Standard Deviation

Gareth37

Hello,

Im trying to use standard deviation and probability to help me make sports predictions. At the bottom is what I got on Wikipedia.

Ive read on another forum that the average num of points in Spain soccer was 52.1 and the same in England. However, the standard deviation in England was 15.85 and Spain it was 13.47. How did they work this out? What is the reasoning for the difference in standard deviation?

Also, does anyone know of any other mathematical techniques that can help me make probablility predictions. I know neural networks can be used but what about standard deviations and othe prrobability mats?

Thanks for any help.




From Wikipedia
Sports

Another way of seeing it is to consider sports teams. In any set of categories, there will be teams that rate highly at some things and poorly at others. Chances are, the teams that lead in the standings will not show such disparity, but will be pretty good in most categories. The lower the standard deviation of their ratings in each category, the more balanced and consistent they might be. So, a team that is consistently bad in most categories will have a low standard deviation. A team that is consistently good in most categories will also have a low standard deviation. A team with a high standard deviation might be the type of team that scores a lot (strong offense) but also concedes a lot (weak defense), or, vice versa, that might have a poor offense but compensates by being difficult to score on—teams with a higher standard deviation will be more unpredictable.

Trying to predict which teams, on any given day, will win, may include looking at the standard deviations of the various team "stats" ratings, in which anomalies can match strengths vs. weaknesses to attempt to understand what factors may prevail as stronger indicators of eventual scoring outcomes.

In racing, a driver is timed on successive laps. A driver with a low standard deviation of lap times is more consistent than a driver with a higher standard deviation. This information can be used to help understand where opportunities might be found to reduce lap times.

LeixlipRed

The standard deviation can be viewed simply as how far apart your data is spread. So in England the teams are further apart points wise on average than in Spain.

ZorbaTehZ

Think of it like this: if 3 teams finished with 1, 11 and 21 points respectively the average would be 11. And if you had 3 other teams that finished with 10, 11 and 12 points the average would be 11 too - they'd have the same average, but a very different standard deviation - standard deviation is a measure of the average 'deviation' from the mean, ie the average amount that the data are not equal to the mean if that makes sense.

Peyton Manning

Its basically the average distance between each actual score and the mean.

cavedave

Standard deviation works for things like height. Where most people are around the average. A few are very tall (but not 1000 times as tall) and a few are very short. It does not work for things like wealth where Bill gates is so much richer then the average that power laws are more appropriate models then normal (gaussian) distributions

Normal distribution (the bell curve) might make sense in most sports but you do have to look out for black swan events. Things no one saw coming. So for example the uses of those slidy chairs in rowing, or having a really tall guy block the ring in basketball (they changed the rules because of this) in sport (and possibly life) "cheats" from outside what you consider the game can come along and change results from a normal distribution to something else. Then everyone copies the "cheat" or the rules change and things go back to a normal distribution but it is worth considering.

Oh and if you are interested in maths for soccer prediction have a read of this http://plus.maths.org/issue46/risk/index.html

Gareth37

I would imagine that there is a relationship between a team's sequence of results and their standard deviation and/or variance calculations.

For example, Reading are a very attacking side and have a poor defence. As a result they have the least number of draws. Also, their sequence of results vary a lot, no long winning runs and no long losing runs (and no long draws run of course). The standard deviation must reflect this?

Also, take 2 teams playing head to head. One team may be scoring a lot and the other conceding a lot, will the standard deviation be able to predict the scoreline, comparing each team's standard deviation of goal difference?

I know that this is used by bookmakers and Im just trying to work out how.

ZorbaTehZ

Gareth37 wrote:

For example, Reading are a very attacking side and have a poor defence. As a result they have the least number of draws. Also, their sequence of results vary a lot, no long winning runs and no long losing runs (and no long draws run of course). The standard deviation must reflect this?

You'd expect the peak of their interval to be very near the overall average across all teams (like in the link above) though there's probably some other statistical tool that might be better at giving you info about that. Maybe someone else knows of one. :rolleyes:

Gareth37 wrote:

Also, take 2 teams playing head to head. One team may be scoring a lot and the other conceding a lot, will the standard deviation be able to predict the scoreline, comparing each team's standard deviation of goal difference?

Well, you could use their goals scored per game average to try and predict the scoreline. What the standard deviation will tell you is how 'reliable' that average is, ie if the sd is large then its not very 'accurate'. (Although when you're talking about that particular stat, I'd expect that it would be very difficult to use it usefully considering how premiership games generally have scores that are lowish)

LeixlipRed

My advice is to bet on end of season meaningless EL 1st division games. They're always thrown