# Sports Statistics (esp. Volleyball) - need help understanding the rationale for using “Ratio” column.

If you look at the Standings for the NBA, NFL, or MLB, the first columns are Wins, Losses, and Win%. The Win% is calculated as #Wins / (#Wins + #Losses) or #Wins / #GamesPlayed. This makes sense to me. Looking at today's standings for Major League Baseball, I see:

• BOS 79 34 0.699
• NYY 68 42 0.618
• TBR 56 56 0.500

But, my sport is Volleyball. For some reason, instead of a Win% column, they (always?) have a Ratio Column, for both Sets and Points, such as this table

When I was working on a website for my volleyball league/team, I instinctively created a Win% column because that makes sense to me. But, when I saw another person's league website he'd created using Ratio, I wrote to him telling him that Ratio made no sense; the values in that column are not comparable. Is Italy 4x better than China? What does that even mean? He told me that Ratio is used on all the official sites: FIVB, etc. I checked and he's right.

But, I think this is wrong. I think that Ratio makes absolutely no sense, especially when you consider a team who doesn't drop a single set. France won three matches 3-0, so they won 9 sets and lost 0. So the ratio is undefined, and they put "MAX". To me, it would make much more sense to put 1.000, since they won 100% of their sets. Italy would be 0.666, since they won 2/3 of their sets. More importantly, 1.000 and 0.666 are comparable. France won 1/3 more of their sets than Italy did.

Furthermore, while in Pool A, every match was a 3-0 result, in Pool B, two matches were 3-1 results:

So, am I to understand or discern that the Soviet team is 5.14 (=9.0 / 1.75) times better than the Cuban team? I wouldn't say that, but again, what would that even mean? Not to mention, I feel like it makes even less sense to compare ratios based on different numbers of sets played.

Am I missing something? Is there a good rationale for Ratio? I really want to write to FIVB, etc. and raise this with them. I fear that some intern set up this "Ratio" column decades ago and no one at FIVB has a math background and/or cares enough to pursue it and therefore this column persists despite, IMHO, not having any real meaning.

I realize that this is hardly an important matter. That it pales in comparison to Climate Change, natural disasters, geopolitics, etc., but damn it, I can't stop thinking about this!

What you call win% and what FIVB calls ratio is related by the following formula:

${\rm ratio} = \frac{1}{\frac{1}{{\rm win\%}}-1} = \frac{\rm win\%}{1- {\rm win\%} }$

You can easily verify that by remembering that ${\rm ratio} = \frac{\rm Wins}{\rm Losses}$, while ${\rm win\%} = \frac{\rm Wins}{\rm Wins + Losses}$.

This is an increasing function over the whole relevant interval (${\rm win\%} \in [0,1]$). So in both cases, bigger means better.

Now the question is: Which is more useful? Strictly speaking, both contain the same information, as it is a 1-1 relationship.

You seem to be much in favor of the win%, which is a personal choice, and one I can totally understand.

But your argument about those ratios of ratios making no sense to you, I don't really follow. Do you really think that a baseball team that has a perfect 100% win% over the complete season is just 'double as good' as a team with 50% (which is just average)?

In volleyball, winning several games without loosing a set is much harder than winning with loosing one set, because it requires that much more stability to win the sets in all the circumstances that may come up. In that regard, a 9-0 set result when compared to a 9-1 set result is much more of an improvement than a 9-4 would be over a 9-6.

• I am well aware of the relationship of the two equations; I'm not asking for that to be explained.... I didn't say/imply that a baseball team (A) with a perfect record is twice as good as a team (B) with a 50% win percentage. But, objectively, A has won twice as many games as B (looking at a complete season)...I'm not sure I agree with your assertion that winning 9-0 is much harder than winning 9-1, or that 9-0 a bigger improvement than 9-4 (either 3-2, 3-2, 3-0 or 3-2, 3-1, 3-1) over 9-6 (3-2, 3-2, 3-2). What do you base this assertion on? – Zonker.in.Geneva Aug 6 '18 at 20:57