├── LICENSE ├── README.md ├── balaban ├── JosefinSans-Regular.ttf ├── __init__.py ├── balaban.py └── utils.py └── setup.py /LICENSE: -------------------------------------------------------------------------------- 1 | GNU AFFERO GENERAL PUBLIC LICENSE 2 | Version 3, 19 November 2007 3 | 4 | Copyright (C) 2007 Free Software Foundation, Inc. 5 | Everyone is permitted to copy and distribute verbatim copies 6 | of this license document, but changing it is not allowed. 7 | 8 | Preamble 9 | 10 | The GNU Affero General Public License is a free, copyleft license for 11 | software and other kinds of works, specifically designed to ensure 12 | cooperation with the community in the case of network server software. 13 | 14 | The licenses for most software and other practical works are designed 15 | to take away your freedom to share and change the works. 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It is safest 628 | to attach them to the start of each source file to most effectively 629 | state the exclusion of warranty; and each file should have at least 630 | the "copyright" line and a pointer to where the full notice is found. 631 | 632 | 633 | Copyright (C) 634 | 635 | This program is free software: you can redistribute it and/or modify 636 | it under the terms of the GNU Affero General Public License as published by 637 | the Free Software Foundation, either version 3 of the License, or 638 | (at your option) any later version. 639 | 640 | This program is distributed in the hope that it will be useful, 641 | but WITHOUT ANY WARRANTY; without even the implied warranty of 642 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 643 | GNU Affero General Public License for more details. 644 | 645 | You should have received a copy of the GNU Affero General Public License 646 | along with this program. If not, see . 647 | 648 | Also add information on how to contact you by electronic and paper mail. 649 | 650 | If your software can interact with users remotely through a computer 651 | network, you should also make sure that it provides a way for users to 652 | get its source. For example, if your program is a web application, its 653 | interface could display a "Source" link that leads users to an archive 654 | of the code. There are many ways you could offer source, and different 655 | solutions will be better for different programs; see section 13 for the 656 | specific requirements. 657 | 658 | You should also get your employer (if you work as a programmer) or school, 659 | if any, to sign a "copyright disclaimer" for the program, if necessary. 660 | For more information on this, and how to apply and follow the GNU AGPL, see 661 | . 662 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # balaban 2 | The basic goal of `balaban` is to improve the modelling of uncertainty in common player-level metrics (e.g., pass completion percentages, 3 | goals per 90, xG per shot, xA per 90). This is done through Bayesian hierarchical models for the 4 most common types of metric: 4 | 1. Absolute counts per 90 (passes, shots, assists, goals, tackles etc.) 5 | 2. Success rates (pass completion, tackle success, shots on target etc.) 6 | 3. Model-derived 'expected' successes per action (xA per key pass, xG per shot) 7 | 4. Model-derived 'expected' successes per 90 (xA, xG) 8 | 9 | If you have suggestions for other models you'd like to see, please let me know via [Twitter](https://twitter.com/AnEnglishGoat). 10 | 11 | Here's an [example notebook](https://colab.research.google.com/drive/1CRybRbZXe3Y6AkPh__7jaKCF9O2EaSa6#offline=true&sandboxMode=true). 12 | 13 | **TODO:** 14 | 15 | * ~~There appears to be a way of scraping with Selenium. This is great news and I'll write a function that just requires the league name to pull the latest data from fbref so users don't have to worry about downloading and formatting csv files.~~ This is done now. See the section on [Data Preparation](#data-preparation) below. 16 | * A few of the models are conjugate (don't require MCMC as they can be computed analytically) so I will write much faster sampling functions for those when I've got some time. 17 | * Something that will take more time is turning this thing into a Heroku web app. I really want it to be easy to produce the radar for any given player. I also want fans/analysts to acknowledge that quite often you can't really say much about how good a player is at a particular thing via these sort of stats. *When you can't, it's good to know that you can't.* 18 | 19 | **What does this get me?