I wrote an article that was published over at Nikita’s The Tennis Notebook. It dives into a cluster analysis I did using year-end ATP rankings since 1972. You can find the article here:
With the baseball playoffs upon us, I have decided to start building a simulator to determine series outcomes once they start. I decided to make this as generic as possible. This simulator is not specific to baseball or even to a particular series length.
Obviously, the first parts to think about I addressed in my previous post relating to home field advantage, ratings and the probability a team would win a single game versus a specific opponent.
I will come back to this later in the month, as we get closer to the playoffs and I tie this all together.
Let’s assume for today that we know the probability a specific that Team A will defeat Team B. Let’s also assume, for matters of simplicity, that this single-game probability remains the same throughout the a series, regardless of any possible home field advantage.
Since we are dealing with a single probability and no perceived home field advantage, all we need for inputs are: p(Team A wins a single game), the current series record of the two teams and the numbers of games to win the series (e.g., 1 for a one-game series, 3 for a five-game series and 4 for a seven-game series).
All of my code is listed here on github, https://gist.github.com/sixmanguru
Like I said, let’s keep this simple. Probabilities, current series record, length of series.
The function calls for the series probabilities, give Team A holding a 54% chance to win a single game, the series is just beginning (0-0) and it takes for games to win the series (seven-game series).
Here’s the abbreviated (rounded to four digits).
([0.085, 0.1565, 0.1799, 0.1655], 0.5869, [0.0448, 0.0967, 0.1306, 0.141], 0.4131)
The first list contains the probabilities that Team A wins the series EXACTLY 4-0, 4-1, 4-2 or 4-3. The number trailing is the total probability Team A wins the series.
The second list contains the probabilities Team A loses the series EXACTLY 0-4, 1-4, 2-4, 3-4, with the total probability they lose the series following.
Let’s assume the only thing you change is the fact that Team A now leads the series 3-0.
([0.54, 0.2484, 0.1143, 0.0526], 0.9553, [0, 0, 0, 0.0448], 0.0448)
As you can see above, there exists no change for Team B to win the series now 4-0, 4-1 or 4-2 and they have a 4.5% chance to even win the series at all. This can be verified by 0.46^4, which is approximately 0.0448.
Now let’s assume that it is a one game series.
([0.54], 0.54, [0.46], 0.46)
As you can see, it is one game, so the original probabilities are returned.
Finally, as a test, we say Team A trails the series 3-4 in a seven-game series.
It quickly returns (0,1). It is impossible for Team A to win and certain that Team B will win.
The two biggest limitations to resolve (assuming you accept the theory that you can actually assign a probability to the function at all) remain to be the possibility of a home field advantage and how it would play out based on the series’ format (i.e., 2-3-2 vs. 2-2-1-1-1 and such)
Lastly, I would like to thank Jeff Sackmann, the author of Tennis Abstract and several other endeavors. His original python code for simulating a tennis match was the foundation for this project. His Python code for tennis Markov Chains can be found here, http://summerofjeff.wordpress.com/2011/01/13/python-code-for-tennis-markov/
Today I was enamored with the FiveThirtyEight.com article, Inside the Shadowy World of High-Speed Tennis Betting. The article mentions the courtsiders who would sit court side at a tennis match and try to relay information quicker than the tournament computers to betting partners. Great read. Not sure these courtsiders were really doing anything illegal.
Buried deep in the article was a mention of the system this one organization created to predict the outcome of tennis matches for betting purposes. It links to a website, Summer of Jeff, and a post, Python Code for Tennis Markov. If you follow the links to the gitHub site, there is some pretty elaborate Python code for generating probabilities based on Markov Chain theory. The code is pretty easy to use, if you understand Python and statistics, although it needs some cleaning up if you plan on using it for entire match prediction (hint: the matchProbs function needs some fixes to run).
The biggest issue is determining the initial probabilities. You need to create each server’s probability to win a point.
To do this, I decided to hit the trusty ATPworldtour.com website and pulled that information up.
For the year Roger Federer has won 90% of all service games, but only 70% of his service points. On clay this season, he is 89% and 67%. On the other hand, Dmitry Tursunov has won 22% of return games and 36% of return points. On clay he is 24% and 37%. Assuming the majority of these results came from ‘inferior’ players, we might suggest that these numbers regress to each other. I am going to say that Federer is likely to win 65% of his service points. One down.
Now when Tursunov serves, he’s won 75% of service games and 61 of service points, 70%-60% on clay. Federer has won 29% of service return games and 41% of points, 27%-40% on clay. That seems to work out quite nicely to 60-40, so Federer’s return probability will be 40%.
Plugging this into the handy code mentioned above, we get that Federer is a 78.5% favorite to win tomorrow.
