# Basketball Model Methodology & Changes

## Simulating the Season

###### The season is the hardest part to calculate. I calculated the win percentage of the home team of each game, 56 games in total. Each game is simulated by a random number, and if the random number is greater than the win percentage, the away team is calculated as the winner, but if less than , the home team is the winner. This calculated for every game of the season. The season is simulated 10,000 times to fulfill the law of large numbers, which states the larger number of trials, the closer to the expected value you will get. Below is a visual of this and how the observed value becomes closer to the expected values. ## Changes to Model

###### The first one was city champions. At first I had it calculated for the best district record, and not the best city record. This change had no effect on the model, just the final data.The next was the margin of victory index. I felt a complete ELO index would take into account the margin of victory. So how it was calculated was I took the win probability of the underdog and created a spread. This was calculated by an algorithm I regressed from previous data. Then I took the margin of victory and found the difference between the two. So if a team was favored by 8 points and won by 13, their margin of victory index for that game would be 5. That is then added to the ELO change based off of win percentage. I capped the margin of victory index at 20 points per game. So if a team beat or lost by more than 20 to their expected results, it would stop at 20. Below is a graph of the New calculated ELO v. old ELO. The biggest difference is Molina, their starting ELO was a bit over estimated, so the margin of victory index helped get their true ELO sooner, rather than later. 