{"cells":[{"metadata":{"_uuid":"8f2839f25d086af736a60e9eeb907d3b93b6e0e5","_cell_guid":"b1076dfc-b9ad-4769-8c92-a6c4dae69d19","trusted":true},"cell_type":"code","source":"\"\"\"\nI have used only spreadsheet tools and website publicly available tools to do a simple analysis\n\nAlso, this is the first contest in which I am actively participating and therefore creating a kernel\n\nSo, I am just going to use these comments of this this kernel to explain my analysis.\n\nConcussion Frequency\n37 concussions\n6584 games (post season excluded due to missing concussion data)\n1 in every 178 games\n0.56% chance in each game\n\nPre-Season\n12 Pre-Season\n736 games\n1 in 61 games, 1.6% chance in each game\n\nRegular Season\n25 Regular Season\n5848 games\n1 in 234 games, 0.43% chance in each game\n\nSo it seems pretty clear that there is substantially higher probability of consussion in pre-season games.\nAs such, my recommendations will center on that issue.\nBut first, what about the statistical significance of the difference in probability bwtween pre-season\nand regular-season? To address this I use a z score calculator as shown below:\n\nhttps://www.socscistatistics.com/tests/ztest/Default2.aspx\n\nZ Score Calculator for 2 Population Proportions\nSuccess!\n\nYou'll find the values for z and p below. Blue means your result is significant, red means it's not.\n\nSample 1 Proportion (or total number)\n12\n\nSample 1 Size (N1)\n736\n\nSample 2 Proportion (or total number)\n25\n\nSample 2 Size (N2)\n5848\n\nSignificance Level:\n0.01 chosen\n0.05\n0.10\n\nOne-tailed or two-tailed hypothesis?:\nOne-tailed\nTwo-tailed chosen\n\nThe value of z is 4.1144. The value of p is < .00001. The result is significant at p < .01.\n\nSo the above seems to indicate that the difference is statistically significant, assuming\nI used the tool properly.  That is, the possibility of this much difference has a less than 1% chance\nof occuring randomly.\n\nSo I have chosen to base my recommendations on this one finding.\n\nI don't see a way to reliably evaluate the efficacy of rule changes so I am instead recommending \nto the NFL that they consider using pre-season games as a test-bed for potential rule changes.  \nThat is, whatever rule changes are highest ranked (along with variations thereof) could potentially\nbe tested during the pre-season, where the like would have a magnified effect, allowing evaluation \nafter fewer games played.\n\"\"\"\n\n# This Python 3 environment comes with many helpful analytics libraries installed\n# It is defined by the kaggle/python docker image: https://github.com/kaggle/docker-python\n# For example, here's several helpful packages to load in \n\nimport numpy as np # linear algebra\nimport pandas as pd # data processing, CSV file I/O (e.g. pd.read_csv)\n\n# Input data files are available in the \"../input/\" directory.\n# For example, running this (by clicking run or pressing Shift+Enter) will list the files in the input directory\n\nimport os\nprint(os.listdir(\"../input\"))\n\n# Any results you write to the current directory are saved as output.\n\n","execution_count":null,"outputs":[]},{"metadata":{"_cell_guid":"79c7e3d0-c299-4dcb-8224-4455121ee9b0","collapsed":true,"_uuid":"d629ff2d2480ee46fbb7e2d37f6b5fab8052498a","trusted":false},"cell_type":"code","source":"","execution_count":null,"outputs":[]}],"metadata":{"kernelspec":{"display_name":"Python 3","language":"python","name":"python3"},"language_info":{"name":"python","version":"3.6.4","mimetype":"text/x-python","codemirror_mode":{"name":"ipython","version":3},"pygments_lexer":"ipython3","nbconvert_exporter":"python","file_extension":".py"}},"nbformat":4,"nbformat_minor":1}