PredictGuru
Saturday, October 23, 2010
Page Rank kind of ranking for test cricket teams
The official ranking for test teams in ICC is quite complicated http://en.wikipedia.org/wiki/ICC_Test_Championship#Test_championship_calculations . It seems a bit confusing with all the arbitrary point calculations. (40 points, 90 points etc). And although it tries to give more points to a weaker team that beats a stronger team, the effect is not uniform. The scoring scheme can be made more elegant by a simple page rank kind of algorithm.
The idea is, if India beats Australia in a series 2-1, Indias score would be (score-of-australia)*2/3 and australias score would be (score-of-india)*1/3. At the end of a given time period, lets say india beat aus 2-0, SA 3-1 and lost to bangladesh 1-0. Indias score would be:
india-score = k(india-score + 2/2*aus_score + 3/4*sa_score +0*bangladesh_score)
similarly for bangladesh, bang-score = k(bang-score + 1*india-score + other series)
where k is a constant.
This leads to a linear set of equations which can be solved by using the eigen-value decomposition. Each eigen vector is a solution, which in this case becomes a possible team score. We can take the vector that corresponds to the maximum eigen value.
The data for all the test series played until now is available from cricinfo at http://stats.cricinfo.com/ci/content/records/335431.html. I used a slightly modified version of the above scoring scheme, The score I used was (number of wins)/(total-matches + 1) . Just to score more for a comprehensive 3-0 win (3/(3+1) = 0.75) v/s a 1-0 win (0.5) The scores for the last 3 years, that is 2007 and beyond are
"India" 0.5994906420666286
"Australia" 0.48114889162515917
"South Africa" 0.46906326930865216
"England" 0.27645475105538375,
"Sri Lanka" 0.29340243047144315
"West Indies" 0.11112461214397185
"Pakistan" 0.09815656282323282
"New Zealand" 0.05997455303303149
"Bangladesh" 0.03152476327152151,
If scored this way, Australia still seem to have a higher ranking as compared to the ICC ranking where they are number currently number 5. I also tried plotting the scores for the last 130 years of test cricket. Here are the results.
As expected, India is rising now whereas Australia is falling, WI dominated a decade after 75. Surprising thing is England started both the world wars winning against Australia and immediately after the wars, Australia was on top.
Here is the clojure code for doing all this, jblas is needed for eigen decomposition and jfreechart for plotting.
The idea is, if India beats Australia in a series 2-1, Indias score would be (score-of-australia)*2/3 and australias score would be (score-of-india)*1/3. At the end of a given time period, lets say india beat aus 2-0, SA 3-1 and lost to bangladesh 1-0. Indias score would be:
india-score = k(india-score + 2/2*aus_score + 3/4*sa_score +0*bangladesh_score)
similarly for bangladesh, bang-score = k(bang-score + 1*india-score + other series)
where k is a constant.
This leads to a linear set of equations which can be solved by using the eigen-value decomposition. Each eigen vector is a solution, which in this case becomes a possible team score. We can take the vector that corresponds to the maximum eigen value.
The data for all the test series played until now is available from cricinfo at http://stats.cricinfo.com/ci/content/records/335431.html. I used a slightly modified version of the above scoring scheme, The score I used was (number of wins)/(total-matches + 1) . Just to score more for a comprehensive 3-0 win (3/(3+1) = 0.75) v/s a 1-0 win (0.5) The scores for the last 3 years, that is 2007 and beyond are
"India" 0.5994906420666286
"Australia" 0.48114889162515917
"South Africa" 0.46906326930865216
"England" 0.27645475105538375,
"Sri Lanka" 0.29340243047144315
"West Indies" 0.11112461214397185
"Pakistan" 0.09815656282323282
"New Zealand" 0.05997455303303149
"Bangladesh" 0.03152476327152151,
If scored this way, Australia still seem to have a higher ranking as compared to the ICC ranking where they are number currently number 5. I also tried plotting the scores for the last 130 years of test cricket. Here are the results.
As expected, India is rising now whereas Australia is falling, WI dominated a decade after 75. Surprising thing is England started both the world wars winning against Australia and immediately after the wars, Australia was on top.
Here is the clojure code for doing all this, jblas is needed for eigen decomposition and jfreechart for plotting.
