I know that might sound funny cos 50.1% is higher than 49.5%. However in statistics we need to factor out the effects of randomness. (Imagine if I had two coins and spin each one 50 times. One coin comes up heads 48% of the time, the other 52% of the time. And yet the proportion of heads for both coins will be equal given enough spins (say something in the thousands or tens of thousands). The current disparity can be explained by random chance). I will show the working below and I know it all looks a bit esoteric and bizarre but trust me - this is exactly the methods used by people in many, many walks of life to discover if new drugs are effective, if cars are safe, if machine components work etc. I'm using a test for differences in proportions and assuming a normal distribution* H[SUB]0[/SUB]: A[SUB]p[/SUB] = R[SUB]p[/SUB] H[SUB]1[/SUB]: A[SUB]p[/SUB] > R[SUB]p[/SUB] This means we are testing the "null" hypothesis that AVB's win ratio was the same as Harry's vs the alternate hypothesis that AVB's win ratio was higher than Redknapps, once you take into account the natural fluctuations created by randomness. The figure I get below, the p-score, gives the percentage chance of getting the data we have (AVB wins 53.7% of matches, harry 49.3%), or something more extreme IF the two proportions are, in the long run, actually the same. Normal cut-off points for a test like this would be a P-score of 0.05 or 0.1 (0.01 if you're doing something extremely important like testing a new drug). To be as open as possible let's say that if we get a p-value of 0.1 (10%) or below we can say that we have significant evidence that AVB's win ratio is higher than Redknapp's. A[SUB]p[/SUB] (AVB win proportion): 0.537 A[SUB]n[/SUB] (AVB games) : 54 R[SUB]p[/SUB] (Redknapp win proportion): 0.493 R[SUB]n[/SUB] (Redknapp games): 144 p (pooled proportion): 0.505 q (1 - pooled proportion): 0.495 Using: A[SUB]p[/SUB] - R[SUB]p[/SUB]/ square root of ((pq/A[SUB]n[/SUB]) + (pq/R[SUB]n[/SUB])) We get: 0.537 - 0.495 / sq root of (0.00463 + 0.00174) = 0.526 This z-score gives up a p-value of 0.291. So the number had to be less than 10%. In fact it's 29.1%. We are therefore very confident indeed that we have no evidence whatsoever that AVB's win ratio was truly better than Harry's. *This is the only potential snag - I think that it is fair to say that the two samples are independent but you could argue otherwise. I think, however, that the other criteria for this test are met.
? Think you're talking about the misapplication of stats ("A player is more betterer at football if his passing completion is more higher than the other socerball player"). Here I am simply testing the claim that 29/54 shows a significantly different proportion to 71/144. I am not going on to make claims about what this says about either manager or how they should manage etc. I'm just using a widely-used tool for comparing two proportions to see if there really is a difference.
All you had to say was that the Arry data "population" size was 3 times the size of AVBs' . Therefore much less likely to be influenced by positive/negative bias in that population data. Which I stated earlier today. This, coupled with the fact that the difference in the win ratios is not significant, is why the AVB stat is quite unremarkable.
Sure the sample sizes are the key thing though actually if you pretend that AVB got that win ratio after the same amount of games as Harry (144) you still get a p-score of 0.228. In other words there is still a 22.8% chance that the differences in numbers would happen through chance even if their win rates were, in reality, exactly the same over time.
Unfortunately this won't hold up in the pub or the workplace for people wishing to counter the Avb win ratio stat! As most people would need a college course to understand!!
Simplification for simpletons!....like me! How many more wins would avb need to increase his win ratio by another 10% over 150 games. How many more wins would Harry need to increase his win ratio by another 10% over 300 games Answer is.... ****ed if I know!, but Harry would need to win twice as many to keep the stats between the two equal...or avb would need to win less games to keep win ratio parity.
Just remember the coin analogy. When two coins that ACTUALLY have the same ratios of heads over time one will look "better" after just 50 or 150 tosses. The question is "how much better and how many tosses?". IN this case the ratios are very close and the number of data are relatively small. We cannot be justified in concluding that one ratio is higher than the other here. Put it this way - if Sherwood takes over and wins four games out of five he will have a win ratio of 80%. But that would not mean he was way, way, better at producing wins that Harry or AVB. A coin could easily come up heads 4 times out of 5.
