I'm improving my 0 game solution so that there can't be a negative H-rating < 100%

IF #W = 0

THEN the numerator defaults to (#O/2) – 1

and the denominator defaults to #0 + #L

This way as you lose more more and more games in that category, the denominator increases by 1 while the numerator remains constant.  Over time, if all you play are games in that category, your H-rating will approach but never reach -100%

The technical flaw with this is that a player can never actually attain an H-rating of -100%unless .. unless of course you add that if there are no wins across all categories, the H-rating is -100%

Hugh wrote:
Yertle won 86% of his (two-player) GearWars games. Before the 2h-1 transformation, the H-rating would have been 86%. After, it is 72%, meaning that he won 72% more than the norm. I prefer the 86%, because it is direct, whereas "72% better than average", while understandable, does not express the ratio directly. To think about what it is to perform 72% better than the norm, my mind wants to convert it to "ah, that means I win 86% of the time".

So the debate is:

Do we want a gamesize adjusted win percentage, or a gamesize adjusted statistic that describes the percentage of games you have won above or below the expected norm?

M57 wrote:

The H-score is a statistic that describes the percentage of games you have won above or below the expected norm.  It is calculated as follows:

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I left out all that Gamesize adjusted jargon because anyone that has the ability to question that aspect of it should be able to interpret the calculations well enough to see that it's included.

The main documentation improvement, if it is one, seems to have little to do with the 2h-1 transformation.  You might be correctly saying that the gamesize adjusting jargon is unnecessary.  Here is what the corresponding documentation WITHOUT the 2h-1 transformation might look like:

"The H-score is a statistic that describes the percentage of games you have won.  It is calculated as follows:"

Or if you want to hint that it handles multiplayer games, "The H-score is a statistic that describes the percentage of games you have won relative to the expected norm."

This is somewhat vague, possibly leaving someone to wonder how it handles multiplayer games.  But the same can be said of the "percentage of games you have won above or below the expected norm".  Please point me to where the actual psychological or documentation improvements are and tell me why they are improvements.

"The H-score is a statistic that describes the percentage of games you have won." 

This is factually incorrect.  A statistic that describes the percentage of games you have won is your Win Percentage.  We already have that statistic.

The "relative to the expected norm" phrase is necessary in my opinion, and "gamesize adjusted" further clarifies things because it speaks directly to what was taken into account to define the norm.

The decision to include or not include the formula in the description could weigh on the need for the "gamesize adjusted jargon, but the whole point of the statistic was to normalize the different gamesizes to each other.

M57 wrote:

Consider a player goes 2/4 in a pair of 2-player games and 0/1 in an 8 player game.

Our oldhscore equation would give us (2+0)/(4+7) = 2/11which translates to a -77% H-Rating after subtracting ½ and multiplying by 2, which hardly seems fair. When the numerator of one of the partials is 0 in a heavily populated game, the denominator kicks in hard.

No, it is (2 + 0)/(4 + 1) = 2/5.  The 2h-1 gives -20%.  Winning 0 games gives 0 old H-rating, -100% new H-rating - in neither scenario is it a flaw.

M57 wrote:

The "relative to the expected norm" phrase is necessary in my opinion, and "gamesize adjusted" further clarifies things because it speaks directly to what was taken into account to define the norm.

True, I agree.  I was going with a very loose interpretation of the word "describes".  Yeah, expected norm has to be there.

Hugh wrote:  I prefer the 86%, because it is direct, whereas "72% better than average", while understandable, does not express the ratio directly. To think about what it is to perform 72% better than the norm, my mind wants to convert it to "ah, that means I win 86% of the time".

QFT. And if we do insist on keeping the "% better than expected" approach, scale it to 100 as the norm rather than 0. Like OPS+.

Hugh wrote:

M57 wrote:

Consider a player goes 2/4 in a pair of 2-player games and 0/1 in an 8 player game.

Our oldhscore equation would give us (2+0)/(4+7) = 2/11which translates to a -77% H-Rating after subtracting ½ and multiplying by 2, which hardly seems fair. When the numerator of one of the partials is 0 in a heavily populated game, the denominator kicks in hard.