Jo-Wilfried Tsonga has won 68% of service points, 65% on clay, while Jerzy Janowicz has won 34% of return points all season and an improved 36% on clay. What is crazy about this is you might suggest that Janowicz is a better clay court than hard court player. Well, amazingly, he had not won a single clay court match this spring before winning his first two rounds at Roland Garros. Oh well. I am still going to give his the benefit and place Tsonga as 65% to win a point on serve.
Returning, Tsonga has been 34% for the year and 35% on clay, while Janowicz has won 62% on serve and 68% on clay. Again Janowicz stats are much better on the terre battue. I am going to just split this straight and leave Tsonga’s return percentage at 34%.
We all know the French crowd will be pulling for their man, so that may be the edge, however, the stats say that Janowicz looks to be a slight favorite at 56.1%. Moving Tsonga’s serve percentage up just a point makes this a dead heat.
Looking at the odds at SportsBook.com, Federer is -2500, so that’s a ridiculous bet, but Janowicz is actually +325 v. Tsonga, so that may be worth a play. I hope to look into this more as the tournament progresses.
It has been too, too long since I have posted anything on here. I have been active on twitter (@TXCollege10s) and keeping up with the season as it progresses, but have not had a whole lot of time to really repost all of the articles.
I decided it was time to update the rankings program, so here we go. Please let me know where you see mistakes. NOTE: The records for each team indicate only matches against DI opponents. So please do not e-mail me that the record is wrong, unless you are certain that has been checked.
I have NOT proofed this. I am into crowdsourcing…. or just lazy. I understand I am missing certain schools that have just moved to D1 (Abilene Christian) or have moved from D1… Next week will be more complete.
There are quite a few teams ranked with 0-0 records and sitting at 375.
|1||Ohio State University||13||0||1175.66|
|2||University of Southern California||7||1||1129.26|
|4||University of Virginia||6||1||1057.88|
|5||University of Oklahoma||8||1||1046.29|
|7||Texas A&M University||8||3||976.56|
|8||University of Notre Dame||9||2||976.45|
|9||University of Illinois||6||4||976.21|
|10||University of Texas||9||2||976.11|
|11||University of Tennessee||10||2||976.03|
|14||Mississippi State University||9||2||935.64|
|17||University of Kentucky||7||3||923.26|
|18||University of Florida||4||4||907.44|
|20||Wake Forest University||4||2||884.99|
|21||University of Georgia||3||5||864.35|
|24||University of Memphis||3||2||825.7|
|26||North Carolina State||9||1||820.38|
|29||Penn State University||9||0||794.42|
|30||University of Michigan||3||4||791.81|
|31||Virginia Commonwealth University||8||4||790.0|
|32||University of South Carolina||5||3||788.47|
|33||Boise State University||6||2||782.23|
|34||University of Mississippi||1||2||763.03|
|35||Louisiana State University||5||2||762.76|
|38||University of Tulsa||8||5||758.49|
|39||University of Oregon||8||1||745.0|
|41||Florida State University||9||2||737.15|
|42||University of Alabama||4||3||731.57|
|43||University of Louisville||6||2||720.89|
|47||University of South Florida||3||0||683.86|
|48||San Diego State University||5||2||678.08|
|49||Texas Tech University||4||3||677.29|
|50||University of Nebraska||4||3||677.15|
|51||University of Denver||5||2||677.06|
|52||University of Utah||8||2||676.86|
|53||University of New Mexico||11||3||676.57|
|55||University of Iowa||5||0||663.18|
|56||University of Minnesota||4||4||651.41|
|57||University of Washington||4||4||646.64|
|58||Michigan State University||4||5||644.78|
|60||University of Arkansas||6||4||633.44|
|62||University of San Diego||1||2||629.52|
|63||University at Buffalo||4||0||622.73|
|64||University of Wisconsin||4||3||617.51|
|65||Santa Clara University||3||1||616.19|
|68||University of Louisiana at Lafayette||5||2||604.83|
|69||East Tennessee State University||3||5||589.05|
|70||Wichita State University||3||4||588.87|
|71||Georgia State University||4||5||588.74|
|73||University of Miami (Florida)||3||2||573.95|
|74||Old Dominion University||6||1||565.44|
|75||University of Nevada||4||1||564.36|
|77||Texas A&M-Corpus Christi||8||4||562.84|
|78||University of Arizona||8||6||562.66|
|79||U.S. Air Force Academy||2||2||559.83|
|80||Brigham Young University||5||6||559.67|
|81||Middle Tennessee State University||2||6||557.17|
|83||University of North Florida||4||0||549.89|
|87||University of South Alabama||6||3||536.26|
|89||Illinois State University||2||3||531.63|
|90||Western Michigan University||6||3||531.46|