A difference in win ratios of less than one unit, is just not statistically significant. If you run the calcs on Arry vs Keithy or St Nicholson (where the population sizes increase by > 2-4 times) , then things will be more interesting. AVBs' stats compare well in population size with Shreeves and Pleat. Notable too that they all arguably inherited a decent squad from their predecessors.
well.... even though i don't understand this thread, the one thing I'll learn from it is who the clever people are on this forum.
AVB: If he managed 150 games and had a win ratio 10% greater than current (about 64%) he would have won 96 games. So that would mean he would have to win 67 games out of the "next" 96 (70% of them). Harry: If he managed 300 games and increased his win ration by 10% (to about 59%) then he'd have to have won 178 games. So he'd have had to have won 107 games out of his "next 156 (69% or them). I have absolutely no idea what that shows us. But thanks for making me do that, NSS! Is this sudden dedication to stats going to be AVB's lasting legacy? when the football's so dire you've gotta talk and debate about something I guess...
Ok mate that cleared things up...... Honest!, I'll just make sure I use tosses and and not tossers!! No I get the point, I think! as I probably made a similar point earlier on when saying the win ratio between Redknapp and Avb can't be compared as they managed for different periods, such as four years to a year and a half. So while Avb has currently a better win ratio, Redknapps win ratio is over a longer period and Avb wouldn't have continued at the same win ratio, his ratio would have declined.
Wow, a very long winded and slightly head spinning way of making a case for your point of view. Here's a simpler version⦠if Tim Sherwood takes charge of just one game tomorrow night and wins, he has a 100% win ratio. That doesn't make him a better manager than AVB or Harry, it just shows this calculation was created using far less data which makes the argument for these types of stats objective rather than conclusive. At the end of the day, managers are judged on many variables by us fans. Wins, losses and draws at base level. Then score lines, style of play, cup runs, cup wins and league finishes when all is said and done. Football is art, not science so I hate it when science gets used in these instances to make a case for one argument against another. We could all see that the AVB project was swiftly going south from our own inclinations and observations based on numerous factors. Was he a better manager than Harry? No chance. Was he worse than Ramos? Possibly. Was he the worst ever? No way. But these judgements are all made based on our own observations, experiences and expectations and I think we can all agree, regardless of some lucky wins, good wins, bad losses and the odd draw here or there, that he wasn't the right man for our football club. We move onwards and hopefully upwards.
Do you not get the simpleton version? My answer is actually correct, I'm messing about with the '**** knows' comment, but thats because there is no answer, in number anyway, the number of wins I asked for is irrelevant because I never gave a win rate figure to calculate with for either manager. Like I say any stat has to use "number of games" in its calculation, and as soon as you do that, you calculate by 150 for avb and 300 for Harry. All it gives you is a false stat once people start extrapolating.
No, the stats showed that Brunt had more assists and goals than Xavi over a season, not just relatively meaningless stats like pass completion. The stats don't tell the story, which is why moneyball works for some sports, like baseball, but has yet to be used effectively in football. It doesn't work for football though, as narrow margins are the difference between success and failure. There were a number of season where the difference between Wenger and Ferguson would've been extremely marginal and not statistically different enough to be classed as anything other than luck. One picked up trophy after trophy, title after title, while the other just missed out, again and again. That's not luck. Villas-Boas wasn't sacked because his stats didn't match up. Neither was Redknapp. On field success won't have even been the whole story behind either move, as the game is about more than just that.
If Utd beat Stoke tomorrow in the League Cup and West Ham at home on Saturday, Moyes will have a win percentage of 59%, the equal of SAF, proving that Utd have not suffered any diminution in the quality of manger since SAF's retirement. Right?
Lennypops, why not look a the 99 percentiles, AV lost a match 6-0 and Redknapp didn't. Redknapp won a match 9-1 and AVB didn't. Therefore Redknapp is tops on both counts. I bet if you did the 95 percentiles Redknapp would come out on top as well. Plus Redknapp didn't bother with the wafer, take the wafer results out of the equation I'd guess Redknapp would have come out better.
