I like Carol, and I like Rachel, but who's better?

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Graeme Cole
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I like Carol, and I like Rachel, but who's better?

Post by Graeme Cole » Fri Aug 23, 2013 9:17 pm

There's only one way to find out...

Image

Thanks to Mike Brown's diligent note-taking over the years, and the huge effort to digitise those notes, undertaken by lots of people who aren't me, we can settle this.

Let's get all the nitty-gritty methodology out of the way first. These statistics exclude all numbers rounds for which the target or contestant declarations are not known. Besides that, all shows are included up to the end of series 68.

Assumptions

If one or both of the contestants solved a numbers round, the arithmetician is generally not asked for her solution. So for all these stats, I've made the assumption that the arithmetician always does at least as well as the contestants - that is, if either contestant maxed it, the arithmetician did too. I expect this assumption is nearly always correct anyway, and where it isn't, I don't see any reason to suppose making this assumption would skew the results more towards one arithmetician than the other.

The wiki, and therefore the database, doesn't record whether the arithmetician solved it in the 30 seconds or needed some extra time. So the best we can do here is just assume that if the wiki says the arithmetician solved it, they solved it, and not bother about how long it took.

What to measure

We mustn't mix results for different types of pick. Some picks, like 6 small and 4 large, are harder than others, and in the earlier years the easier selections (1 large, 2 large) were much more common. So we can't just lump them all together into one average, we've got to look at them separately.

The most obvious performance indicator is the max percentage - for each round, ask "did Carol/Rachel (or either of the contestants) correctly declare the closest possible for this round?" and work out the percentage. The problem with this is that the arithmetician doesn't usually give her working if it's not an exact solution. Also, Rachel gets told when a numbers game isn't possible (don't know if this was true for Carol as well), and this can arguably make the task of finding a non-exact but optimal solution easier - if you know that 637 isn't possible, you know not to bother looking for 91*7, for example. So to avoid this problem entirely, in all the tables below, I've only looked at the numbers games that were solvable exactly, and considered how many were solved by the arithmetician or the contestants.


Overall average

This is probably the table you want to see. It's the main table which includes all of Carol's and all of Rachel's games (up to 28th June 2013). As you can see, on average, Rachel steamrolls over Carol in all five picks.

Code: Select all

              LARGES    SOLVED     TOTAL         %           Includes all known solvable numbers games
     Carol         0       653       770    84.805
                   1      7820      8225    95.076
                   2      1303      1404    92.806
                   3       219       256    85.547
                   4       272       350    77.714

    Rachel         0       219       239    91.632
                   1      1747      1785    97.871
                   2       566       592    95.608
                   3       121       127    95.276
                   4       167       184    90.761

Breakdown by year

The table above shows four and a half years of Rachel, and 26 years of Carol. Carol's average over those 26 years is weaker than Rachel's average, but there's more to the story if we look at smaller parts of Carol's career.

When Carol was Rachel's age, she was very, very good. For example, over the whole of 1987 and 1988, there were 509 1-large games which were solvable exactly. Not a single one over those two years went unsolved in the studio.

Let's look at 80s Carol...

Code: Select all

              LARGES    SOLVED     TOTAL         %           Includes all known solvable numbers games, 1982-1989 and 2009 onwards
    80s Carol      0        69        74    93.243
                   1      1333      1366    97.584
                   2       288       293    98.294
                   3         6         7    85.714
                   4         3         4    75.000

    Rachel         0       219       239    91.632
                   1      1747      1785    97.871
                   2       566       592    95.608
                   3       121       127    95.276
                   4       167       184    90.761
Picks of three large and four large were almost unheard of in the early days, so we'll ignore those. But 80s Carol outperforms Rachel on 6 small and 2 large, whereas Rachel still has a very slight edge on 1 large.

How about 90s Carol?

Code: Select all

              LARGES    SOLVED     TOTAL         %           Includes all known solvable numbers games, 1990-1999 and 2009 onwards
    90s Carol      0       235       256    91.797
                   1      2810      2904    96.763
                   2       298       324    91.975
                   3        74        83    89.157
                   4        91       107    85.047

    Rachel         0       219       239    91.632
                   1      1747      1785    97.871
                   2       566       592    95.608
                   3       121       127    95.276
                   4       167       184    90.761
And here's noughties Carol...

Code: Select all

              LARGES    SOLVED     TOTAL         %           Includes all known solvable numbers games from 2000 onwards
    00s Carol      0       349       440    79.318
                   1      3677      3955    92.971
                   2       717       787    91.105
                   3       139       166    83.735
                   4       178       239    74.477

    Rachel         0       219       239    91.632
                   1      1747      1785    97.871
                   2       566       592    95.608
                   3       121       127    95.276
                   4       167       184    90.761
So Carol started off very well, then eventually tailed off a bit. That's also shown if we plot it on a graph. On this graph, data points representing a fewer than ten known occurrences of a particular numbers pick in a year have been excluded.

