Monday, 12 March 2012

My tussles with Sam

Regular readers of this blog -- I've been led to believe that such exist -- will have noticed that Sam Gaffney has been kind enough to post comments with his performance on the games, and various other snippets.  It has been natural enough to compare results between us.

Sam was the only contestant to defeat me during the main part of the series (while I was playing from home, that is; obviously I lost against Brett while playing in the studio).  Of the nine televised games that Sam has played, in the head-to-head comparison I have won five and Sam has won four.  Close, and the aggregate scores are also pretty close (throughout this post, two values separated by a slash will comprise head-to-head score on the left and the corresponding solo score on the right):

Me516 / 60157.33 / 66.78
Sam505 / 58656.11 / 65.00

Obviously a mere nine games with that degree of closeness can hardly be conclusive.  Sam and I have been using the other games to stage a series of virtual matches between us, and it certainly serves as evidence for the suggestion that any single game is somewhat of a lottery.  Below are some statistics arising from these games (episodes 348 to 390, since he was present at the filming of episodes outside that range).

(As a minor point of scoring: Sometimes we have been unable to tell who solved a conundrum first, usually with single-second solves.  As a matter of expediency I have scored these as five points for each of us.  Also, only the first conundrum is used for scoring even if a second was available; my recollection is that this costs Sam a little, but our games were not tied at that point so it is appropriate.)

Firstly, the games won:


That's a pretty compelling advantage to Sam, but let's look at the aggregates and averages.  Averages are per-game for the "All" column, and per-round for the others.

Me2574 / 30321361 / 15471058 / 1175155 / 310
59.86 / 70.516.33 / 7.208.20 / 9.113.60 / 7.21
Sam2639 / 30701286 / 15251148 / 1205205 / 340
61.37 / 71.405.98 / 7.098.90 / 9.344.77 / 7.91

My average solo game was a bit under a point less than Sam's, but that expanded to approximately a point and a half of difference in the head-to-head comparison.  The individual round scores conform pretty much with expectations also: A slight average advantage to me on the letters, and more noticeable advantages to Sam on the other rounds, particularly the conundrum where Sam's greater solving speed is a factor.

There's something not apparent from the above, but which shows up clearly in the results organised by time: The three weeks leading up to the finals showed a marked shift in advantage to Sam.  This time also corresponds to environmental changes for each of us: Sam had been away on holidays and was actually playing two episodes a night in order to catch up; and I was undergoing a period of disrupted sleep patterns.  It is not at all clear if those factors effected results, or to what extent, but I certainly felt off my game for much of that period.  There's a third factor as well, which I'll get to later.

So here are the same statistics again, but split into those two ranges: First the 28 episodes from 348 to 375, and then the 15 episodes from 376 to 390.

Games won (episodes 348 to 375 first, then episodes 376 to 390):


The shift occasioned by those three weeks is clear.  (I want to stress that I did not cherry-pick those three weeks as the best splitting point, although they are close -- one game afterward would have made the difference more extreme -- but they do correspond to those external shifts as stated.)  Here's the breakdown for the first period:

Episodes 348 to 375

Me1655 / 1958 884 / 1003666 / 755105 / 200
59.11 / 69.936.31 / 7.167.93 / 8.993.75 / 7.14
Sam1643 / 1959765 / 951743 / 788135 / 220
58.68 / 69.965.46 / 6.798.85 / 9.384.82 / 7.86

As can be seen, up until that point I was close to even (and actually slightly ahead on head-to-head aggregate, although just behind on solo aggregate).  And here is the breakdown for those three weeks:

Episodes 376 to 390

Me 919 / 1074477 / 544392 / 420 50 / 110
61.27 / 71.606.36 / 7.258.71 / 9.333.33 / 7.33
Sam 996 / 1111521 / 574405 / 417 70 / 120
66.40 / 74.076.95 / 7.659.00 / 9.274.67 / 8.00

If we just look at my solo performance, then the situation seems rosy; I've gained not quite two points a game, and my numbers performance is significantly better, my letters and conundrum marginally so.

But looking at Sam's statistics shows that things have gone much better for him.  Sam gained a bit over four points on solo game score, which translated into almost eight points in the head-to-head situation.  His solo letters are almost a point better which stretched to a point and a half in the head-to-head comparison, and almost all of his gain can be attributed to that.  Is this the benefits of the vacation, or perhaps of playing multiple games a day?