** 20 | 21 | The ultimate output is a radar-like plot of the model estimates for various metrics. The intensity of green represents our certainty 22 | about the players *percentile rank* for the given metric, taking into account sample size and the inherent variability of the metric. 23 | 24 | ![alt text](https://i.imgur.com/JlQadAq.png "Mikel Merino") 25 | 26 | Darker greens mean we're more confident in that value, so we're fairly sure that Merino's 'true' passing success rate is around the league 27 | median for midfielders. We're also fairly sure that he ranks pretty highly (somewhere around the 85th percentile) for successful passes 28 | into the final 3rd per 90. However, because assists are pretty rare and Merino hasn't done anything particularly spectacular, we're not 29 | very certain about his xA rankings, despite him having played a decent number of games. He's not particularly special and he's unlikely 30 | to be in the top 50% of expected assisters but, aside from that, we can't say much. It's important to remember that 'sample size' 31 | isn't just about the number of minutes played. 32 | 33 | The red numbers are the median and 90% credible intervals for the actual value we're trying to estimate (e.g., successful balls into the 34 | penalty area per 90). Essentially, we're 90% sure his true value lies between the two numbers in the brackets. 35 | 36 | 37 | **Who cares?** 38 | 39 | Probably not many people, but when assessing a player I think it's useful to have: 40 | * A reasonable estimate of the uncertainty associated with each metric (due to sample sizes, the general variability of the metric) 41 | * A reasonable estimate of the uncertainty associated with where players *rank* on each metric (i.e., their percentiles) 42 | * The use of prior information to temper crazy estimates from small sample sizes (you're average until you sufficiently prove otherwise) 43 | 44 | **Why hierarchical modelling?** 45 | 46 | It gets us all three of the things I mentioned above in a principled way. The 'hierarchical' part of the name comes from the fact that 47 | there are two levels to the model: the population level and the individual level. The idea is that we can use the data from *everybody* in the 48 | population (say all midfielders in La Liga) to give us an idea about what a reasonable estimate looks like. As an example, if a guy has played 49 | 180 minutes and registered a pass completion percentage of 31%, we can use the information in the rest of the data to infer that he probably isn't *that* bad 50 | because there is practically nobody with a decent sample size who has that sort of pass completion level. However, we have learned a little 51 | bit about this player. We know he's probably not a *really* good passer, because a really good passer wouldn't be putting up such bad numbers 52 | even over a small number of passes. This is the tradeoff in hierarchical modelling. The resulting estimate, rather than just being a '31%' without 53 | much context, would be quite a wide distribution covering the lower portion of the population. 54 | 55 | 56 | ## **How can I use it?** 57 | 58 | You can install via `pip install balaban`. 59 | 60 | You can install by cloning this repo: `git clone https://github.com/anenglishgoat/balaban` 61 | 62 | Or you can modify this [Colab notebook](https://colab.research.google.com/drive/1CRybRbZXe3Y6AkPh__7jaKCF9O2EaSa6#offline=true&sandboxMode=true) by signing in with your Google account. 63 | 64 | Here is the usage pipeline: 65 | 66 | ### **Data preparation** 67 | 68 | You have a few options: 69 | 70 | #### **Either**: 71 | 72 | Generate a `.csv` file containing the data you want to include. You can download these directly from the 'Squad & Player Stats' tabs on the fbref competition pages, like the one for the [Premier League](https://fbref.com/en/comps/9/Premier-League-Stats). I had to modify the downloaded `.xls` file a little bit in Excel before saving it as a `.csv`. 73 | 74 | 75 | 76 | I just removed the additional row at the top (which contained extra labels about pass types) and changed the file type to `.csv`. 77 | 78 | Once that's done, you can just pass the filepath of the `.csv` to `balaban.bosko`. 79 | 80 | #### **Or**: 81 | 82 | You can scrape from fbref -- to do so you will need to have downloaded the appropriate `chromedriver.exe` file from [here](https://sites.google.com/a/chromium.org/chromedriver/downloads) and made a note of the filepath. You can then run 83 | ``` 84 | from balaban import scrape_top_five_leagues 85 | df = scrape_top_five_leagues('path/to/chromedriver.exe', league_names) 86 | ``` 87 | `league_names` is a list that defaults to `['epl', 'laliga', 'bundesliga', 'ligue1', 'seriea']`, but you can pass any subset of those to reduce the time it takes to scrape. 