Image

Initially, Rachel solved relatively few 6 small and 4 large rounds, but she turned that around pretty quickly. No prizes for guessing when Rachel discovered the 4 large tricks. And yes, in 2012, all solvable 4 large games (34 of them) were solved in the studio. Not sure how much of that is due to Rachel and how much to Jack Worsley, but there it is. (19 of the 34 were solved by one or both contestants.)

So we've learned that Carol was as good as Rachel is now when she started, but her average is dragged down by the later years. Since 2011, Rachel has had a 90% solve rate in all five numbers picks. In 2011 and 2012 they were all greater than 95%. We're only half way through 2013, so it might yet be true for this year as well. She solves them just as consistently as Carol did at her best in the 1980s - and back then, 1 large and 2 large were the only picks worth practising.

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Andy Platt
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Re: I like Carol, and I like Rachel, but who's better?

Post by Andy Platt » Fri Aug 23, 2013 11:16 pm

Interesting, nice one Graeme.

What's surprising to me is how excellent their solve rates are in 6 small. The rest is pretty much logical/expected, including Carol's decline as she gets older.

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Re: I like Carol, and I like Rachel, but who's better?

Post by Gavin Chipper » Fri Aug 23, 2013 11:50 pm

Andy Platt wrote:Interesting, nice one Graeme.

What's surprising to me is how excellent their solve rates are in 6 small. The rest is pretty much logical/expected, including Carol's decline as she gets older.
I wonder if the decline was down to less practising because of other commitments or generally less inclination to do so than actual mental decline though. It's not as if she was that old, and I don't think mental decline at that age is particularly pronounced.

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Re: I like Carol, and I like Rachel, but who's better?

Post by Thomas Carey » Sat Aug 24, 2013 12:36 am

Is it bad that I get really excited when I see a new thread by Graeme Cole?
cheers maus

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Re: I like Carol, and I like Rachel, but who's better?

Post by Clive Brooker » Sat Aug 24, 2013 3:11 pm

Graeme Cole wrote:The wiki, and therefore the database, doesn't record whether the arithmetician solved it in the 30 seconds or needed some extra time. So the best we can do here is just assume that if the wiki says the arithmetician solved it, they solved it, and not bother about how long it took.
This deficiency in the data fatally undermines any analysis along these lines in my view. Whether an arithmetician is recorded as having given a correct solution is partly dependent on editing, the whim of the producer and other such factors, none of which can be assumed to have remained constant over the years.

Having had a quick look at a couple of Mike's scans, the information may well be there (to the end of series 64 at least) so perhaps the situation can be retrieved.

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Re: I like Carol, and I like Rachel, but who's better?

Post by Dave Preece » Sat Aug 24, 2013 4:01 pm

Excellent as ever Graeme, any chance of answering my last 'Ask Graeme!' question please?

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Re: I like Carol, and I like Rachel, but who's better?

Post by Mike Brown » Sat Aug 24, 2013 9:34 pm

Clive Brooker wrote:Having had a quick look at a couple of Mike's scans, the information may well be there (to the end of series 64 at least) so perhaps the situation can be retrieved.
The info is certainly out there (as they say in a certain TV show) - I still keep the same notes even if I haven't uploaded them recently. I suspect the recaps will also specify late offerings from Rachel.

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Re: I like Carol, and I like Rachel, but who's better?

Post by Dave Preece » Sun Aug 25, 2013 2:56 am

Not that it matters, but Carol obviously didn't get the famous James Martin's best-ever solve...

;-)

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Re: I like Carol, and I like Rachel, but who's better?

Post by Clive Brooker » Sun Aug 25, 2013 12:29 pm

Mike Brown wrote:
Clive Brooker wrote:Having had a quick look at a couple of Mike's scans, the information may well be there (to the end of series 64 at least) so perhaps the situation can be retrieved.
The info is certainly out there (as they say in a certain TV show) - I still keep the same notes even if I haven't uploaded them recently. I suspect the recaps will also specify late offerings from Rachel.
I'm sure recent recaps will, the art of recapping having developed so much in the last couple of years, but it hasn't always been so. If I wanted consistency of approach I'd go to your scans every time.

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Re: I like Carol, and I like Rachel, but who's better?

Post by sean d » Mon Aug 26, 2013 8:58 am

Great stuff Graeme thanks. To be honest I'm surprised to see Carol (or young Carol for want of a better phrase) as close to Rachel. As has been said the stats aren't very reliable as we don't really know how well each did in 30 seconds, on "I'll have another look" efforts etc, but it's still interesting to see. It's worth noting as well that Rachel has greater resources for practice, and I'd assume she benefits in this analysis from a higher level of performance from more recent contestants.

