Analysis of NAF statistics

[AndeeT]

Hi Moraiwe,

If the league is set up to score a draw as 1/3 of a win that does make sense (noting the same point I made above about re-calculating the proportions given the new total).


Best Wishes,

AndeeT

[dode74]

We are talking about win% as opposed to loss%. Win% = (wins + draws/2)/n and loss% = (wins + draws/2)/n. Win% + loss% total games. You're attempting to redefine win%, which is not going to help.

Moraiwe - this is a question about balance as defined by the BBRC, and they use draws/2. If your league chooses to use draws/3 that is a house rule and has no bearing on the balance criteria set.

[Moraiwe]

Given the title, I was pretty sure it was a discussion about NAF stats, not about balance. As such, you probably want to use the system the games were played under.

[dode74]

See second post.

[Moraiwe]

Dode, are you sure you mean the second post? Mentions nothing about balance, but about measuring performance. As such, I think it supports the argument you should use a formula that more accurately measures the success of the teams.

If you play under a 3-1-0 system, it's silly to suggest a 1-2-0 record is as good as 2-0-2.

[AndeeT]

Hi,

I think the penny has just dropped for me in terms of (wins+(draws/2)). After reading the wikipedia page for "winning percentage" I now see that the the other half of the drawn games are given to the loss games total. Sorry I failed to understand this before; please ignore my misguided ramblings in my posts above!

I failed to see that draw games were divided equally between wins and losses. For example;

WIN_DRAW_LOSS_PROPORTIONS.jpg

Which preserves the concept that; (win proportion) + (draw proportion) + (loss proportion) = 1.

Soooo...after all that (!), I think I am convinced that we can use the standard formula of confidence interval for a proportion for (win+(draw/2)).

By the same logic, (win+(draw/3)) would have to mean that a third of the draws go the 'win total', a third go the 'loss total' and a third remain as draws. I think? And by extension, I guess it's still valid to use the standard formula for confidence interval for a proportion.

Thanks for persevering dode. LOL.

Best Wishes

AndeeT

(EDIT for table jpg. I can't format forum posts for toffee!)

[dode74]

Dode, are you sure you mean the second post? Mentions nothing about balance, but about measuring performance. As such, I think it supports the argument you should use a formula that more accurately measures the success of the teams.

That's fair, although the second post (in this thread, by Cyberdelf) specifically stated win% as it is usually measured. If you want to know about it with reference to a 3-1-0 system then you can, of course, do that.

If you play under a 3-1-0 system, it's silly to suggest a 1-2-0 record is as good as 2-0-2.

Ofc. That's highly contextual with respect to the environment, though: points isn't relevant in tournament play (I don't know if we have a tournament vs league filter for NAF data - doesn't look like it), and MM often uses very different ranking systems - the current Cyanide system is based on win% modified for games played, for example.

[dode74]

By the same logic, (win+(draw/3)) would have to mean that a third of the draws go the 'win total', a third go the 'loss total' and a third remain as draws. I think?

I am not suggesting it should be measured in this manner, but I think Moraiwe is talking about points totals. That means you can divide it into two categories: games which gain points and games which do not. Since each draw is worth 1/3 of a win then only 1/3 of the points from a draw will count towards the "points gained" category, while 2/3 of draws will count towards the "points not gained" category. I think, therefore, that the "points gained" proportion is (wins + draws/3)/n and the "points not gained" proportion is (losses + draws*2/3)/n, where n is games played.

[Moraiwe]

points isn't relevant in tournament play

Not sure I understand this. Why not? Every tournament I've entered gave points based on whether you won, drew or lost and ranked the entrants based on these points.

[dode74]

Not sure I understand this. Why not? Every tournament I've entered gave points based on whether you won, drew or lost and ranked the entrants based on these points.

I was talking KO tournaments. Swiss is another animal entirely and awards points differently still. I guess the point I am making is that 3-1-0 is far from "the norm", particularly outside scheduled leagues, and will vary considerably with environment.

[Moraiwe]

I've never heard of a KO Blood Bowl tournament. Can you give me any examples?

I agree with the variability in formats is pretty large. What do you think is the 'norm', and why?

[rolo]

Just out of curiosity, does adding ties into the mix (somehow or other) change things in any meaningful way?

The point of these charts (at least for me) is comparing different race's performance, and seeing how that relates to to that race's popularity. So the exact numbers aren't as important as their positions relative to one another. And unless some races tie games much more or less than others, I wouldn't expect adding ties (whether as a third of a win, or half a win, or 100% of a win) to affect races' relative "success".

The chart makes me think, "Undead and Wood Elves are the two most successful teams in the game, and both are quite popular", "High end 'Tier 2' teams such as Pro Elves seem to perform about as well as many 'Tier 1' teams but are much less popular", or "Humans and especially Orcs are much more popular than their performance would seem to indicate". Would basing the chart on Win/Tie rate instead of just Win rate change any of those opinions?

I'm not trying to insult the effort that anyone's put into this, mind you. Just standing up for laziness.

[Darkson]

I agree with the variability in formats is pretty large. What do you think is the 'norm', and why?

I don't think there is a "norm", so unless you want to recalculate for every single points system for every single tournament/league then it makes sense to use the metric the win% was based on, which is (w+d/2)/g.
Sure, 3/1/0 makes more sense for your stats (and other leagues/tournaments that use it) but it would make no sense for my leagues o tournaments (for example).

[dode74]

I've never heard of a KO Blood Bowl tournament. Can you give me any examples?

I was thinking online, of which there are plenty of examples. I play there most so it's my default - apologies if that added to the confusion. That said, Swiss doesn't normally work on 3-1-0 either, does it?

I agree with the variability in formats is pretty large. What do you think is the 'norm', and why?

Depends. I don't think it's worthwhile lumping everything together since there are clear differences between TT and online (MM in particular) but do agree with Darkson that if you're going to aggregate then win% makes more sense.

rolo - take a look at the initial chart here and the one I produced here. You can see WE have moved below UD, and that HE have dropped to KHE and DWA have moved above SKA. Some relative movement does happen if you use win% as opposed to percentage of wins. I'd be very careful about what I would infer from the performance data on these charts for reasons already stated.

[Moraiwe]

That said, Swiss doesn't normally work on 3-1-0 either, does it?

I don't think a Swiss tournament in Australia exists that uses 2-1-0. They all use systems where a win is at least 2.5 times the value of a draw. Same with the leagues I know of. I was led to believe by an online poll I saw a while back that most events/leagues do the same.

I guess I'm just not aware of enough 2-1-0 events/leagues that warrant it being considered a default.