88 | 89 | #### **Or**: 90 | 91 | Use a pandas dataframe you've generated another way. Just make sure it has columns called 'Player' (player names; *strings*), 'Squad' (team names; *strings*), 'Pos' (playing positions; *strings*; as per fbref, these are one of `DF`, `MF`, `FW`. They can be combined like `MF,FW`), '90s' (number of 90s played, *float*). 92 | 93 | ### **Setting up a bosko object** 94 | 95 | ``` 96 | import balaban 97 | bos = balaban.bosko(df, league_season_string, query_position) 98 | ``` 99 | 100 | This makes a Croatian striker/Python class containing your data that we'll add fitted models to later on. 101 | 102 | * `df` is either a pandas dataframe, a filepath to your csv file, 103 | or a url to your csv file. As long as either your csv file or dataframe have the columns 'Player', 'Squad', 'Pos' & '90s, you're all good. 104 | * `league_season_string` is a character string for plotting purposes. It goes where "La Liga, 2019/20" is in the Merino example above. 105 | * `query_position` is an (optional) character string defining a position filter. For example, if it's `'MF'`, the models will only be fitted on players 106 | for which the string `'MF'` appears in the Pos column. 107 | 108 | ### **Adding models** 109 | 110 | The following function call estimates a model: 111 | ``` 112 | bos.add_model(a,b,model_type,model_name) 113 | ``` 114 | *Note*: the first time you try to add a model, there might be a delay of a couple of minutes. That's PyMC3 compiling some stuff. 115 | 116 | `model_type` specifies which of the four possible models will be estimated. The options are 117 | * `'count'` 118 | - estimate a hierarchical Poisson model. Suitable for 'count per 90' type metrics. 119 | - if `model_type == 'count'`, `a` is the total number of observed actions (goals, passes, etc.) 120 | - if `model_type == 'count'`, `b` is the total number of minutes played 121 | * `'success_rate'` 122 | - estimate a hierarchical Binomial model. Suitable for success rate metrics. 123 | - if `model_type == 'success_rate'`, `a` is the total number of *successful* actions (goals, completed passes, etc.) 124 | - if `model_type == 'success_rate'`, `b` is the total number of *attempted* actions (shots, attempted passes, etc.) 125 | * `'xSpA'` 126 | - estimate a hierarchical Beta model. Suitable for expected success metrics per required action. 127 | - if `model_type == 'xSpA'`, `a` is the total expected successful actions (e.g., xA, xG) 128 | - if `model_type == 'xSpA'`, `b` is the total number of *attempted* corresponding actions (e.g., key passes, shots) 129 | * `'xSp90'` 130 | - combine a count model and an xSpA model to obtain expected successes per 90 131 | - if `model_type == 'xSp90'`, `a` is a *previously estimated* xSpA model 132 | - if `model_type == 'xSp90'`, `b` is a *previously estimated* count model 133 | - previously estimated models can be retrieved via `bos.get_model(name)`. For example, to estimate an xG90 model: 134 | 135 | ``` 136 | bos.add_model('Sh', 'Minutes', 'count', 'Shots/90') 137 | bos.add_model('xG', 'Sh', 'xSpA', 'xG/Shot') 138 | bos.add_model(bos.get_model('xG/Shot'), bos.get_model('Shots/90'), 'xSp90', 'xG/90') 139 | ``` 140 | * `'adj_pass'` 141 | - estimate a length-adjusted pass completion model. It combines two hierarchical binomial models for passes longer than 25 yards and passes shorter than 25 yards. Essentially a very simple expected passing model. 142 | - the estimates are the overall passing success rates if the proportion of long passes is set to the average among the cohort. i.e. it adjusts the pass success rate so that everybody has the same long:short pass ratio -- if you're playing mostly long balls, your pass success will naturally be low. This model attempts to correct for that. 143 | - if `model_type == 'adj_pass'`, `a` is a list of the form `[successful long passes, total successful passes]` 144 | - if `model_type == 'adj_pass'`, `b` is a list of the form `[attempted long passes, total attempted passes]` 145 | 146 | 147 | `model_name` is also the character string that will be used as a label on any subsequent plots. 