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):

	Points	Average
Me	516 / 601	57.33 / 66.78
Sam	505 / 586	56.11 / 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:

Me	16
Sam	25
Tied	2

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.

	All	L	N	C
Me	2574 / 3032	1361 / 1547	1058 / 1175	155 / 310
	59.86 / 70.51	6.33 / 7.20	8.20 / 9.11	3.60 / 7.21
Sam	2639 / 3070	1286 / 1525	1148 / 1205	205 / 340
	61.37 / 71.40	5.98 / 7.09	8.90 / 9.34	4.77 / 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):

Me	12	4
Sam	14	11
Tied	2	0

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

	All	L	N	C
Me	1655 / 1958	884 / 1003	666 / 755	105 / 200
	59.11 / 69.93	6.31 / 7.16	7.93 / 8.99	3.75 / 7.14
Sam	1643 / 1959	765 / 951	743 / 788	135 / 220
	58.68 / 69.96	5.46 / 6.79	8.85 / 9.38	4.82 / 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

	All	L	N	C
Me	919 / 1074	477 / 544	392 / 420	50 / 110
	61.27 / 71.60	6.36 / 7.25	8.71 / 9.33	3.33 / 7.33
Sam	996 / 1111	521 / 574	405 / 417	70 / 120
	66.40 / 74.07	6.95 / 7.65	9.00 / 9.27	4.67 / 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)

	Letters		Numbers
Me: 348–375	72	2.57	64	2.29
376–390	30	2.00	35	2.33
Sam: 348–375	65	2.32	70	2.50
376–390	33	2.20	37	2.47

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.