Versus Par

[JimBentley]

A while ago (about two year ago, in fact) I wondered if there could be a way to rank players on the letters and numbers games, automatically, based on their offerings in each round as compared against what was actually available. I concluded that there wasn't - there are too many external factors - but had a go anyway, because I like to pursue these things UNTIL I AM SATISFIED.

I am still not satisfied, but this is what my spreadsheet spat out (minimum eight games, but with David O'D included:

1 Craig Beevers (Series 57) ....................... -5.21
2 David O'Donnell (Series 58) ..................... -4.40
3 Conor Travers (Series 54) ...................... -3.42
4 Matthew Shore (Series 54) ..................... -3.08
5 Paul Howe (Series 54) ........................... -2.97
6 Aaron Webber (Series 56) ...................... -1.71
7 Steven Briers (Series 55) ....................... -1.32
8 Jon Corby (Series 54) ............................ -1.15
9 Jeffrey Hansford (Series 57) .................... -0.71
10 Richard Brittain (Series 55) .................... -0.69
11 James Hurrell (Series 57) ....................... -0.43
12 Michael Bowden (Series 54) .................... -0.33
13 Anita Freeland (Series 56) ...................... -0.21
14 Keith Maynard (Series 54) ....................... 0.01
15 Michael MacDonald-Cooper (Series 58) ......... 0.48
16 Joy Longworth (Series 55) ....................... 0.65
17 Dave von Geyer (Series 57) ...................... 1.10
18 David Edwards (Series 57) ....................... 1.24
19 Nick Wainwright (Series 56) ..................... 1.34
20 Stu Horsey (Series 55) ........................... 1.58
21 Steve Baines (Series 57) ......................... 1.69
22 Amey Deshpande (Series 56) .................... 1.98
23 Dundas Keating (Series 56) ...................... 2.23
24 Jean Webby (Series 56) .......................... 2.30
25 Mikey Lear (Series 57) ........................... 2.35
26 James Roberts (Series 57) ....................... 2.43
27 Christine Armstrong (Series 54) ................. 2.63
28 Vivienne Mead (Series 56) ........................ 2.65
29 Chris McHenry (Series 55) ........................ 2.76
30 Tony Warren (Series 55) .......................... 3.35
31 Andrew Blades (Series 55) ........................ 4.07

I'm sure you've guessed already, but it's like a par score in golf, so the further below zero you are, the better. As you can tell, my par is tough and the values are moreorless meaningless at the moment, but I'm working on that.

I've a gut feeling that it's sort of in the right order(ish) so it's not a complete dead loss, but I also have a gut feeling that it's a load of bollocks. I want to factor in difficulty of words and difficulty of numbers, but to get the program to do that automatically is a big job (and even if completed, couldn't be objective).

Anyhow, you're a bunch of clever people, is this worth pursuing, or is it - given the vagaries of the game - pretty much a pointless exercise?

[Jon O'Neill]

I have always maintained that the most accurate idea of how good a player is (after actually looking at every round and judging by brains) is maxima scored, where Paul Howe will be much higher I would've thought.

[Jon O'Neill]

Actually, I think I might've misunderstood what your program is actually doing. My new initial response is: well done!

[JimBentley]

I agree, to a point, because that's how you're not going to get beaten. But one thing that doing all the recaps has taught me is that maximums are not all the same. Sometimes there's a letters round with 20 seven-letter words and nothing better, and anyone could get a seven. Sometimes there's one seven and 30 sixes, and it's quantifying the difference between these sorts of rounds that becomes important. But what if the seven is impossibly obscure? Does that make a difference? I guess it does.

Similarly, with the numbers. If the selection is 100, 4, 6, 3, 2, 1 and the target is 600, then whilst I would expect everyone to get a maximum, it says nothing. If the target is 941, it at least says something. But it's hard to marry everything up into a coherent whole. I think - to use the charming American expression - I'm pissing into the wind with this.

[Conor]

If this is like the par score on UKGameshows, then one criticism is that it punishes disallowed words harshly.

