# Calculate standard deviation from ratio of two variables

Ok here is my problem. For my research I am investigating if we can use twitter to create sports data. One part of the problem is for example this:

We now for example that in the 6th minute of the game a goal is scored. Now we need to know by what team it was scored. We are investigating if we can learn this by looking at the ratio in tweets from fans from both teams. We expect that when team 1 scores a goal, team 1's fans will tweet more than the other team compared to the minute before/more than some average ratio.

For this I have calculated for each minute in a game the amount of people tweeting for team 1 and for team 2. Now I need to come up with some sort of measure of deviation from the mean ratio between those teams. One thing that I did is normalize the amount of tweets per minute as one team might have a larger fanbase.

I can calculate the ratio by taking the normalized_count_team1/normalized_count_team_2 for each minute.

However now I am stuck. My math is not very good, but it seems to me that by doing this, the ratio when in favor of team 1 can be from 1 to infinity, while the other way around when the ratio is in favor of team 2 it can only be from 0 - 1. It seems that there would be a problem in calculating some deviation from the mean ratio here.

Anybody an idea how I would be able to for example say: in this minute there is a significant deviation from the mean ratio to for example team 1's side, therefore we think the goal was scored by team 1?

Thanks a lot in advance, you'd be helping me out a lot.

p.s. I read something about the Cauchy distribution here http://en.wikipedia.org/wiki/Normal_distribution#Related_distributions but don't really understand it and don't know if this is the right direction I should be looking.

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If you are worried about the asymmetry of your measure, then you could use use $\frac{\text{count_team1}}{\text{count_team1}+\text{count_team2}}$ – Henry Jul 16 '12 at 20:08
Or $\log (c_1/c_2)=\log c_1-\log c_2$. – joriki Jul 16 '12 at 21:06