Timeline for Standard deviation of game results about predictions from a rating system
Current License: CC BY-SA 3.0
19 events
| when toggle format | what | by | license | comment | |
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| Aug 23, 2012 at 21:44 | vote | accept | user8812 | ||
| Jul 29, 2012 at 12:07 | comment | added | user8812 | @Cardinal thanks for the advice re: pinging - I didn't realise and couldn't figure why when I tried to add at MichaelC it didn't show. From the screenshots above does my logic appear sound that this is normal distributed? (sorry for asking I just have close to no relevant background in this kind of thing and am not 100% sure on this). | |
| Jul 29, 2012 at 0:37 | comment | added | cardinal | @user8812: If writing a comment under an answer or a question, the author of the post (and most recent editor) will automatically get a notification (even if you don't address them using @). For example, Michael is going to get pinged in addition to you when this comment gets posted. :) | |
| Jul 28, 2012 at 23:30 | history | edited | Michael R. Chernick | CC BY-SA 3.0 |
added 534 characters in body; added 1055 characters in body
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| Jul 28, 2012 at 21:50 | comment | added | user8812 | sorry I meant to ping you on the above (I hope this makes sense). The nudges you've provided me in the right direction I think have resolved this and I would be happy to accept an answer on that basis. | |
| Jul 28, 2012 at 21:36 | comment | added | user8812 | I think I have definitely have got this being normally distributed now around the 33.2 mark in terms of standard deviation/the stochastic element. I've added links in to screenshots from an Excel workup I've done on a KS Test which suggests normal distribution and a QQ plot which again suggests normal distribution (I have corrected the link above). img42.imageshack.us/img42/7521/aflkstestresult.jpg - is the ks and img641.imageshack.us/img641/7367/aflnormalprobability.jpg is what I think is the QQ. If this matches what you were thinking I'm happy to accept an answer. | |
| May 23, 2012 at 21:53 | comment | added | user8812 | I tried to figure out what I needed to do for a QQ plot in Excel but I don't think that I could quite figure it out but I think I've managed a normal probability plot. I've posted a jpeg of the plot here: imageshack.us/photo/my-images/641/aflnormalprobability.jpg - from my very basic understanding of this the fact that it is approximately in a straight line would suggest a normally distributed data set? Providing I'm on the right lines I will redefine the bins and post fresh Chi Squared data. | |
| May 18, 2012 at 19:13 | comment | added | Michael R. Chernick | Q-Q stands for quantile vs quantile. It is like log paper for normal distributions. Things are scaled so that normally distributed data will fall close to a straight line. It provides an informal graphical check. I think redefining the bins will help with the validity of the chi square test. | |
| May 18, 2012 at 17:52 | comment | added | user8812 | Incidentally the sample size of 567 is the last 3 full years of AFL data (in the same way the Stern study went with 3 full years of NFL data) I just wanted to make sure there was enough data in there to make a reasonable study. | |
| May 18, 2012 at 17:49 | comment | added | user8812 | The sample size is 567 - and I do have bins with fewer than 5 observations, I'll try and post the histogram but I don't know if the formatting will work in a comment: Bin Frequency -120 0 -90 2 -70 5 -50 31 -40 31 -30 38 -25 27 -20 19 -15 24 -10 47 -5 35 0 21 5 35 10 38 15 23 20 34 25 26 30 26 40 43 50 26 70 25 90 8 120 3 More 0 - I don't know what a Q-Q plot is but I will find out and come back with the info. I've done the Chi Squared in Excel and had it verified by someone. I intend to try and do a K-S test on this next. Bin number starts at -120 with 0, -90 with 2, etc. | |
| May 17, 2012 at 21:17 | comment | added | Michael R. Chernick | Since the ratio of the standard deviation tio the standard error should be the sqaure root of n, your sample size must be close to 600. I calculated 576 and looking at our data again I see count =567 is probably your sample size and that would make sense. I would like to see a histogram and a Q-Q plot. The conclusion is non-normal but it is not yet clear to me that the departure from normality is large enough to worry about. | |
| May 17, 2012 at 21:17 | comment | added | Michael R. Chernick | What is the sample size and do you have bins with fewer than 5 observations? I ask these questions because very small departures from normality can be detect in large samples. Also the chi square test is approximate and doesn't work well when there are bins with fewer than 5 observations. The median seems a lot larger than the mean which would indicate high skewness. But that doesn't show up in the skewness statistic.The standard deviation is large but the standard error is small which indicate a large sample size. | |
| May 17, 2012 at 20:30 | comment | added | user8812 | DESCRIPTIVE STATISTICS Mean 0.00000160 Standard Error 1.395945948 Median 0.393745022 Standard Deviation 33.2399324 Sample Variance 1104.893106 Kurtosis 0.030249713 Skewness 0.081407243 Range 221.2779953 Minimum -104.080249 Maximum 117.1977463 Sum 0.000908841 Count 567 Confidence Level(95.0%) 2.741866796, Chi Squared Statistic = 223.79, df=21 (24 filled bins, 2 parameters), p=0 (so I reject the null hypothesis but I'm not sure what this means). I can provide further information if it helps (e.g. the histogram) but any nudges in the right direction would be appreciated. | |
| May 17, 2012 at 20:19 | comment | added | user8812 | I went away and looked into the Chi Square test, and carried out a Chi Square test on the error of my prediction against the result: | |
| May 13, 2012 at 16:15 | comment | added | user8812 | Thanks for the heads up. I'm keen to improve the models generally (side interest) and I'm just keen to refine the AFL one (hence why I worked up the last three years data to get a clearer idea of the e value as I figured the 2012 one was wrong or there wasn't enough data yet most likely). I know the model is generally solid though as it has gone 11/21 on general bet-able outcomes (so far this weekend - one game remaining) and 6 out of 7 on totals (which these models seem sharp on - 10% return off of my German Ice Hockey model - or the totals are badly handicapped). | |
| May 13, 2012 at 16:02 | comment | added | Michael R. Chernick | Other prominent members that I have not yet mentioneed are Carl Morris and Scott Berry. | |
| May 13, 2012 at 16:02 | comment | added | Michael R. Chernick | The American Statistical Association has a section on Statistics in Sports. Hal Stern whose article you cited is a member of that section. He has written substantially on sports. other members Jim Albert and Michael Schell have written books specifically on baseball. You might want to consider joining the association and the section. On the ASA website there is an eGroup for the section where questions like yours are discussed. I am a member but haven't actively done research in it. Many members of the section have though. | |
| May 13, 2012 at 15:41 | comment | added | user8812 | Thanks for the information - it's helpful to get a better understanding (we did this kind of thing at school but there was never a practical application so it was difficult to see where it was relevant). I would say what I am doing is essentially logistic but instead of coding 0 and 1, I am using actual games scores (which does affect the ratings as they are skewed by one-sided results). I am definitely keen to try and get a general approximation for e (if there is such a things as best fit for stochastic elements) and the given the past data you can get access to I think this achievable. | |
| May 13, 2012 at 12:29 | history | answered | Michael R. Chernick | CC BY-SA 3.0 |