[Paul Howe]

I would say an algorithm should give "easiness" points to a word based on its probability of appearance, the availability of prefixes and suffixes, and its length. For the common letters part, you'd have to be careful not to give things like INITIAND a high easiness rating; whatever algorithm Soo (or is it Charlie now?) uses for Anahack seems to do a decent job. You also have to be careful that any such system doesn't penalise having a word disallowed too heavily.

For the prefixes and suffixes, things like -ING and -IEST would obviously have to be easier than UN- or -ILY.

Of course, no such system will be perfect. I remember laughing at Craig being surprised that Conor and Chris missed NEUROGLIA because its a "high probability" word, when in fact its possibly never appeared on Countdown before, and you certainly wouldn't want to classify such a word as easy. Also, plenty of prefixed and suffixed words will be obscure and difficult to spot, and hence falsely classified as easy.

The best way would be to manually go through the dictionary and rate each word by hand, but I'm sure you don't want to do that AGAIN.

I'm not sure how you would do the numbers.

Is it worth it? I'm not sure, personally I quite like where I'm ranked at the moment! Also, I really liked "Win Beadle's Money" as well!

[Charlie Reams]

Yes, maxima counting is much more stable in that respect, and the flat vs hard rounds problem is not that significant over 88 rounds anyway. Jono and I started doing stats on this at some point but we got bored, because boys are like that. Once the wiki project is complete, we'll be able to summon all kinds of stats at will. Which is cool.

[Martin Gardner]

I'm a big baseball fan which is the most (stupidly) statistic obsessed sport in the world. There's this big debate about who's the best player ever, ever since Barry Bonds hit his 756th home run. What it comes down to is there's no single way to do it that's better than any other. Statistics tend to have strengths and weakness and it generally comes down to personal opinion. Sure the statistics are there but which statistics are the most meaningful is essentially personal opinion. Obviously there are other factors in Countdown - disallowed words for example, or games where the player fails to score but offers a valid solution. I think invalid words is such a big one especially if it's a fairly common word - best ever word I saw disallowed was REROUTES which is such an everyday word it's unbelievable. I suppose RER is an ugly beginning to a word, but I bet RERUN was in there.

Anyway to sum up, there's really no one "best" way to do it.

Martin

[Martin Gardner]

I can see if you picked 9 Scrabble tiles that NEUROGLIA would be very probable, but in Countdown we don't often get 5 vowels. I do think Scrabble players tend to overvalue learning 9-letter words anyway, went they do get played they're often just an 8 with an S on the end anyway. So for Countdown NEUROGLIA is low prob because we only get 5 vowels rarely.

Martin

[Charlie Reams]

You certainly have a talent for stating the obvious, Martin. Also the main difference between Craig Beevers and Barry Bonds is that only one of them is a cheating bastard.

[Gavin Chipper]

I'd be tempted to say that things average out over time and someone probably won't have harder games on average over a whole run than someone else, but then I think they do sometimes change the way the letters come out so some people do have it easier than others.

I would say it's not a pointless exercise, but I don't know how much disallowed words affect your scores. Actually I've just seen that Conor has posted about that too.

You could have a scoring system for each round that has a high drop-off between the best word and one letter less and increasingly smaller gaps as you go down. That way you are rewarding good words more. Having a word disallowed wouldn't be much different to just not doing well in that round. A good player having a few words disallowed wouldn't lose out to a consistently average scorer who might have a higher "raw score".

[Ben Pugh]

You certainly have a talent for stating the obvious, Martin. Also the main difference between Craig Beevers and Barry Bonds is that only one of them is a cheating bastard.

And one is the victim of racism.

[Craig Beevers]

Of course, no such system will be perfect. I remember laughing at Craig being surprised that Conor and Chris missed NEUROGLIA because its a "high probability" word, when in fact its possibly never appeared on Countdown before, and you certainly wouldn't want to classify such a word as easy. Also, plenty of prefixed and suffixed words will be obscure and difficult to spot, and hence falsely classified as easy.

