to be fun. Whatever the flaws of the scoring system, they will be perceived only by very inquisitive users like myself! CWs remains by far the best Android Scrabble available. And I will try to find some other measure of intellectual performance (to be defined!). I also admit that writing this post, preparing and collecting the data is fun too, maybe even meta-fun? ↩︎
3. Some facetious reader may want to suggest that this observation is itself is a sign of cognitive decline! ↩︎
4. The more you play Scrabble, the more you realize that there is a lot of logic in the scoring system. In fact, it largely conditions the strategy. For instance, if the first word you play is longer than 5 letters, and if it is not centered on the starting square, it will be very easy for the programme to come up with a seven-letter word that counts double twice. Therefore, in most cases, I prefer to start with a short word! ↩︎
5. The developer, SL, suggested that I root my devices, which would give me access to the score files. Not knowing exactly what I would find there, I prefer to abstain. On the other hand, if CWs should actually give me the original date, time and score of all games played, this would indeed be a treasure trove for a third post on the subject. ↩︎
6. The very hard level is not, actually very hard. It is characterized by the fact that CWs only exceptionally plays 7-letter words, which carry a bonus of 50 points. With some experience one learns how to take advantages of the idiosyncrasies built into the CWs algorithms. I win about 81%, 67% and 65% of the games, respectively, on the A32, A9+ tablet and Kindle Fire. Approximately half of the wins are achieved thanks to the “end of game bonus” because the CWs programme tends to keep difficult letters (Y, W) for the end. ↩︎
7. To be sure I don’t miss any of the the latest inventions that germinated in the brilliant minds of the Very stable genius and his cronies while I was asleep. ↩︎