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paper: Miscellaneous Statistics Projects
Thread created automatically to discuss a document in CDMedia.
Miscellaneous Statistics Projects by Caleb Sykes 
#2




Re: paper: Miscellaneous Statistics Projects
I frequently work on small projects that I don't believe merit entire threads on their own, so I have decided to upload them here and make a post about them in an existing thread. I also generally want my whitepapers to have instructions sheets so that anyone can pick them up and understand them. However, I don't want to bother with this for my smaller projects.

#3




Re: paper: Miscellaneous Statistics Projects
In this post, Citrus Dad asked for a comparison of my Elo and OPR match predictions for the 2017 season. I have attached a file named "Elo and OPR comparison" that does this. Every qual match from 2017 is listed. Elo projections, OPR projections, and the average of the two, are also shown for each match. The square errors for all projections are shown, and these square errors are averaged together to get Brier scores for the three models.
Here are the Brier score summaries of the results. Code:
Total Brier scores OPR Elo Average 0.212 0.217 0.209 Champs only Brier scores OPR Elo Average 0.208 0.210 0.204 
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Re: paper: Miscellaneous Statistics Projects
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#5




Re: paper: Miscellaneous Statistics Projects
I am currently working on a model which can be used to predict who will win the Chairman's Award at a regional or district event. I am not covering district championship Chairman's or Championship Chairman's because of their small sample sizes. The primary inputs to this model are the awards data of each team at all of their previous events, although previous season Elo is also taken into account.
The model essentially works by assigning value to every regional/district award a team wins. I call these points milliChairman's Awards, or mCA points. I assigned the value of a Chairman's win in the current season at a base event of 50 teams to have a value of 1000 mCA. Thus, all award values can be interpreted as what percentage of a Chairman's award they are worth. Award values and model parameters were the values found to provide the best predictions of 20152016 Chairman's wins. At each event, a logistic distribution is used to map a team's total points to their likelihood of winning the Chairman's Award at that event. Rookies, HOF teams, and teams that won Chairman's earlier in the season are assigned a probability of 0%. I have attached a file named 2017_Chairman's_predictions.xlsm which shows my model's predictions for all 2017 regional and district events, as well as a sheet which shows the key model parameters and a description of each. The model used for these predictions was created by running from the period 20082016, with tuning specifically for the period 20152016, so the model did not know any of the 2017 results before "predicting" them. Key takeaways:
More work to come on this topic in the next few hours/days. 
#6




Re: paper: Miscellaneous Statistics Projects
I have added another workbook named "2018 Chairman's Predictions." This workbook can be used to predict Chairman's results for any set of teams you enter. The model used here has the same base system as the "2017 Chairman's Predictions" model, but some of the parameter values have changed. These parameters were found by minimizing the prediction error for the period 20162017.
Also in this book is a complete listing of teams and their current mCA values. The top 100 teams are listed below. Code:
team mCA 1718 9496 503 9334 1540 9334 2834 9191 1676 8961 1241 8941 68 8814 548 8531 2468 8112 2974 8092 27 8047 1885 7881 1511 7786 1023 7641 1305 7635 2614 7568 245 7530 1629 7381 2486 7100 66 7027 3132 6748 1816 6742 1086 6551 1311 6482 1710 6263 2648 6241 125 6223 558 6155 141 6083 1519 6082 1983 6060 4039 5985 33 5851 2771 5780 1902 5582 624 5578 1011 5496 118 5470 2137 5461 1218 5424 2169 5390 910 5382 3284 5353 3478 5344 771 5321 75 5306 2557 5291 233 5287 987 5224 1868 5215 3309 5175 1714 5158 932 5147 1986 5144 537 5138 597 5077 604 5068 2056 5059 2996 5054 4613 5042 399 5029 1477 5010 2220 4994 2337 4955 3618 4896 4125 4823 217 4816 1730 4803 359 4784 2655 4714 2500 4706 694 4695 1923 4667 708 4662 1622 4661 1987 4655 2642 4655 1671 4630 4013 4627 772 4626 2415 4622 4063 4604 540 4501 433 4440 4525 4426 384 4412 3476 4384 2485 4333 3008 4325 303 4307 1711 4288 2590 4266 3142 4264 3256 4260 836 4251 3880 4250 1678 4244 2471 4237 230 4230 78 4224 
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Re: paper: Miscellaneous Statistics Projects
I got a question about historical mCA values for a team, so I decided to post the start of season mCA values for all teams since 2009. This can be found in the attached "Historical_mCA" document.

