"No, the stats showed that Brunt had more assists and goals than Xavi over a season, not just relatively meaningless stats like pass completion" That's being picky. So the Brunt thing was about assists and goals scored. My point was that in this example someone might take quantitative data and try to form qualitative conclusions erroneously. What I'm doing here is quite different. I am using a statistical tool to test a quantative claim. I'm using numbers to test a claim about numbers - that claim being that AVBs win ratio was better than Harry's. I do not (unlike the AVB supporters) go on to make qualitative claims about either manager or their abilities.
What I'm doing is not to say "player x has higher stats in this criteria therefore he must be better". This is dodgy ground. It's more like one person saying that a player has 55/100 shots on target and someone saying that someone who has 22/45 shots on target gets more of his shots on target. This is a purely statistical claim and should be tested accordingly. Who is the best player is best decided by watching football.
Possibly not, but it skews the stats. If you play your best side in the wafer, get key players injured, you stand a chance of getting totally blown away in the next league match. In terms of Win Draw or Lose, a 6-0 defeat counts the same as a 1-0 defeat. In terms of team morale, a 6-0 defeat is probably worth 3 or 4 1-0 defeats. People are saying in AVB's defence, that he was unlucky with injuries, that's a little bit like saying James Hunt was unlucky with racing cars. AVB broke his defenders when he had already won the bloody group. We all saw the consequences. Both Redknapp and AVB got the balance wrong.
Thanks for this Lenny. Strictly I think your conclusion "We are therefore very confident indeed that we have no evidence whatsoever that AVB's win ratio was truly better than Harry's" is too strong. I think it would be better put as 'The evidence is not sufficient to show that AVB's win ratio is not better than Harry's simply by chance'. In more technical jargon the test shows that there is not sufficient evidence to reject the null hypothesis, but can't allow you to conclude that the null hypothesis is actually correct. It looks as if you'd need an awful lot more than 54 matches to get a significant answer (assuming the win per cent remained the same for AVB). This is strong supporting evidence that clubs sack managers way too often: often a run of results of fewer than 10 matches is cited as a reason and I suspect this would almost never be statistically significant. I quite like Deedub's approach of looking at the extremes: perhaps it is true that a very bad result tells us something. But Arsenal lost 8-2 at Old Trafford and Utd also had a heavy beating from City and I doubt that is sufficient to conclude that Harry is better than Wenger or Ferguson
In principle the narrower the margins the more luck should play a part. So it's certainly possible that Arsenal's trophy drought might well be a matter of bad luck. I guess the counter argument is that weaknesses and strengths get amplified in times of stress - what people call the 'winning' mentality. So Arsenal get about the same number of points as Man Utd and win the same number of cup matches on average but tend to be found out in the key games when stress levels are higher. This suggests another measure of how good a manager is: success in important games. That would not be a good stat for Harry
Can you calculate that Lenny? My back of the envelope suggests that you would need about 250 matches for each manager
What happens if we take AVB's percentage and compare it to either the first or last 54 matches of Harry's reign? Who is best? Why do i care?
Avb took over the club in a stronger position. Redknapp took over in a weaker position but a false position. So I don't believe you can compare the first 54 matches. Martin Jol taking us from mid table to top four contenders was more impressive then Avb having us finish 5th, even if Jol had an interior win rate and Jol made a bigger impact on the club and fanbase.
43% of pilots admit to falling asleep during flight. 33% of them reported waking up to find their co-pilots had fallen asleep as well. Does this mean that 33% of flights do not need the pilot? Does this mean that we should reduce our flying by a third? Does it mean that pilots are highly skilled at choosing the right moment for a nap. What we don't know is how long they sleep for and how honest those that don't fall asleep are. How can I use this information?
Lenny's analysis shows that it probably doesn't matter because it will make the significance of the results even less because of the smaller sample. But if we assume both Harry and AVB were sacked because of their recent results then Harry's last 16 matches were worse than AVB's. This would not be a sensible criterion in either case (as the thread shows that you need 100s of matches to be sure of a trend)
I thought this would be really easy so couldn't work our why I kept getting a negative answer (-245). Did it right through about three times. Then realised that the change in the number of games played by AVB would change the pooled proportions too. So then there were Xs everywhere and quadratics being divided by quadratics I have this ridiculous sum in front of me. This is not like the algebra in the textbook - no-one's engineered this one so all the numbers are nice and you can just factor and cancel. And I badly need to go to bed. There are literally envelopes everywhere in front of me. I blame AVB for this.
It's not reasons for the actions or lack of them we are looking for but reasons for knowing about it. What can you do with this knowledge and how does it contribute to your life?
OK - I just started shoving numbers into a pretend-epic reign of AVB. And whether he kept that win-ratio up for 250 games, 1000 games or even 3000 still the difference was not significant! For 3000 I got a p-score of 0.15, so still nowhere near the minimum of 0.1 for significance. So when one guy has won 49% of his 144 games and the other has won 53.7% of his 3000 games we still do not have sufficient evidence to conclude that the win ratios are not actually the same. Blimey! So what does that show you? Probably that most people reading this will think "Statistics? What a load of bollocks!". I think we're gonna need Harry back for a bit to increase his "games played" number so that a clearer statistical distinction can be made. He'll understand.
OK - I really am going to bed now. But if you give them both 250 games with those win-ratios you are still way, way off having a significant difference (p-score = 0.164). Jesus Christ, statistics - give common sense a break! I'll wake up in a few hours and there'll be a football match. Thank God. Hey! And one where we have no defenders! That'll be interesting one way or the other...