148 | 149 | `a` and `b` can be either: 150 | * character strings referring to columns in your input `.csv` or pandas dataframe 151 | * arrays containing the values themselves (this allows you to use sums of columns or data not in the original csv/data frame) 152 | 153 | ### **Plot the results** 154 | 155 | Once all of the models you're interested in have been estimated, you can plot the results using 156 | ``` 157 | bos.make_plot(query_player,subtit_text,model_names,use_pretty_font) 158 | ``` 159 | * `query_player` is a character string 160 | * `subtit_text` is a character string defining the first part of the plot subtitle. It goes where 'Passing metrics' appears on the Merino plot. 161 | * `model_names` is an (optional) list of models to plot. Defaults to all of them. 162 | * `use_pretty_font` is an (optional) Boolean telling me whether you want to use the nice font in the example above (`True`) or 163 | the matplotlib default font (`False`). Defaults to `True`. 164 | -------------------------------------------------------------------------------- /balaban/JosefinSans-Regular.ttf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/anenglishgoat/balaban/5fdeb43884a06465a4760e6447924b7c59bf69df/balaban/JosefinSans-Regular.ttf -------------------------------------------------------------------------------- /balaban/__init__.py: -------------------------------------------------------------------------------- 1 | from balaban.balaban import bosko 2 | from balaban.balaban import scrape_top_five_leagues 3 | -------------------------------------------------------------------------------- /balaban/balaban.py: -------------------------------------------------------------------------------- 1 | class bosko: 2 | def __init__(self, df, league_season_string, query_position=None): 3 | import pandas as pd 4 | import pymc3 as pm 5 | if isinstance(df, str): 6 | df = pd.read_csv(df) 7 | df['Minutes'] = df['90s'] * 90 8 | if query_position is not None: 9 | to_keep = [(query_position == str(pos)[0:2]) for pos in list(df['Pos'])] 10 | df = df[to_keep] 11 | self.df = df 12 | self.league_season_string = league_season_string 13 | self.models = [] 14 | self.labels = [] 15 | 16 | def add_model(self, a, b, model_type, name): 17 | from balaban.utils import estimate_model 18 | import numpy as np 19 | if isinstance(a, str): 20 | a = self.df[a] 21 | if isinstance(b, str): 22 | b = self.df[b] 23 | a = np.array(a) 24 | b = np.array(b) 25 | new_model = estimate_model(a, b, model_type) 26 | self.models.append(new_model) 27 | self.labels.append(name) 28 | 29 | def delete_model(self, name): 30 | import numpy as np 31 | which_mod = np.min(np.where(self.labels == name)[0]) 32 | del self.models[which_mod] 33 | del self.labels[which_mod] 34 | 35 | def get_model(self, name): 36 | import numpy as np 37 | which_mod = np.min(np.where(np.array(self.labels) == name)[0]) 38 | return self.models[which_mod] 39 | 40 | def make_plot(self, player_query, subtit_text, model_names=None, use_pretty_font=True, dpi=125): 41 | import matplotlib.pyplot as plt 42 | import matplotlib.font_manager as fm 43 | import matplotlib 44 | import numpy as np 45 | import os 46 | from balaban.utils import obtain_player_quantiles 47 | from importlib_resources import path as get_font_path 48 | if use_pretty_font: 49 | font_path = get_font_path('balaban', 'JosefinSans-Regular.ttf') 50 | try: 51 | with font_path as f: 52 | fname = str(f) 53 | fp_title = fm.FontProperties(fname=fname, size=10) 54 | fp_subtitle = fm.FontProperties(fname=fname, size=9) 55 | fp_labels = fm.FontProperties(fname=fname, size=8) 56 | fp_medians = fm.FontProperties(fname=fname, size=7) 57 | except: 58 | fp_title = fm.FontProperties(size=10) 59 | fp_subtitle = fm.FontProperties(size=9) 60 | fp_labels = fm.FontProperties(size=8) 61 | fp_medians = fm.FontProperties(size=7) 62 | else: 63 | fp_title = fm.FontProperties(size=10) 64 | fp_subtitle = fm.FontProperties(size=9) 65 | fp_labels = fm.FontProperties(size=8) 66 | fp_medians = fm.FontProperties(size=7) 67 | 68 | player_list = np.array(self.df['Player']) 69 | team_list = np.array(self.df['Squad']) 70 | mins_played = np.array(self.df['Minutes']) 71 | 72 | if model_names is not None: 73 | which_mods = [self.labels.index(m_name) for m_name in model_names] 74 | models = [self.models[i] for i in which_mods] 75 | labels = [self.labels[i] for i in which_mods] 76 | 77 | else: 78 | models = self.models 79 | labels = self.labels 80 | 81 | pl = np.where(player_list == player_query)[0][0] 82 | n_bars = len(models) 83 | fig = plt.figure(dpi=dpi) 84 | ax = plt.subplot(111, projection='polar') 85 | p90_collected = [None] * n_bars 86 | for j in range(n_bars): 87 | h, p90 = obtain_player_quantiles(models[j], pl) 88 | p90_collected[j] = p90 89 | ax.bar(np.pi / 2 + j * 2 * np.pi / n_bars, 90 | 1, 91 | color='white', 92 | edgecolor='seagreen', 93 | width=2 * np.pi / n_bars, 94 | linewidth=0.2) 95 | for i in range(1, 25): 96 | ax.bar(np.pi / 2 + j * 2 * np.pi / n_bars, 97 | h[1][i] - h[1][i - 1], 98 | alpha=h[0][i] / np.max(h[0]), 99 | color='seagreen', 100 | width=2 * np.pi / n_bars, 101 | bottom=h[1][i - 1]) 102 | 103 | ax.axis('off') 104 | for quantile in [0.25, 0.5, 0.75]: 105 | ax.plot(np.linspace(0, 2 * np.pi, 200), quantile * np.ones(200), c='gray', 106 | alpha=0.2 + 0.3 * (quantile == 0.5), ls='--') 107 | ax.plot(np.linspace(0, 2 * np.pi, 200), np.ones(200), c='gray', alpha=0.5) 108 | 109 | fig.suptitle(player_list[pl] + ' (' + team_list[pl] + '), ' + self.league_season_string, y=1.04, fontsize=10, 110 | fontproperties=fp_title) 111 | tit = ax.set_title(subtit_text + '; 90s played: ' + str(mins_played[pl] / 90), fontsize=9, y=1.1, 112 | fontproperties=fp_subtitle) 113 | theta = np.pi / 2 + np.arange(n_bars) * 2 * np.pi / n_bars 114 | theta_lower = np.pi / 2 + np.arange(n_bars) * 2 * np.pi / n_bars + np.pi / 20 115 | rotations = np.rad2deg(theta) - 90 - 180 * ((theta > np.pi) & (theta < 2 * np.pi)) 116 | rotations_lower = np.rad2deg(theta_lower) - 90 - 180 * ((theta_lower > np.pi) & (theta_lower < 2 * np.pi)) 117 | 118 | for idx in range(n_bars): 119 | lab = ax.text(theta[idx], 1.2, labels[idx], 120 | ha='center', 121 | va='center', 122 | rotation=rotations[idx], 123 | rotation_mode="anchor", 124 | fontsize=8, 125 | fontproperties=fp_labels, ) 126 | lab = ax.text(theta[idx], 1.075, 127 | f'{p90_collected[idx][1]:.3}' + ' (' + f'{p90_collected[idx][0]:.3}' + ', ' + f'{p90_collected[idx][2]:.3}' + ')', 128 | ha='center', 129 | va='center', 130 | rotation=rotations[idx], 131 | rotation_mode="anchor", 132 | fontsize=9, 133 | fontproperties=fp_medians, 134 | color='firebrick') 135 | plt.show() 136 | 137 | 138 | def scrape_top_five_leagues(path_to_chromedriver, league_names=['epl', 'laliga', 'bundesliga', 'ligue1', 'seriea']): 139 | from selenium import webdriver 140 | import pandas as pd 141 | import numpy as np 142 | from balaban.utils import get_col_dtype 143 | from selenium.webdriver.chrome.options import Options 144 | 145 | top_5_league_nums = np.array(['9', '12', '20', '13', '11']) 146 | top_5_league_names = np.array(['Premier-League', 'La-Liga', 'Bundesliga', 'Ligue-1', 'Serie-A']) 147 | league_codes = ['epl', 'laliga', 'bundesliga', 'ligue1', 'seriea'] 148 | league_names = list(league_names) if (type(league_names) is np.ndarray) or ( 149 | type(league_names) is tuple) else league_names 150 | league_names = [league_names] if type(league_names) is str else league_names 151 | 152 | try: 153 | league_matches = np.isin(league_codes, league_names) 154 | except: 155 | raise ValueError( 156 | "league_names should be a list of characters. Available options are 'epl', 'laliga', 'bundesliga', " 157 | "'ligue1', 'seriea'") 158 | 159 | if np.sum(league_matches) == 0: 160 | raise ValueError( 161 | "league_names should be a list of characters. Available options are 'epl', 'laliga', 'bundesliga', " 162 | "'ligue1', 'seriea'") 163 | elif np.sum(league_matches) != len(league_names): 164 | raise ValueError( 165 | "league_names contains strings that weren't matched. Available options are 'epl', 'laliga', 'bundesliga', " 166 | " 'ligue1', 'seriea'") 167 | 168 | chrome_options = webdriver.ChromeOptions() 169 | chrome_options.add_argument('--headless') 170 | chrome_options.add_argument('--no-sandbox') 171 | chrome_options.add_argument('--disable-dev-shm-usage') 172 | browser = webdriver.Chrome(path_to_chromedriver, chrome_options=chrome_options) 173 | 174 | top_5_league_names = list(top_5_league_names[league_matches]) 175 | top_5_league_nums = list(top_5_league_nums[league_matches]) 176 | 177 | categories = ['passing', 'shooting', 'misc','possession','defense','gca','passing_types'] 178 | all_players_df = pd.DataFrame() 179 | for lnum, lnam in zip(top_5_league_nums, top_5_league_names): 180 | for category in categories: 181 | url = 'https://fbref.com/en/comps/' + lnum + '/' + category + '/' + lnam + '-Stats' 182 | browser.get(url) 183 | if category == 'passing': 184 | my_table = browser.find_element_by_id('div_stats_passing') 185 | my_table = my_table.find_element_by_xpath("table") 186 | df = pd.read_html(my_table.get_attribute('outerHTML'))[0] 187 | col_names = np.array( 188 | [('Unnamed:' not in val[0]) * (val[0] + ': ') + val[1] for val in df.columns.values]) 189 | tmp = np.array(df)[:, np.r_[1, 3, 4, np.arange(7, df.shape[1] - 1)]] 190 | tmp = np.c_[np.tile(lnam, tmp.shape[0]), tmp] 191 | tmp_col_names = np.r_[np.array('League'), col_names[np.r_[1, 3, 4, np.arange(7, df.shape[1] - 1)]]] 192 | league_df = pd.DataFrame(tmp) 193 | league_df.columns = tmp_col_names 194 | league_df = league_df[league_df['Player'] != 'Player'] 195 | league_df = league_df.astype(league_df.apply(get_col_dtype).to_dict()) 196 | league_df.index = league_df['Player'] 197 | else: 198 | my_table = browser.find_element_by_id('div_stats_'+category) 199 | my_table = my_table.find_element_by_xpath("table") 200 | df = pd.read_html(my_table.get_attribute('outerHTML'))[0] 201 | col_names = np.array( 202 | [('Unnamed:' not in val[0]) * (val[0] + ': ') + val[1] for val in df.columns.values]) 203 | tmp = np.array(df)[:, np.r_[1, np.arange(8, df.shape[1] - 1)]] 204 | tmp_df = pd.DataFrame(tmp) 205 | tmp_df.columns = col_names[np.r_[1, np.arange(8, df.shape[1] - 1)]] 206 | tmp_df = tmp_df[tmp_df['Player'] != 'Player'] 207 | tmp_df = tmp_df.astype(tmp_df.apply(get_col_dtype).to_dict()) 208 | tmp_df = tmp_df.set_index(list(tmp_df)[0]) 209 | league_df = pd.concat([league_df, tmp_df], axis=1, sort=False) 210 | 211 | all_players_df = pd.concat([all_players_df, league_df]) 212 | 213 | return all_players_df 214 | -------------------------------------------------------------------------------- /balaban/utils.py: -------------------------------------------------------------------------------- 1 | def fit_counts_model(counts, mins_played): 2 | ## estimates a hierarchical poisson model for count data 3 | ## takes as input: 4 | ## counts, a numpy array of shape (num_players,) containing the total numbers of actions completed (across all games) 5 | ## mins_played, a numpy array of shape (num_players,) containing the total number of minutes each player was observed for 6 | ## returns: 7 | ## sl, a numpy array of shape (6000,N) containing 6000 posterior samples of actions per 90 (N is the number of players in the 8 | ## original data frame who have actually played minutes) 9 | ## sb, a numpy array of shape (6000,2) containing 6000 posterior samples of the population-level gamma shape parameter & 10 | ## the population-level mean 11 | ## kk, boolean indicating which players have actually played minutes 12 | import numpy as np 13 | import pymc3 as pm 14 | kk = (mins_played > 0) & np.isfinite(counts) 15 | mins_played = mins_played[kk] 16 | counts = counts[kk] 17 | N = counts.shape[0] 18 | 19 | with pm.Model() as model: 20 | beta = pm.HalfNormal('beta', sigma=100) 21 | mu = pm.HalfFlat('mu') 22 | lambdas = pm.Gamma('lambdas', alpha=mu * beta, beta=beta, shape=N) 23 | lambda_tilde = lambdas * mins_played 24 | y = pm.Poisson('y', lambda_tilde, observed=counts) 25 | approx = pm.fit(n=30000) 26 | sl = approx.sample(6000)['lambdas'] * 90 27 | sb = np.c_[approx.sample(6000)['beta'], approx.sample(6000)['mu']] 28 | return [sl, sb, kk, 'count'] 29 | 30 | 31 | def fit_successes_model(successes, attempts): 32 | ## estimates a hierarchical binomial model for success rate data 33 | ## takes as input: 34 | ## successes, a numpy array of shape (num_players,) containing the total numbers of successful actions (across all games) 35 | ## attempts, a numpy array of shape (num_players,) containing the total numbers of attempted actions (across all games) 36 | ## returns: 37 | ## sl, a numpy array of shape (6000,N) containing 6000 posterior samples of success probabilites (N is the number of players in the 38 | ## original data frame who have actually attempted a pass) 39 | ## sb, a numpy array of shape (6000,2) containing 6000 posterior samples of the population-level beta parameters 40 | ## kk, boolean indicating which players have actually attempted a pass 41 | import numpy as np 42 | import pymc3 as pm 43 | import pymc3.distributions.transforms as tr 44 | import theano.tensor as tt 45 | kk = (attempts > 0) & np.isfinite(successes) 46 | attempts = attempts[kk] 47 | successes = successes[kk] 48 | N = attempts.shape[0] 49 | 50 | def logp_ab(value): 51 | ''' prior density''' 52 | return tt.log(tt.pow(tt.sum(value), -5 / 2)) 53 | 54 | with pm.Model() as model: 55 | # Uninformative prior for alpha and beta 56 | ab = pm.HalfFlat('ab', 57 | shape=2, 58 | testval=np.asarray([1., 1.])) 