I wasn't particularly surprised Chris missed it, but Conor has basically made himself into a top Countdown contestant by practising on words like NEUROGLIA and it's only 57th in the probability lists (the fact that it has 5 vowels doesn't change things particularly in this case). The difficulty of NEUROGLIA is relative, to someone who's done a lot of practising I'd expect them to find it 'easy' to spot - of course it's always possible you miss such a word, particularly if you don't spend much time looking for the 9.

[Conor]

I wasn't particularly surprised Chris missed it, but Conor has basically made himself into a top Countdown contestant by practising on words like NEUROGLIA and it's only 57th in the probability lists (the fact that it has 5 vowels doesn't change things particularly in this case). The difficulty of NEUROGLIA is relative, to someone who's done a lot of practising I'd expect them to find it 'easy' to spot - of course it's always possible you miss such a word, particularly if you don't spend much time looking for the 9.

To be honest, I'm more surprised that I'd never actually came across it considering it's such high probability.

[JimBentley]

If this is like the par score on UKGameshows, then one criticism is that it punishes disallowed words harshly.

I don't think it does. If a player has an eight disallowed and their opponent gets a seven, then the program puts their offering down as a six (offering nonwords should be punished, but not to the point of an effective declaration of nothing). I admit I've had to manually alter a few rounds, but I think I've done it reasonably fairly. My problem is automating everything; as has been mentioned, without going through the dictionary again, that's going to be tricky.

[Conor]

If this is like the par score on UKGameshows, then one criticism is that it punishes disallowed words harshly.

I don't think it does. If a player has an eight disallowed and their opponent gets a seven, then the program puts their offering down as a six (offering nonwords should be punished, but not to the point of an effective declaration of nothing). I admit I've had to manually alter a few rounds, but I think I've done it reasonably fairly. My problem is automating everything; as has been mentioned, without going through the dictionary again, that's going to be tricky.

Ah, that's a pretty good system.

[Gavin Chipper]

If this is like the par score on UKGameshows, then one criticism is that it punishes disallowed words harshly.

I don't think it does. If a player has an eight disallowed and their opponent gets a seven, then the program puts their offering down as a six (offering nonwords should be punished, but not to the point of an effective declaration of nothing). I admit I've had to manually alter a few rounds, but I think I've done it reasonably fairly. My problem is automating everything; as has been mentioned, without going through the dictionary again, that's going to be tricky.

I think that's a bit dubious. Sometimes people might go for an eight in a desparate hope because they have to win the round. Their next best might only be a five, or a four! I would say that if you've got a robust enough system, then giving them a nothing shouldn't punish them too much anyway.

[Paul Howe]

I wasn't particularly surprised Chris missed it, but Conor has basically made himself into a top Countdown contestant by practising on words like NEUROGLIA and it's only 57th in the probability lists (the fact that it has 5 vowels doesn't change things particularly in this case). The difficulty of NEUROGLIA is relative, to someone who's done a lot of practising I'd expect them to find it 'easy' to spot - of course it's always possible you miss such a word, particularly if you don't spend much time looking for the 9.

Well, 57th on the list of 5-voweled nines (I presume?), but assuredly much lower because what you're actually interested in is the probability of it being the longest word in the selection, which most of the time will be a 7 or 8. And this in a selection which is rarely chosen. I think a rational learner would go through a lot of other things (in particular, becoming ultra-proficient at the numbers) before getting that deep into the five vowel nines, and if anyone has invested enough time to make learning them rational, then fair play.

Truthfully though, I thought it was the sort of thing Conor might come up with after you posted it on c4c, I was just tickled by your use of the term high probability.

[Jon O'Neill]

If this is like the par score on UKGameshows, then one criticism is that it punishes disallowed words harshly.

I don't think it does. If a player has an eight disallowed and their opponent gets a seven, then the program puts their offering down as a six (offering nonwords should be punished, but not to the point of an effective declaration of nothing). I admit I've had to manually alter a few rounds, but I think I've done it reasonably fairly. My problem is automating everything; as has been mentioned, without going through the dictionary again, that's going to be tricky.

I think that's a bit dubious. Sometimes people might go for an eight in a desparate hope because they have to win the round. Their next best might only be a five, or a four! I would say that if you've got a robust enough system, then giving them a nothing shouldn't punish them too much anyway.