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| (ns test_cricket_ranking.data_processor | |
| (:require [clojure.contrib.string :as str-utils :only (join)]) | |
| (:use [util.charting charts]) | |
| (:import [org.jblas DoubleMatrix Eigen]) | |
| (:import (java.io BufferedReader FileReader)) | |
| (:import (org.jfree.data.time Year TimeSeries TimeSeriesCollection ))) | |
| (defn year_str_of_line [line] (nth (.split line "\t") 1)) | |
| (defn match_year [line] | |
| (Integer. (.trim (nth (.split (year_str_of_line line) "/") 0)))) | |
| (defn match_between_dates? [line start_date end_date] | |
| (let [year_of_match (match_year line)](and | |
| (>= year_of_match start_date) | |
| (<= year_of_match end_date)))) | |
| (def countries | |
| [ "Australia" "Bangladesh" "England" "India" | |
| "New Zealand" "Pakistan" "South Africa" "Sri Lanka" | |
| "West Indies" "Zimbabwe" ]) | |
| (def countries_pattern (re-pattern (str-utils/join "|" countries))) | |
| (defn get-country-names [line] | |
| (take 2 (re-seq countries_pattern line))) | |
| (defn teams [line, playing_countries] | |
| (map #(playing_countries %) (get-country-names line))) | |
| (defn winner [line, playing_countries] | |
| (or (playing_countries (.trim (nth (.split line "\t") 3))) (nth (teams line playing_countries) 0))) | |
| (def score-pattern | |
| (re-pattern "([0-9]*)-([0-9]*) \\(([0-9]*)\\)")) | |
| (defn scores [line] | |
| (let [wins (nth (re-seq score-pattern (nth (.split line "\t") 4)) 0) | |
| winner_score (Double. (nth wins 1)) | |
| loser_score (Double. (nth wins 2)) | |
| total_matches (Double. (nth wins 3))] | |
| [(/ winner_score (+ total_matches 1)) (/ loser_score (+ total_matches 1))])) | |
| (defn populate_matrix [line d playing_countries] | |
| (let [teams (teams line playing_countries) scores (scores line) winner (winner line playing_countries) | |
| loser (if (== winner (nth teams 0)) (nth teams 1) (nth teams 0))] | |
| (.put d winner loser (+ (.get d winner loser) (nth scores 0))) | |
| (.put d loser winner ( + (.get d loser winner) (nth scores 1))))) | |
| (defn to_matrix [file_name start_year end_year playing_countries] | |
| (let [d (DoubleMatrix/eye (count playing_countries))] | |
| (with-open [rdr (BufferedReader. (FileReader. file_name))] | |
| (doseq [line (filter #(match_between_dates? % start_year end_year) (line-seq rdr))] | |
| (populate_matrix line d playing_countries))) d)) | |
| (defn playing_countries [result_file start_year end_year] | |
| (let [country_names (set (flatten (flatten (for [line (filter #(match_between_dates? % start_year end_year) | |
| (.split (slurp result_file) "\n"))] (get-country-names line ))))) indexes (range (count country_names))] (zipmap (sort country_names) indexes))) | |
| (defn abs [x] (if (pos? x) x (- x))) | |
| (defn arg-max [coll] | |
| (last (last (sort (seq (zipmap coll (range (count coll)))))))) | |
| (defn get_max_eigen_index [d len] | |
| (arg-max (let [idxs (range len) vals (for [i idxs] (abs (.real (.get d i i))))] vals))) | |
| (defn compute_scores_by_teams [result_file start_year end_year, playing_countries] | |
| (map abs (let [m (to_matrix result_file start_year end_year playing_countries) | |
| size (count playing_countries) | |
| ev (Eigen/eigenvectors m) | |
| eigen_vectors (get ev 0) | |
| eigen_values (get ev 1) | |
| top_eigen_value_index (get_max_eigen_index eigen_values size) | |
| all_team_scores (.getColumn eigen_vectors top_eigen_value_index)] | |
| (for [team_id (range size)] (.getReal all_team_scores team_id))))) | |
| (defn compute_ranks [result_file start_year end_year] | |
| (let [playing_countries (playing_countries result_file start_year end_year)] | |
| (if (empty? playing_countries) {} | |
| (zipmap (sort (keys playing_countries)) | |
| (compute_scores_by_teams result_file start_year end_year playing_countries))))) | |
| (defn plot-scores [data] | |
| (let [country_specific_ts {:au (TimeSeries. "Australia") :bn (TimeSeries. "Bangladesh") :en (TimeSeries. "England") :in (TimeSeries. "India") | |
| :nz (TimeSeries. "New Zealand") :pk (TimeSeries. "Pakistan") :sa (TimeSeries. "South Africa") :sl (TimeSeries. "Sri Lanka") | |
| :wi (TimeSeries. "West Indies") :zm (TimeSeries. "Zimbabwe")}] | |
| (doseq [year (sort (keys data))] | |
| (let [year_entry (Year. year) year_data (data year)] | |
| ;(println (:au country_specific_ts)) | |
| (.add (:au country_specific_ts) year_entry (get year_data "Australia" 0)) | |
| (.add (:bn country_specific_ts) year_entry (get year_data "Bangladesh" 0)) | |
| (.add (:en country_specific_ts) year_entry (get year_data "England" 0)) | |
| (.add (:in country_specific_ts) year_entry (get year_data "India" 0)) | |
| (.add (:nz country_specific_ts) year_entry (get year_data "New Zealand" 0)) | |
| (.add (:pk country_specific_ts) year_entry (get year_data "Pakistan" 0)) | |
| (.add (:sa country_specific_ts) year_entry (get year_data "South Africa" 0)) | |
| (.add (:sl country_specific_ts) year_entry (get year_data "Sri Lanka" 0)) | |
| (.add (:wi country_specific_ts) year_entry (get year_data "West Indies" 0)) | |
| (.add (:zm country_specific_ts) year_entry (get year_data "Zimbabwe" 0)) | |
| )) | |
| (let [tc (TimeSeriesCollection.)] | |
| (.addSeries tc (:au country_specific_ts)) | |
| (.addSeries tc (:bn country_specific_ts)) | |
| (.addSeries tc (:en country_specific_ts)) | |
| (.addSeries tc (:in country_specific_ts)) | |
| (.addSeries tc (:nz country_specific_ts)) | |
| (.addSeries tc (:pk country_specific_ts)) | |
| (.addSeries tc (:sa country_specific_ts)) | |
| (.addSeries tc (:sl country_specific_ts)) | |
| (.addSeries tc (:wi country_specific_ts)) | |
| (.addSeries tc (:zm country_specific_ts)) | |
| (plot-time-series-collection tc "Year" "Score")) | |
| )) | |
| ( plot-scores (zipmap (range 1890 2011) (for [year (range 1890 2011)] | |
| (compute_ranks "/Users/karthik/workspace/clojure_matlab/td" (- year 3) year)))) | |
| ;(compute_ranks "/Users/karthik/workspace/clojure_matlab/td" 2007 2011) |
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