|91||Northern Illinois University||4||3||531.37|
|93||Wake Forest University||2||0||527.03|
|97||Univ. of Wisconsin-Green Bay||5||4||523.47|
|98||Eastern Kentucky University||2||3||522.04|
|101||East Carolina University||7||3||520.08|
|102||Coastal Carolina University||4||3||511.65|
|104||Univ. of San Francisco||3||3||500.41|
|105||University of South Florida||2||0||495.53|
|108||Northern Arizona University||3||3||491.79|
|109||Cleveland State University||3||4||491.59|
|110||New Mexico State University||5||3||491.43|
|111||Ball State University||3||2||491.42|
|112||University of Southern Mississippi||5||4||491.27|
|113||George Washington University||1||3||488.45|
|114||Eastern Illinois University||3||2||488.34|
|115||St. John’s University||1||2||488.1|
|116||College of William and Mary||7||6||488.06|
|117||U.S. Naval Academy||3||3||484.19|
|120||Saint Joseph’s University||1||2||472.37|
|124||UC Santa Barbara||2||3||469.0|
|125||College of Charleston||1||3||468.99|
|126||University of the Pacific (California)||2||3||468.59|
|127||Wright State University||3||4||468.5|
|134||University of Detroit Mercy||2||5||462.02|
|137||Loyola Marymount University||2||2||457.7|
|138||South Dakota State||2||2||457.45|
|139||Florida Gulf Coast University||2||5||455.06|
|140||Florida Atlantic University||4||4||454.88|
|141||Univ. of Maryland-Baltimore County||3||3||453.58|
|145||Austin Peay State University||2||1||446.69|
|146||University of Delaware||2||1||446.47|
|147||Univ. of Texas at San Antonio||1||4||445.6|
|149||George Mason University||2||1||442.99|
|151||Saint Mary’s College of California||2||2||442.05|
|152||University of North Florida||0||5||440.46|
|153||U.S. Military Academy||1||0||439.33|
|155||University of Portland||2||2||438.39|
|156||James Madison University||2||2||437.61|
|157||Montana State University-Bozeman||1||2||437.26|
|158||University of Toledo||3||9||437.08|
|160||Jacksonville State University||2||3||435.93|
|161||Utah State University||3||5||431.13|
|163||Stony Brook University||1||1||423.66|
|164||University of Connecticut||3||3||423.13|
|165||Appalachian State University||1||1||419.72|
|167||South Carolina State||1||2||414.42|
|168||Kennesaw State University||3||4||414.29|
|169||University of Texas-Pan American||2||6||412.5|
|171||North Carolina Central University||1||4||408.88|
|175||University of Hawaii||1||3||402.62|
|176||University of New Orleans||1||1||401.0|
|177||Youngstown State University||1||5||399.96|
|180||University of Idaho||2||6||396.51|
|181||Eastern Washington University||1||2||393.36|
|182||Saint Louis University||2||3||392.99|
|184||University of Richmond||3||6||391.56|
|186||Florida A&M University||2||6||386.05|
|188||University of South Carolina-Upstate||1||3||381.84|
|189||Norfolk State University||1||3||379.75|
|190||Robert Morris University||0||0||375.0|
|191||Mississippi Valley State University||0||0||375.0|
|192||La Salle University||0||0||375.0|
|193||St. Peter’s College||0||0||375.0|
|194||Univ. of Maryland-Eastern Shore||0||0||375.0|
|198||Coppin State College||0||0||375.0|
|199||Centenary College (Louisiana)||0||0||375.0|
|200||Sacred Heart University||0||0||375.0|
|201||Mount St. Mary’s University||0||0||375.0|
|202||Univ. of Arkansas Pine Bluff||0||0||375.0|
|204||Western Kentucky University||0||0||375.0|
|206||Fairleigh Dickinson University||0||0||375.0|
|207||George Washington University||0||0||375.0|
|209||Portland State University||0||1||371.36|
|210||Murray State University||0||3||370.94|
|211||St. Francis Univ. (Pennsylvania)||1||3||368.62|
|212||Tennessee State University||0||1||367.5|
|215||Oral Roberts University||1||5||361.89|
|216||Univ. of Northern Colorado||0||1||360.7|
|217||Univ. of Illinois at Chicago||1||4||357.83|
|219||Loyola College (Maryland)||0||1||353.1|
|220||Idaho State University||0||1||351.29|
|222||Univ. of Dayton||1||5||349.46|
|223||Alabama A&M University||0||3||348.78|
|224||University of Pennsylvania||0||2||348.1|
|225||Nicholls State University||0||3||347.55|
|228||Georgia Southern University||1||5||339.49|
|233||Alcorn State University||0||4||334.86|
|235||Morehead State University||0||2||333.68|
|237||University of Texas at Arlington||0||4||327.69|
|242||Tennessee Tech University||0||5||319.4|
|243||St. Francis College (New York)||0||3||319.0|
|244||Morgan State University||0||4||318.36|
|246||Western Illinois University||0||4||316.79|
|250||University of Hartford||0||4||301.44|
|252||Jackson State University||0||8||293.71|
|254||St. Bonaventure University||0||5||286.25|
|255||Prairie View A&M University||0||5||285.24|
|256||Alabama State University||0||6||283.27|
|259||Chicago State University||0||8||265.79|