So you're saying that giving them 4 or 5 less than they had is preferable to giving them 1 or 2 more? Hmmmmm.

[Gavin Chipper]

So you're saying that giving them 4 or 5 less than they had is preferable to giving them 1 or 2 more? Hmmmmm.

Well, the point is that we don't know what they got. But the ranking score for number of letter doesn't have to be linear.

As an example, you could have a scoring system where the ranking score for each word is double what it is for the next one down (this is just a random example and not necessarily any good). Someone might go for an 8 for 32 points but have it disallowed. Other chap gets 7 (16). We could give the first player 8 points, or just nothing. But at the end of the day, when 32 points could be up each time, 8 doesn't matter too much.

Also is the system that we always give them one less letter than their opponent? Because then their opponent might be rubbish and only get three. What if they also declare wrongly or declare nothing? Basing it on their opponent is shaky.

[Gavin Chipper]

One last post for now - if this is about par, then if in your games you get a lot of easy distributions, you might always get the best word (say it's an 8) but there might be lots of 8s, so it might be par so you don't get anywhere.

One way of doing it might be to have the letters games given a ranking according to difficulty, and you get a separate average score for each type of game. And then these are then also averaged in some way, so that the weighting is not forced by what letters come up but by what you decide.

[Charlie Reams]

That still rewards plodders over flair players.

It has to be said that there is still some imbalance in the scores available. Had John Delaney gone on to be an octochamp with a perfect score, he could've made an incredible 1100. Had Neil Green done the same, he would've made just 964. (These are the most extreme "octopossibles" on record, but even crazier examples have probably occurred.) Nevertheless 964 would still be the highest ever total by a large margin, so I guess we'll just have to blame all players ever for being crap.

[Charlie Reams]

You certainly have a talent for stating the obvious, Martin. Also the main difference between Craig Beevers and Barry Bonds is that only one of them is a cheating bastard.

And one is the victim of racism.

Are you sure about that?

[Dinos Sfyris]

You certainly have a talent for stating the obvious, Martin. Also the main difference between Craig Beevers and Barry Bonds is that only one of them is a cheating bastard.

And one is the victim of racism.

I'm certainly not bothered about the colour of Craig's skin. He's my friend!

[Charlie Reams]

They obviously rigged the letters so he couldn't beat the octototal of our Great White Hope, Julian Fell. I'm just waiting for the drug scandal to break.

[Craig Beevers]

I wasn't particularly surprised Chris missed it, but Conor has basically made himself into a top Countdown contestant by practising on words like NEUROGLIA and it's only 57th in the probability lists (the fact that it has 5 vowels doesn't change things particularly in this case). The difficulty of NEUROGLIA is relative, to someone who's done a lot of practising I'd expect them to find it 'easy' to spot - of course it's always possible you miss such a word, particularly if you don't spend much time looking for the 9.

Well, 57th on the list of 5-voweled nines (I presume?), but assuredly much lower because what you're actually interested in is the probability of it being the longest word in the selection, which most of the time will be a 7 or 8. And this in a selection which is rarely chosen. I think a rational learner would go through a lot of other things (in particular, becoming ultra-proficient at the numbers) before getting that deep into the five vowel nines, and if anyone has invested enough time to make learning them rational, then fair play.

Truthfully though, I thought it was the sort of thing Conor might come up with after you posted it on c4c, I was just tickled by your use of the term high probability.

No 57th on the list of ALL 9s (using Scrabble's letter distribution to derive the most/least probable - using Countdown's letter distribution wouldn't alter things a great deal other than if you factored in the 5 vowel bit, but it would still be right up there). It doesn't matter about what me or any 'rational learner' has gotten up to because this all in relation to what Conor knows. You're not seeing the true worth of 9s anyway - they may not come up often but they're the only 'set' in a selection and they're worth 18 points - whereas with shorter words there can be a loads of them and they're worth less points. So if you looked an average octochamp run, there might be what about 100 points hinging on spotting 9s (ignoring the conundrum), you might have around 300-400 points each on 7s and 8s (very roughly speaking - 8s may be more valuable then 7s or vice versa) where there'll often be multiple 'sets' that produce anagram(s).