59 | pm.Potential('p(a, b)', logp_ab(ab)) 60 | 61 | lambdas = pm.Beta('lambdas', alpha=ab[0], beta=ab[1], shape=N) 62 | 63 | p = pm.Binomial('y', p=lambdas, observed=successes, n=attempts) 64 | approx = pm.fit(n=30000) 65 | sl = approx.sample(6000)['lambdas'] * 100 66 | sb = approx.sample(6000)['ab'] 67 | return [sl, sb, kk, 'success'] 68 | 69 | 70 | def fit_expected_successes_per_action_model(xS, attempts): 71 | ## estimates a hierarchical binomial model for success rate data 72 | ## takes as input: 73 | ## sp, a numpy array of shape (num_players,) containing the expected successes per action for each player (e.g. xG per shot, xA per KP) 74 | ## attempts, a numpy array of shape (num_players,) containing the total numbers of attempted actions for each player (e.g. shots, key passes) 75 | ## returns: 76 | ## sl, a numpy array of shape (6000,N) containing 6000 posterior samples of success probabilites (N is the number of players in the 77 | ## original data frame who have registered non-zero expected succcesses) 78 | ## sb, a numpy array of shape (6000,3) containing 6000 posterior samples of: the population-level & observation-level beta 'sample size' 79 | ## parameters and the population-level mean 80 | ## kk, boolean indicating which players have actually registered non-zero expected successes 81 | import numpy as np 82 | import pymc3 as pm 83 | kk = (attempts > 0) & (xS > 0) 84 | sp = xS[kk] / attempts[kk] 85 | attempts = attempts[kk] 86 | N = attempts.shape[0] 87 | 88 | with pm.Model() as model: 89 | v = pm.HalfNormal('v', shape=2, sigma=100) 90 | mu = pm.Uniform('mu') 91 | lambdas = pm.Beta('lambdas', alpha=mu * v[0], beta=(1 - mu) * v[0], shape=N) 92 | y = pm.Beta('y', 93 | alpha=lambdas * (attempts * (v[1] + 1) - 1), 94 | beta=(1 - lambdas) * (attempts * (v[1] + 1) - 1), 95 | observed=sp) 96 | approx = pm.fit(n=30000) 97 | sl = approx.sample(6000)['lambdas'] 98 | sb = np.c_[approx.sample(6000)['v'], approx.sample(6000)['mu']] 99 | return [sl, sb, kk, 'expected'] 100 | 101 | 102 | def fit_expected_successes_per90_model(xSuccess_model, attempts_model): 103 | ## the inputs are two models which should have been returned by: 104 | ## fit_expected_successes_per_action_model (first argument) 105 | ## fit_counts_model (second argument) 106 | ## the input models should estimate 107 | ## the number of actions attempted per 90 (e.g. shots or key passes) -- fit on count data 108 | ## the probability per action that they lead to the corresponding desired outcome (e.g. goal or assist) -- fit on xG/xA data 109 | kk = (xSuccess_model[2] & attempts_model[2]) 110 | sl = (attempts_model[0][:, kk[attempts_model[2]]] * xSuccess_model[0][:, kk[xSuccess_model[2]]]) 111 | return [sl, [], kk, 'expected_per90'] 112 | 113 | 114 | def fit_adj_pass_model(successes, attempts): 115 | ## inputs are two lists in the form: 116 | ## successes = [successful long passes, total successful passes] 117 | ## attempts = [attempted long passes, total attempted passes] 118 | ## returns: 119 | ## sl, a numpy array of shape (6000,N) containing 6000 posterior samples of success probabilites (N is the number of players in the 120 | ## original data frame who have registered non-zero expected succcesses) 121 | ## sb, an empty list 122 | ## kk, boolean indicating which players have actually registered non-zero expected successes 123 | ## 'adj_pass', character string indicating the model type. 124 | import numpy as np 125 | import pymc3 as pm 126 | import pymc3.distributions.transforms as tr 127 | import theano.tensor as tt 128 | LonCmp = successes[0] 129 | TotCmp = successes[1] 130 | LonAtt = attempts[0] 131 | TotAtt = attempts[1] 132 | kk = (LonCmp > 0) & np.isfinite(LonAtt) 133 | LonCmp = LonCmp[kk] 134 | LonAtt = LonAtt[kk] 135 | TotCmp = TotCmp[kk] 136 | TotAtt = TotAtt[kk] 137 | ShCmp = TotCmp - LonCmp 138 | ShAtt = TotAtt - LonAtt 139 | average_long_tendency = np.mean(LonAtt / TotAtt) 140 | N = np.sum(kk) 141 | 142 | def logp_ab(value): 143 | ''' prior density''' 144 | return tt.log(tt.pow(tt.sum(value), -5 / 2)) 145 | 146 | with pm.Model() as model: 147 | # Uninformative prior for alpha and beta 148 | ab_short = pm.HalfFlat('ab_short', 149 | shape=2, 150 | testval=np.asarray([1., 1.])) 151 | ab_long = pm.HalfFlat('ab_long', 152 | shape=2, 153 | testval=np.asarray([1., 1.])) 154 | pm.Potential('p(a_s, b_s)', logp_ab(ab_short)) 155 | pm.Potential('p(a_l, b_l)', logp_ab(ab_long)) 156 | 157 | lambda_short = pm.Beta('lambda_s', alpha=ab_short[0], beta=ab_short[1], shape=N) 158 | lambda_long = pm.Beta('lambda_l', alpha=ab_long[0], beta=ab_long[1], shape=N) 159 | 160 | y_short = pm.Binomial('y_s', p=lambda_short, observed=ShCmp, n=ShAtt) 161 | y_long = pm.Binomial('y_l', p=lambda_short * lambda_long, observed=LonCmp, n=LonAtt) 162 | approx = pm.fit(n=30000) 163 | s_sh = approx.sample(6000)['lambda_s'] 164 | s_lo = approx.sample(6000)['lambda_l'] 165 | sl = average_long_tendency * s_lo + (1 - average_long_tendency) * s_sh 166 | return [sl, [], kk, 'adj_pass'] 167 | 168 | 169 | def estimate_model(a, b, model_type): 170 | if model_type == 'count': 171 | out = fit_counts_model(a, b) 172 | elif model_type == 'success_rate': 173 | out = fit_successes_model(a, b) 174 | elif