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Re: I like Carol, and I like Rachel, but who's better?

Post by David Williams » Mon Aug 26, 2013 11:29 am

Fascinating. I'd always thought Rachel was just better than Carol, and the age aspect hadn't occurred to me at all. Some observations.

Carol would sometimes say when a contestant had beaten her, but I don't recall Rachel ever doing so.

Carol factorised. If she was going for, say, 639 and there was a 9, she'd try to make 71 from the other numbers, knowing that if she failed she'd be 9 away but it didn't matter because she only had to show her solution if she was spot on. This slightly improves her chances of getting it exactly, but lessens her chances of an optimal solution if the target is impossible. Rachel doesn't seem to do this.

At the risk of offending anyone, I'm still highly dubious of this "Two away is as good as it gets on this one" stuff. I'm noticing now that Nick only does his "For perfection, we turn to Rachel" shtick when there actually is a solution, so I'm beginning to think he's in the know as well.

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Re: I like Carol, and I like Rachel, but who's better?

Post by Adam Gillard » Mon Aug 26, 2013 11:42 am

David Williams wrote:At the risk of offending anyone, I'm still highly dubious of this "Two away is as good as it gets on this one" stuff. I'm noticing now that Nick only does his "For perfection, we turn to Rachel" shtick when there actually is a solution, so I'm beginning to think he's in the know as well.
Yeah, it seems to fly in the face of "we never use computers / calculators for solutions" (paraphrasing). We know from Damian that this is true with regards to Rachel always doing calculations in her head, but then saying immediately after the round that it was an unreachable target could seem to a viewer who is not in the know as though everything is done with a computer / calculator. I remember in Ed's final that straight after a numbers round while they were turning around the board, Rachel turned to us and said that was the only way of getting within 15 either side of the target (see Round 5). I think it's good in that it does justice to the contestant who didn't solve it exactly, but did get as close as was possible, but at the same time, it makes it look like Rachel is being fed solutions.
Mike Brown: "Round 12: T N R S A E I G U

C1: SIGNATURE (18) ["9; not written down"]
C2: SEATING (7)
Score: 108–16 (max 113)

Another niner for Adam and yet another century. Well done, that man."

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Re: I like Carol, and I like Rachel, but who's better?

Post by Thomas Carey » Tue Aug 27, 2013 2:38 am

Adam Gillard wrote: I remember in Ed's final
Humble.
cheers maus

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Re: I like Carol, and I like Rachel, but who's better?

Post by Countdown Team » Thu Aug 29, 2013 9:18 am

Adam Gillard wrote:I think it's good in that it does justice to the contestant who didn't solve it exactly, but did get as close as was possible, but at the same time, it makes it look like Rachel is being fed solutions.
We've never once had an email, letter, phone call from any viewer suggesting that Rachel is fed answers though, so if it looks like she's being fed answers, why is nobody telling us?

For the record, she's never been fed answers and won't be, just in case someone from the Daily Mail wants to put that in a quote. ;)

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Re: I like Carol, and I like Rachel, but who's better?

Post by Rhys Benjamin » Thu Aug 29, 2013 9:22 am

Countdown Team wrote:Daily Mail
I'd be more worried about the Daily Mirror to be honest, it claimed that the 2008/09 recession was the Queen's fault... :roll:
The forum's resident JAILBAKER, who has SPONDERED several times...

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Re: I like Carol, and I like Rachel, but who's better?

Post by David Williams » Thu Aug 29, 2013 11:09 am

Countdown Team wrote:We've never once had an email, letter, phone call from any viewer suggesting that Rachel is fed answers though, so if it looks like she's being fed answers, why is nobody telling us?
Because nobody's noticed, or nobody cares, or nobody's watching? I'm a viewer. I'll send you an email if you'd like.

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Re: I like Carol, and I like Rachel, but who's better?

Post by Countdown Team » Fri Aug 30, 2013 8:14 am

David Williams wrote:
Countdown Team wrote:We've never once had an email, letter, phone call from any viewer suggesting that Rachel is fed answers though, so if it looks like she's being fed answers, why is nobody telling us?
Because nobody's noticed, or nobody cares, or nobody's watching? I'm a viewer. I'll send you an email if you'd like.

The only people who think she looks like she's being fed answers are the very same people who know only too well that she's not, ie some former contestants on this forum. ;)

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Re: I like Carol, and I like Rachel, but who's better?

Post by David Williams » Fri Aug 30, 2013 8:54 am

Countdown Team wrote:The only people who think she looks like she's being fed answers are the very same people who know only too well that she's not, ie some former contestants on this forum. ;)
Strange, but true!

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