[David O'Donnell]

I thought Craig termed it 'high probability' because it comes up on ANAHACK. I have to admit though that I have seen it several times on ANAHACK and still missed it on Conor's game.

[Ben Pugh]

You certainly have a talent for stating the obvious, Martin. Also the main difference between Craig Beevers and Barry Bonds is that only one of them is a cheating bastard.

And one is the victim of racism.

Are you sure about that?

Yes. Look at the vast difference in the treatment of Barry Bonds and Lance Armstrong by the American public.

[Craig Beevers]

Look at the vast difference in the treatment of Barry Bonds and Lance Armstrong by the American public.

Huh? Barry Bonds is an arse, that's why people don't like him.

Also I don't see how you could attribute a vast difference in treatment down to racism in such a racially diverse group as the American public.

[Gavin Chipper]

That still rewards plodders over flair players.

My system? I don't see why really. Obviously the plodders are being rewarded in the particular rounds where the flair players have their words disallowed, but that's how it should be. I can't see any other way. However, the scoring system that we use for the best words could be stretched as high as we like or not as the case may be, so whether we reward flair players or plodders is up to how we do it.

I think the best way to reward flair players is not to not give them no score when they declare no valid word, but to reward them accordingly for producing brilliant words.

[Ben Pugh]

Also I don't see how you could attribute a vast difference in treatment down to racism in such a racially diverse group as the American public.

Racism still exists in America, it's less than 50 years since the Civil Rights Act, you only have to go back a few years to Hurricane Katrina to see how strongly people still feel about race. There are places in America where you wouldn't want to go, for both white and black people.

[Charlie Reams]

Lots of successful baseballers are black. Lots are disgraced drug cheats are white. So maybe there's a special kind of racism which discriminates against Barry Bonds and not any other sportsman, or maybe Bonds lied to a Grand Jury and people (who would be critical of that at the best of times) are particularly harsh on him because he already has a reputation as a total jerk. Not everything bad that happens to a black person is due to some kind of secret racist pact, and it's horribly patronising (to black people and to Americans) to assume otherwise.

[Paul Howe]

No 57th on the list of ALL 9s (using Scrabble's letter distribution to derive the most/least probable - using Countdown's letter distribution wouldn't alter things a great deal other than if you factored in the 5 vowel bit, but it would still be right up there). It doesn't matter about what me or any 'rational learner' has gotten up to because this all in relation to what Conor knows. You're not seeing the true worth of 9s anyway - they may not come up often but they're the only 'set' in a selection and they're worth 18 points - whereas with shorter words there can be a loads of them and they're worth less points. So if you looked an average octochamp run, there might be what about 100 points hinging on spotting 9s (ignoring the conundrum), you might have around 300-400 points each on 7s and 8s (very roughly speaking - 8s may be more valuable then 7s or vice versa) where there'll often be multiple 'sets' that produce anagram(s).

So you think if Countdown was played forever (or just for a couple of thousand years perhaps) NEUROGLIA would be 57th in the frequency list of nines? If you just pulled 9 random letters out of a scrabble bag, there'd be 1 5 vowel selection for every 3 3 OR 4 vowel selections, a much higher ratio than occurs than on the show, and I'd guess that the nines are more dense in the 4 voweled selections at least. If you made a list of words of that are most likely to be a winning word, or even a winning darren, according to the distribution of selections on the show, I think it would be well down the list (although yes, the 18 point bonus does make it more valuable). Anyway, I wasn't trying to provoke a debate, just trying to make the point that Jim's word ranking algorithm shouldn't class words like NEUROGLIA as easy (after all, Conor, one of the most knowledgable players in the history of the game, not to mention Chris Wills, didn't spot it)

[Craig Beevers]

Also I don't see how you could attribute a vast difference in treatment down to racism in such a racially diverse group as the American public.

