The following code can be used to create projections for the Men’s and Women’s Kaggle March Madness Tournament.
[Note: This code, without explanations, can be found in ‘making_stage2_predictions.R’]
library(rvest)
library(XML)
library(RCurl)
library(dplyr)
library(reshape2)
library(lme4)
library(tidyverse)
source("add_win_it_all_guess.R")
source("cross_ratings.R")
source("scrape_dolphin.R")
source("utils.R")
source("match_dolphin_to_games.R")
source("match_538_to_games.R")
source("modify_538_ratings.R")A full description of Nate Silver’s Methodology is described here.
The following code reads in the 538’s ratings and splits them into Men’s and Women’s ratings.
x538 <- read.csv("stage2data/fivethirtyeight_ncaa_forecasts.csv")
M538 = x538 %>% filter(gender=="mens")
W538 = x538 %>% filter(gender=="womens")
M538 <- M538 %>% dplyr::select(team_name, team_rating)
W538 <- W538 %>% dplyr::select(team_name, team_rating)Suppose that I think that the Men’s Gonzaga team is underrated and should have a rating of 100 instead of 96.47. I can change their score to 100 using the modify_538_ratings function.
M538 = modify_538_ratings(M538, "Gonzaga", 100)Likewise, if I think that the women’s Stanford team is over-rated by 538 and should really only have a rating of 95, I use the code:
W538 = modify_538_ratings(W538, "Stanford", 95)Note, that I need to use 538’s team name spellings when using this function so take a look at M538 and W538 before using it.
Next, we read in the Sample Submission files (with the games we need to project) and match up each game with 538 ratings.
Wgames = match_538_to_games("stage2data/WSampleSubmissionStage2.csv", W538, "W")
Mgames = match_538_to_games("stage2data/MSampleSubmissionStage2.csv", M538, "M")The last step is to make predictions for each game. We can use the following formula for the change that team 1 (with a rating of r1) beats team 2 (with a rating of r2):
\[prediction\ = \frac{1}{1 + 10^{(r_2 - r_1)\cdot\frac{30.464}{400}}}\]
In R, we create the function…
pred538 <- function(r1, r2){
1/(1+ 10^((r2-r1)*30.464/400))
}… and then apply this function to each game.
Wgames = Wgames %>% mutate(Pred = pred538(team1rating, team2rating))
Mgames = Mgames %>% mutate(Pred = pred538(team1rating, team2rating))While added pure guesses is likely to doom your submission to a terrible log loss score, it might also give a chance to win!
I’ve written two functions to help add guesses.
add_win_it_all_guess gives one team a 100% chance to win all of its games. If this team doesn’t win the tournament, you’ll be out of luck. If I want to bank on Stanford winning all of it’s games in the women’s tournament, I would run the following (note the third parameter is “W”, this would be “M” if you are making predictions for the men’s tournament):
Wgames = add_win_it_all_guess(Wgames, "Stanford", "W")This function can be used twice in succession, however. If I think that Stanford will win all of it’s games except its match-up against South Carolina and South Carolina will win it all, I would run this function twice, first with Stanford and then with South Carolina:
Wgames = add_win_it_all_guess(Wgames, "Stanford", "W")
Wgames = add_win_it_all_guess(Wgames, "South Carolina", "W")The other guessing function add_teamA_beats_teamB_guess simply predicts the outcome of one matchup. If, for instance, I want to predict that Miami beats South Florida in the first round of the women’s tournament, I can run the code:
Wgames = add_teamA_beats_teamB_guess(Wgames, "Miami Fl", "South Florida", "W")Two warnings! First, I likely isn’t obvious that we need to use “Miami Fl” for Miami. Please check the WTeamSpellings.csv and MTeamSpellings.csv files within the stage2data folder to see the acceptable spellings of these team names. Second, if you’ve run all of the code above, you will have prediction that South Carolina wins it all, Stanford wins except when it faces South Carolina and that Miami beats South Florida in the first round. You can run the code above, to recreate W538 and M538 as well as Wgames and Mgames and start fresh, only making the adjustments you want.
Running all the code above produces two data frames Wgames and Mgames. We can turn these into .csv files that we can submit to Kaggle using the write_submission_file function. The code below takes the Wgames predictions and creates a file called “MyAwesomePredictions.csv” which could be submitted directly to Kaggle.
write_submission_file(Wgames, "MyAwesomePredictions") The cross_ratings function uses the outcomes and scores of regular season games to predict the outcomes of tournament games. We have to point it to the regular season results and the sample submission file and can tell it how much weight to give to win/loss outcomes and how much weight to give to score differentials. The following code would give 80% weight to score differential and 20% weight to win/loss outcomes:
compact_results_file = "stage2data/MRegularSeasonCompactResults.csv"
submission_file = "stage2data/MSampleSubmissionStage2.csv"
Mgames <-
cross_predictions(compact_results_file = compact_results_file,
submission_file = submission_file,
weight_scores = 0.8,
weight_outcomes = 0.2)
I can modify these predictions in the same ways that I modified predictions based on 538 ratings. For example, I can make Gonzaga win it all:
Mgames = add_win_it_all_guess(Mgames, "Gonzaga", "M")
Mgames = add_teamA_beats_teamB_guess(Mgames, "Boise St", "Memphis", "M")
I can also also write these to a .csv file the same way:
write_submission_file(Mgames, "AwesomeCrossRatingsPreds")
Andy Dolphin’s NCAA Men’s Basketball ratings can be found here. This website only has ratings for Men’s teams and the method below can therefore only be used for the Men’s tournament.
We can scrape them and match these ratings to the games we need to project using the following code:
dolphin_ratings <- scrape_dolphin()dolphin now contains Dolphin’s team ratings matched up with TeamID’s.
We can match this with games using:
submission_file = "stage2data/MSampleSubmissionStage2.csv"
Mgames = match_dolphin_to_games(submission_file, dolphin_ratings)You can use Dolphin’s ratings to making predictions by taking the difference in ratings between the two teams and treating that difference as a z-score. Using that z-score and a standard normal table, you can produce a probability. To do this in R, create the function dolphin_pred
dolphin_pred <- function(team1rating, team2rating){
z = team1rating - team2rating
pnorm(z)
}You can use this function by doing:
Mgames = Mgames %>%
mutate(Pred = dolphin_pred(team1rating, team2rating))You can add guesses to these predictions and create a .csv file to submit to Kaggle just as you did with the Mgames data frames created using other methods.
Remember that you get to make two submissions for each tournament! It would serve you well to make them different from each other. If you add guesses, you may want to make the guesses in your two ballots mutually exclusive.
Also, note if you make two submissions to Kaggle and later think better of them, you can make additional submission and then choose the ones that you will use in the competition.
Final Submission Times (2022):
Men’s Tournament - Thursday, March 17th, noon
Women’s - Friday, March 18th, 11 am