I think that some light can be shed on it by going back to a suggestion that Victor made in the comments to an earlier post about the finalists.  The idea is to look at the number of "maximums" for each player -- times where they got the best possible result in a round.  For the finalists there just was not enough data to be useful, but in this case we are starting to get there.  A conundrum maximum is just a solution, and statistics for it can be found in the tables above.  For the other rounds:

Maximums (totals and averages)

Me: 348–375722.57642.29
Sam: 348–375652.32702.50

Note the very large drop in my average letters maximums -- over 20%.  While Sam's maximum percentage also dropped a little, it was by nowhere near as much.  This suggests that -- with all due respect to Sam's play -- the results are more reflective of a drop in my performance than a gain in his.

The as-yet-unmentioned but significant factor here is that those three weeks also happened to be extremely rich in full monties.  There were 14 potential ones in that time, or almost one a game (although they were clustered rather more strongly).  I had a particularly rough time with these; I found two of them, found a third but was unsure and did not risk it, found four (!) others either just as time was running out or just afterwards, and had another which would have been ruled invalid (DUALITIES).  In that time I found just two full monties to Sam's five, a reversal of the earlier section which went five-two the other way.

Is this indicative that I struggle with full monties?  Possibly yes -- certainly I'm not happy about my percentage of finding them within time.  But it might be more accurate to say that the large numbers of them increased the effects of my poor performance during that period.

Is this all me making excuses?  Perhaps!  Make of it what you will.  When all's said and done, Sam has gone away from these games 9 games ahead, a strong indicator of his level of performance.  But I hope to do somewhat better next series; I hope you'll join in.


Mark said...

Ok, at the risk of embarrassing myself, I'll have a go at writing down my answers and posting them on your blog. I'd better start learning multiples of 75!

Sam Gaffney said...

Hi Geoff, I enjoyed your statistical breakdown!

I do feel that I came back from my holiday much stronger on letters play. The first reason I would put this down to is freshness, which I find helps me on letters rounds in particular (though it doesn’t influence numbers rounds greatly). The other reason is that I worked on my technique a little, making an effort not to get bogged down for too many seconds trying one idea (e.g. -IEST). I actually started to run out of steam at about Ep391 from doing two episodes per day, I would be surprised if doing so many in a short space of time had any benefit.

You raise some interesting points about full monties - I always find it interesting that so many nine-letter words get solved in conundrums, yet only three were found in letter rounds by contestants in all of Series 4. My theory on that has two elements:

1. It is much easier to find a nine-letter word when you are looking for it. When you only have, say, a six or seven-letter word, your attention is often fixed on looking for a word one letter longer, particularly when you have a strong opponent sitting next to you in a tight situation. Having said that, there is no guarantee that I would have found MIDSTREAM or ESTABLISH if they had been conundrums.

2. Friendly letter mixes. One full monty that came up in the series was LATENCIES – a word like this is likely enough to be put up by Lily because of its common letters. The difficulty with these nine letters is that they can be shuffled around in all sorts of ways, nothing specific jumps out. Contrast this with the components of EQUIVOCAL, which have very few ways of being assembled, and are unlikely to be found in a letter round.

Incidentally, I have the worst Full Monty performance of all the L&N series winners, only finding ABDUCTION. I can't count the number of times I've seen Andrew, Tony and Jacob huddled together, pointing and laughing at me. I missed MIDSTREAM and ESTABLISH, along with three other words that I had never heard of at time of filming. I do feel that I was a trifle unlucky (along with my Ep345 opponent, Andy) not to have POLEDANCE counted - even if it's not in the dictionary, one still has to find it!

As for Mark, it would be great to see you putting your answers up on this blog, and learn your 75x table ASAP! Next would be the 25x table - this requires triple the work, but is crucial in mixes where 25 is the only large number.

Karen Anderson said...

Geoff, I had wondered whether Friday/Saturday may have been the last of your blog posts so I am pleased that you are going to continue. I, for one, am definitely a regular reader and, in fact, look forward each day to reading your latest post.

Along with Mark, I might also work on learning my 75 times tables. I am fairly good on the numbers for the most part, although occasionally I am let down by my lack of speed with multiples of 75. I am less concerned with multiples of 25 because I find that easier but there is definite room for improvement with my number work.

P.S. I thought at the time, and I still do, that POLEDANCE was a stroke of genius!

Sam Gaffney said...

Thank you Karen! Yes, Geoff's last blogs did have an eerie air of finality...

Geoff Bailey said...

Oh, my; I had not thought that my posts might come across that way. It certainly intend to continue indefinitely with this blog. Thank you for your comments, Karen, and I'm glad that you have been enjoying it.

Thanks also to Mark -- I look forward to hearing about how you do. The good thing is that you'll inevitably improve through the process of playing, so at some point you'll be able to look back at your performances and see that in action.

And Sam: Thanks for your expansive comments, and the friendly competition throughout. You've definitely kept me on my toes!

And heh about the other finalists. *chuckles*