No, it is (2 + 0)/(4 + 1) = 2/5.  The 2h-1 gives -20%.  Winning 0 games gives 0 old H-rating, -100% new H-rating - in neither scenario is it a flaw.

I stand corrected.  But the statistic doesn't differentiate between losing 5 3-player games, and 5 10-player games, right? In both cases, if combined with a 2/4  2-player performance, the H-rating will be the same  (2 + 0 )/(4 + 5) = 2/9

That is absolutely correct. The statistic was designed to

1) Correspond multiplayer to two player percentages so that 0%--->0% 1/n--->1/2, and 100%--->100%.

2) Match the rest of the values in a way consistent with the Global Ranking.

I don't think it would be unreasonable to have a stat that weighs a 10-player loss as being less than a 2-player loss. Such a stat should minimally satisfy property #1 (G-rating only misses the 100%-->100%, the source of its skews).

The H-Rating was designed to satisfy property #2. (Note that our Global Rankings go way up if we win 10-player games, but go down exactly as if we lost a 2-player game when we lose a 10-player game.) By satisfying Property#2, we can predict how a Global Ranking will change assuming a certain H-score performance.

Locally, 10-player losses weighing as much as 2-player losses is indefensible, but the global assumption is that you'll have a nonzero winning percentage of each type, so it has a shot of making sense in the long run. As I disclaimered long ago: it may not reflect "truth", but it does predict/explain relative to Global Ranking.

Ok... so drop the 2*(H-1/2) bit then?

In my opinion, yes. I could be swayed, but it'd have to be a good argument.

I'm not sure if the the "debate" is over yet. Personally, I don't really have a preference; at least not a strong one..

My sense is that the original non-2* number is the easiest to understand. I can describe it in just..

::coughs::

GAWP

::clears throat::

..four words

Not saying debate is dead, just that I stand currently on one side. As always, I speak only for Hugh ;)

asm wrote:QFT. And if we do insist on keeping the "% better than expected" approach, scale it to 100 as the norm rather than 0. Like OPS+.

I like,  ..somewhat

So the blurb would say something to the effect that an H-Score of 100 means you are performing to 100% of the expectations of the norm.  The problem with using such numbers is that the scale is not going to be apparent.. Can you perform to 250% of expectations? You can't, the Rating tops out at 200 and it won't be apparent to most people why).

It makes more sense than 35% being awesome.

Like you said, score of 100 means 100% of expected wins. 250% of expectation is nonsensical; as with a percentile score that doesn't exceed 100, you can't be better than more than everybody. It's scaled to expectations, or looked at a different way it's scaled to an average (except that in this case the 'average' is a theoretical one)... so your performance is displayed as being better or worse than average.

Yeah, but my point is that if 100 is average then your particular H-score would be 135%, which sounds no more nonsensical than 250% to me.

(oldhscore - 0.5) * 100 yeilds a scale from 0 - 200

Errata: the ratings don't top out at 200. The original rating tops out at 100% as does the new suggested scaling. You said "100% of expected wins" when 100% in both cases means "wins 100% of all games played".

The scale will be apparent, 0% to 100%, or -100% to 100%, regardless of which one is used (if for no other reason than the help file could clarify). In Win Percentage land, everyone knows 50% is mediocre. In % above/below something, everyone knows 0% is mediocre. Clarity is not an issue.

Of course, I am with asm in that I prefer a 67.5% win percentage to performing 35% above the norm. I really think our minds will understand the 67.5% number quicker/better.

M57 wrote:

Yeah, but my point is that if 100 is average then your particular H-score would be 135%, which sounds no more nonsensical than 250% to me.

(oldhscore - 0.5) * 100 yeilds a scale from 0 - 200

More errata:  The Alpha conversion is 2*(h - 0.5), or in percentages it is 2*(oldhscore - 50%).  oldhscore ranges from 0% to 100%, so inside the parens is a range of -50% to 50%, making the range -100% to 100%.  

Here are the choices as I see them

h-score
range is 0 to 100 %
(50 is the norm)

Alpha: 2*(h - 0.5)
range is -100% to +100%
(0 is the norm)

Beta: 2*h
range is 0 to 200  
(100 is the norm)