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Re: paper: Miscellaneous Statistics Projects
I was wondering if alliances with surrogates were more or less likely to win than comparable alliances without surrogates. To investigate this, I found all 138 matches since 2008 in which opposing alliances had an unequal number of surrogates. I threw out the 5 matches in which one alliance had 2 surrogates more than the other alliance.
I started by finding the optimal Elo rating to add to the alliance that had more surrogates in order to minimize the Brier score of all 133 matches. This value was 25 Elo points. The Brier score improved by 0.0018 with this change. This means that, in a match between two otherwise even alliances, the alliance with the surrogate team would be expected to win about 53.5% of the time. This potentially implies that it is advantageous to have alliances which contain surrogates. To see if this was just due to chance, I ran 10 trials where I would randomly either added or subtracted 25 Elo points from each alliance. The mean Brier score improvement with this method was 0.00005, and the standard deviation of Brier score improvement was 0.0028. Assuming the Brier score improvements to be normally distributed, we get a zscore of 0.62, which provides a pvalue of 0.54. This is nowhere near significant, so we lack any good evidence that it is either beneficial or detrimental to have a surrogate team on your alliance. Full data can be found in the "surrogate results" spreadsheet. Bolded teams are surrogates. 
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Re: paper: Miscellaneous Statistics Projects
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I actually read that book quite a while back. At the time, I thought it was interesting, but quickly forgot much of it. It was only relatively recently that I realized that the world is full of overconfident predictions, and that humans are laughably prone to confirmation bias. I now have a much stronger appreciation for predictive models, and care very little for explanatory models that have essentially zero predictive power. 
#11




Re: paper: Miscellaneous Statistics Projects
I decided to investigate how important breaks between matches were for team performance. If the effect of rest is large enough, I thought I might add it into my Elo model. I was originally going to use the match start times as the basis, but after finding serious problems with this data set, I switched to using scheduled start times.
Essentially, what I did was to give each team on each alliance an Elo penalty which was determined by how much "rest" they have had since their last match. I tried both linear and exponential fits, and found that exponential fits were far better suited to this effort. I also used the scheduled time data to build two different models. In the first, I looked at the difference in scheduled start times for each team between their last scheduled match and the current match. In the second, I sorted matches within each event by start time and gave each match an index corresponding to its placement on this list (e.g. Quals 1 has index 1, Quals 95 has index 95, quarterfinals 11 has index 96, quarterfinals 22 has index 101, etc...). The best fits for each of these cases were the following: Time difference: Elo penalty per team = 250*exp((t_current_match_scheduled_time  t_previous_match_scheduled_time)/(5 minutes)) Match index difference: Elo penalty per team = 120*exp((current_match_index  previous_match_index)/(0.9)) Both of these models provide statistically significant improvements to my general Elo model. However, the match index method provides about 7X more of an improvement than the time difference method (Brier score improvement of 0.000173 vs 0.000024). This was surprising to me, since I would have expected the finer resolution of the times to provide better results. My guess as to why the indexing method is superior is due to time differences between quals and playoff matches. I used the same model for both of these cases, and perhaps the differences in start times is not nearly as important as the pressure of playing backtoback matches in playoffs. I have attached a table summarizing how large of an effect rest has on matches (using the match index model). Playing back to back matches clearly has a strong negative impact on teams. This generally only occurs in playoff matches between levels. However, its effect is multiplied by 3 since all three alliance members experience the penalty. A 3team alliance who just played receives a 80 Elo penalty relative to a 3team alliance who played 2 matches ago, and a 108 Elo penalty relative to a 3team alliance who played 3 matches ago. 108 Elo points corresponds to 30 points in 2017, and the alliance that receives this penalty would only be expected to win 35% of matches against an otherwise evenly matched opposing alliance. The match index method ended up providing enough improvement that I am seriously considering adding it into future iterations of my Elo model. One thing holding me back from using it is because it relies on the relatively new data of scheduled times. At 4 years old, this data isn't nearly as dubious as the actual time data (1.5 years old), but it still has noticeable issues (like scheduling multiple playoff replays at the same time). You can see the rest penalties for every 2017 match in the "2017 rest penalties" document. The shown penalties are from the exponential fit of the match index model. 
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Re: paper: Miscellaneous Statistics Projects
I'm a bit skeptical, because there are some effects of alliance number on amount of rest during playoffs (e.g. #1 alliances that move on in two matches will always have maximal rest, and are typically dominant). Not sure if you can think of a good way to parse that out, though.

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