You can waffle on for paragraph after paragraph about this and that and tennis matches, I just have to list up a few numbers to show that what you are trying to defend is batshit crazy.
Except that you don't have anything... you're throwing around numbers that have no meaning without being given specific context and claiming they make a point. Is the point that you don't understand math? You made that point earlier by suggesting a linear, cumulative system that would (if I can suss out what you're bitching about) make an even more lopsided ranking than the one you're complaining about.
Not that you'll read this far, but had you actually read my posts you'd find that I don't like the formula being used... at all. What I argue for is the concept of using games played as a modifier on the general record of people in the ranking. I also try to get it through your thick skull that losses giving points is totally irrelevant
mathematically, what matters is the numeric relationship between the points for wins, draws, and losses (and any other conditions like concession wins and concession losses, that may be added). Over and over you seem unable to wrap your head around that.
The reason your mind gets blown so easily is that we're running too much intellectual electricity through too small a machine. Like putting an iPod directly on the power grid.
The win rate of the player with 30 games is more likely to be far on the right tail of the probability distribution than the win rate of the player with 112 games.
That's not true at all and shows a pretty disctinct lack of understanding of probability distributions. We don't know where on the distribution the true value falls
, we simply know the probability that it falls within certain ranges... that's the entire point of a probability distribution. The value we have is most likely
to fall exactly in the center, in both cases, because it is the mean of the observed values
, and the mean of our calculated distribution is, y'know, the mean of observed values.
Everything you and Dode are talking about, for the most part, is total shite.. there's no use of probability distributions in this system, and I've been told we can't since that involves calculations that require more than the at-the-second record of a person's W/D/L.
Similarly, it doesn't matter where someone's theoretical performance is... for any given season of a sport you're looking at how they performed during that season which means the data you have is not a sample of games from that team, it is the sum total of the relevant data, meaning you have the full population of data and the resulting value is not a measure of central tendency it is the de facto final value.. no CIs or probabilities.. it is exactly that.
You can't claim what you claim in quote 2 if you don't assume that the central tendencies used to compute the confidence intervals are comparable. And they are not comparable (without any correction) because one is extrapolated from 30 games and the other from 112.
Sure you can. That's what confidence intervals are, and they take into account sample sizes. The measure of central tendency is fine for everything - it's the mean value, and it makes up the middle of the distribution if you're treating it like a sample, which I see no reason to be doing. The mean is the mean even if you have 30, 112, or 20,000,000 values. Your CI range will just shrink as your sample size increases.
That's why the distributions are emphasised rather than the tendencies. The size of the sample determines the magnitude of the distribution. I am not comparing central tendencies but comparing distributions.
Not in your ranking formula you're not. Not in ANY of the ranking formulas discussed for CCL, in fact. The only place you'll see distributions being used for ranking is in that ranking system I proposed for full TVPlus back in the days of old. Likewise, I don't see there being a good reason to do any of that for seasonal play - you'd need to give a good reason for doing so rather than explaining why you're not going to use seasonal performance
as your measure of ranking for a season and rather plan on using theoretical true performance only sampled by a season
for ranking for a season.
The values of yours 0.05 and 0.95 intervals depend on the value of the central tendencies, you have to start from somewhere! If you want to know the central tendency of my win rate, would you rather measure it over 30 games or over 100 games? Why?
It absolutely doesn't matter... you really, really don't get what a measure of central tendency is but seem to say the words over and over. It is the MEAN of observed values, and because of that it doesnt matter how many games you've played - that only affects the confidence intervals.
The number of datapoints in a sample does not affect the mean, it affects the CI.. the "spread" of the distribution. You're banging your head against the wrong wall here, champ.
You should account for both the variance around the tendency and the variance of your indirect measure of the tendency.
The quoted statement is meaningless drivel coming from someone who doesn't understand basic statistics.... and given the things dode has been posting during the last page of this thread, I can only assume he's drunk.