Racism still exists in America, it's less than 50 years since the Civil Rights Act, you only have to go back a few years to Hurricane Katrina to see how strongly people still feel about race. There are places in America where you wouldn't want to go, for both white and black people.

I don't see your point. You were saying the treatment from a huge group of racially diverse people is dramatically different because the guy concerned is black. The only way this could happen is if there's a lot of strong racism that comes primarily from one direction.

[Charlie Reams]

So you think if Countdown was played forever (or just for a couple of thousand years perhaps) NEUROGLIA would be 57th in the frequency list of nines?

I was actually planning to simulate just that (the latter case!) at some point, so then we'll have an answer.

And don't apologise for causing a debate, Paul - interesting points from both sides and I don't think Craig was terribly offended by your amusement at his optimism!

[Craig Beevers]

Would be cool if you did generate a usability list, based on how many the 'maximum' scores and how many maxima there are in the given selection.

[Ben Pugh]

Lots of successful baseballers are black. Lots are disgraced drug cheats are white. So maybe there's a special kind of racism which discriminates against Barry Bonds and not any other sportsman, or maybe Bonds lied to a Grand Jury and people (who would be critical of that at the best of times) are particularly harsh on him because he already has a reputation as a total jerk. Not everything bad that happens to a black person is due to some kind of secret racist pact, and it's horribly patronising (to black people and to Americans) to assume otherwise.

I'm not saying that everyone who suspects or dislikes Barry Bonds is a big racist but there are undertones of racism in the vilification of Bonds, such as comparisons between him and OJ Simpson, two men who have only their skin colour in common, or the enormous difference between the treatment of Bonds, who has received death threats, and Lance Armstrong, who could not be more highly revered by the American public, despite similarities in their cases.

I don't see your point.

Ignore it, I misunderstood your original post.

[Charlie Reams]

there are undertones of racism in the vilification of Bonds, such as comparisons between him and OJ Simpson, two men who have only their skin colour in common

I haven't heard any such comparisons and I agree that they are a bit unfair, but the two men do have plenty in common - they're both highly successful American sportsmen who were surrounded by legal controversy and consequently suffered a dramatic fall from grace. I take your point, they were both vilified in the media on the basis only of unproved accusations, but I really don't think that has anything to do with them being black - they were both found guilty of some pretty bad stuff in the end.

[Dinos Sfyris]

Am I the only person who hasn't heard of Barry Bonds?

[Joseph Bolas]

Am I the only person who hasn't heard of Barry Bonds?

Nope, but then I don't remember most of the contestants . My memory is crap basically.

[Conor]

Am I the only person who hasn't heard of Barry Bonds?

Nope, but then I don't remember most of the contestants . My memory is crap basically.

Hahah He's a baseball player, recently broke the record for most home runs.

[Matthew Green]

Surely the opponent also comes into play as well? In over 12 years watching countdown, Hazel was by some distance the worst player I've ever seen on the show allowing David to score in every round. Someone half-decent might at least have taken one round off him like the lady who got ESPECIAL.

I remember Craig Beevers played a few players who might have won a couple of games and had some respectable words so he had to be tactful. There were clearly rounds where he played safe with a 7 when he had a likely 8 (MORISTES springs to mind). Had he been playing someone like Hazel and knowing that the century was there even with a couple of disallowed words, this might have been a different story.

[Craig Beevers]

Yea, MODISTES. I did play a stand-in where I scored 128 and I played ridiculously safe against him (not 'risking' 3 words I was virtually certain of when declaring second because I would win the round without them), he scored 36 points and 30 were from the numbers games which were fairly straight forward. But yes I think David has probably played easier contestants on the whole.

[Kirk Bevins]

Soo, on that link you put for John Delaney, it says he lost 91-64 when the game shows 91-54.

[Charlie Reams]

It also says "This article includes round details inferred automatically from the recap. It has not yet been verified by a human and may contain errors."

[Kirk Bevins]

OK. I take it back.

[Charlie Reams]

Haha, no need mate, you are right about the error - I was just pointing out that if you're going to post all the errors in the unchecked articles, well, you'll be here for a while. You can of course edit them yourself if you want to help our little project along.