model_type == 'xSpA': 175 | out = fit_expected_successes_per_action_model(a, b) 176 | elif model_type == 'adj_pass': 177 | try: 178 | out = fit_adj_pass_model(a, b) 179 | except ValueError: 180 | print( 181 | "Check inputs. The inputs should be two lists of the form [successful long passes, total successful passes] & [attempted long passes, total attempted passes]") 182 | elif model_type == 'xSp90': 183 | try: 184 | out = fit_expected_successes_per90_model(a, b) 185 | except ValueError: 186 | print( 187 | "Check inputs. The inputs should be two pre-estimated models. The first argument should be a list returned by a 'counts' model. The second argument should be a list returned by an 'xSpA' model.") 188 | else: 189 | raise ValueError("Invalid model_type. model_type should be one of 'count', 'success_rate', 'xSpA', or 'xSp90'") 190 | return out 191 | 192 | 193 | def obtain_player_quantiles(model, player_index): 194 | model_type = model[3] 195 | import numpy as np 196 | 197 | pind = np.arange(np.shape(model[2])[0])[model[2]] 198 | pind = np.where(pind == player_index)[0] 199 | if pind.shape[0] == 0: 200 | return (np.zeros(25), np.linspace(0,1,26)), np.zeros(3) 201 | 202 | if model_type == 'count': 203 | from scipy.stats import gamma 204 | percentile_hist = np.histogram( 205 | gamma.cdf(model[0][:, pind], 206 | a=np.mean(model[1][:, 1]) * np.mean(model[1][:, 0]), 207 | scale=90 / np.mean(model[1][:, 0])), 208 | bins=25) 209 | per90_quantiles = np.quantile(model[0][:, pind], [0.125, 0.5, 0.875]) 210 | elif model_type == 'success': 211 | from scipy.stats import beta 212 | percentile_hist = np.histogram( 213 | beta.cdf(model[0][:, pind] / 100, 214 | a=np.mean(model[1][:, 0]), 215 | b=np.mean(model[1][:, 1])), 216 | bins=25) 217 | per90_quantiles = np.quantile(model[0][:, pind], [0.05, 0.5, 0.95]) 218 | elif model_type == 'expected': 219 | from scipy.stats import beta 220 | percentile_hist = np.histogram( 221 | beta.cdf(model[0][:, pind], 222 | a=np.mean(model[1][:, 2]) * np.mean(model[1][:, 0]), 223 | b=(1 - np.mean(model[1][:, 2])) * np.mean(model[1][:, 0])), 224 | bins=25) 225 | per90_quantiles = np.quantile(model[0][:, pind], [0.05, 0.5, 0.95]) 226 | elif (model_type == 'expected_per90') | (model_type == 'adj_pass'): 227 | samps_flat = np.random.choice(model[0].flatten(), size=5000) ## downsample to make cdf quicker to compute 228 | sorted_samps = np.sort(samps_flat) 229 | ecdf = lambda x: np.sum(sorted_samps[:, None] < x, axis=0) / len(sorted_samps) 230 | percentile_hist = np.histogram( 231 | ecdf(model[0][:, pind].T), 232 | bins=25) 233 | per90_quantiles = np.quantile(model[0][:, pind], [0.05, 0.5, 0.95]) 234 | else: 235 | print("Invalid model type. Must be one of 'count', 'success', 'expected', 'expected_per90' or 'adj_pass'") 236 | return percentile_hist, per90_quantiles 237 | 238 | 239 | def get_col_dtype(col): 240 | import pandas as pd 241 | import numpy as np 242 | """ 243 | Infer datatype of a pandas column, process only if the column dtype is object. 244 | input: col: a pandas Series representing a df column. 245 | """ 246 | 247 | if col.dtype == "object": 248 | 249 | # try numeric 250 | try: 251 | col_new = pd.to_datetime(col.dropna().unique()) 252 | return col_new.dtype 253 | except: 254 | try: 255 | col_new = pd.to_numeric(col.dropna().unique()) 256 | return np.dtype('float64') 257 | except: 258 | try: 259 | col_new = pd.to_timedelta(col.dropna().unique()) 260 | return col_new.dtype 261 | except: 262 | return "object" 263 | 264 | else: 265 | return col.dtype 266 | -------------------------------------------------------------------------------- /setup.py: -------------------------------------------------------------------------------- 1 | import setuptools 2 | 3 | with open("README.md", "r") as fh: 4 | long_description = fh.read() 5 | 6 | setuptools.setup( 7 | name="balaban", 8 | version="0.0.20", 9 | author="Will Thomson", 10 | author_email="willthomson1991@gmail.com", 11 | description="Bayesian hierarchical models for football", 12 | long_description=long_description, 13 | long_description_content_type="text/markdown", 14 | url="https://github.com/anenglishgoat/balaban", 15 | packages=setuptools.find_packages(), 16 | install_requires=['importlib.resources', 'numpy', 'pymc3', 'pandas', 'matplotlib','selenium'], 17 | classifiers=[ 18 | "Programming Language :: Python :: 3", 19 | "License :: OSI Approved :: MIT License", 20 | "Operating System :: OS Independent", 21 | ], 22 | include_package_data=True, 23 | python_requires='>=3.2', 24 | ) --------------------------------------------------------------------------------