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An Elo Rating System for Bridge
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Elo Rating has been used in Chess and other competitive games and sports. In chess FIDE rating is standard. It is commonly used in tournament to group players with similar level of skills and in chess pairing program. There are a few discussions about bridge rating on this site. Here I propose an system based on Elo's methodology with some examples.

Unlike chess, bridge is played with a pair of players (except individual games). In this bridge rating system, the rating will be assigned to a pair instead of an individual players. A player may have multiple partnerships. Each one will have its own rating. How a player does with one partner will not affect on his rating with other partners.

The rating of a partnership is calculated/updated based on the results from every board they played. The general methodology is to calculate expected performance on every board for every pair and compare it against actual score. If the actual score is better than expected performance, the pair gains rating. If it is worse, it loses rating. For example, pair A played against pair B on a board and A is higher rated. Based on their pre-game rating, A is expected to win 0.5 IMP per board from calculation. If the same board is also played at another table by pair A1 and B1. A1 is also higher rated than B1 but the calculation yields A1 should win 0.4 IMP per board against B1. Now when we compare A vs. A1, the net result is A should score 0.1 IMP better than A1. This is the expected performance. The actual score will be used to calculation cross IMP between A and A1 and results in a rating adjustment. This process is repeated for every table that played this board.

The following page showed the results from applying this methodology on 2005 Bermuda Bowl. I chose these games because it is the earliest from WBF website that had game result per board. The calculation included every board results from Round Robin to Final. I omitted details of calculations. Any one interested could send me a private message with your e-mail and I'll send you my document.

Pair Name                                                                                                  IMP_rating

BOCCHI, Norberto - DUBOIN, Giorgio                                                          2714

CHAGAS, Gabriel - VILLAS-BOAS, Miguel                                                   2692

MULLER, Bauke - DE WIJS, Simon                                                                2668

MECKSTROTH, Jeff - RODWELL, Eric                                                           2654

JANSMA, Jan - VERHEES, Louk                                                                    2641

SADEK, Tarek - EL AHMADY, Waleed                                                          2639

COPE, Tim - HOLMAN, Glen                                                                          2626

BERTHEAU, Peter - NYSTROM, Fredrik                                                        2607

GRECO, Eric - HAMPSON, Geoff                                                                   2600

KHVEN, Max - KHOKHLOV, Alexander                                                         2580

PALAZZO, Luis - FORNASARI, Walter                                                           2573

YANG, Lixin - DAI, Jianming                                                                           2543

MONSEGUR, Martin Sila - MOONEY, Guillermo                                           2523

HACKETT, Justin - HACKETT, Jason                                                             2521

LINDKVIST, Magnus - FREDIN, Peter                                                             2521

CASTELLO BRANCO, Pedro Paulo - CASTELLO BRANCO, Marcelo          2512

VENKATARAMAN, Kadayam Raman - CHOKSHI, Sunit                               2499

CASTANHEIRA, Jorge Carlos - PESSOA, Sofia                                             2492

NADAR, Kiran - SATYANARAYANA, Bachiraju                                             2492

FU, Zhong - ZHAO, Jie                                                                                   2488

MITTELMAN, George - HOBART, Arno                                                         2487

JACOB, Tom - MAYER, Malcolm                                                                    2481

DAGHER, Hani - EL KOURDY, Adel                                                               2478

LAURIA, Lorenzo - VERSACE, Alfredo                                                          2478

SHI, Haojun - ZHUANG, Zejun                                                                       2472

KHOLOMEEV, Vadim - ZLOTOV, Dmitri                                                       2471

HANS, Sartaj - NUNN, Tony                                                                           2451

EKEBLAD, Russ - RUBIN, Ron                                                                        2429

FANTONI, Fulvio - NUNES, Claudio                                                              2427

SUNDELIN, Per Olof - SYLVAN, Johan                                                         2422

PAZ, Nuno - LUIS, Carlos                                                                               2419

BERTENS, Huub - BAKKEREN, Ton                                                               2415

SIMPSON, Colin - PRICE, David                                                                     2411

MADALA, Agustin - LAMBARDI, Pablo                                                          2411

GERIN, Dominique - MATHIEU, Philippe                                                       2406

DE MELLO, Roberto - JANZ, Ricardo                                                             2406

PEREIRA, Paulo Goncalves - SANTOS, Rui Silva                                          2401

CARRUTHERS, John - SILVER, Joseph                                                          2400

MOSS, Brad - GITELMAN, Fred                                                                      2393

JASSEM, Krzysztof - MARTENS, Krzysztof                                                    2376

SOLOWAY, Paul - HAMMAN, Bob                                                                 2374

FURUTA, Kazuo - CHEN, Dawei                                                                     2372

NEWELL, Peter - REID, Martin                                                                         2372

NAKAMURA, Yoshiyuki - SHIMIZU, Yasuhiro                                                2354

THOMSON, Matthew - MARSTON, Paul                                                        2354

TEWARI, Rajeshwar - GUPTA, Subhash                                                         2317

GOWER, Craig - CHU, Wayne                                                                         2313

NICKELL, Nick - FREEMAN, Richard                                                               2309

KRUPOWICZ, Marcin - LUTOSTANSKI, Piotr                                                 2303

GRAVES, Allan - BARAN, Boris                                                                       2279

GROMOV, Andrey - DUBININ, Alexander                                                      2275

HUGHES, Arthur - CASTELEIN, Chris                                                             2270

TOWNSEND, Tom - GOLD, David                                                                  2238

SHIH, Juei-Yu - HUANG, Patrick K. H.                                                            2238

TERAMOTO, Tadashi - MIYAKUNI, Kenji                                                       2232

HORTON, David - MARKEY, Phil                                                                    2173

HISHMAT, Mohamed - NADIM, Tarek                                                            2158

PAZUR, Boguslaw - JAGNIEWSKI, Rafal                                                        2141

KEMPCZYNSKI, Alain - PENTURE, Jack                                                         2122

BARAKAT, Sireen - GHANEM, Marwan                                                          2097

JOATTON, Philippe - RIZK, Rizcallah                                                             2088

YANG, Hsin-Lung - CHIU, Wei-Chun                                                              2036

GHANEM, Ghassan - HATTAR-GHANEM, Nuha                                            1944

This list only included pair that played at least 200 boards. Pairs who played less than 200 boards will had provisional rating and are not listed.

Matchpoint has a different strategy than IMP. The same methodology could be used to determine pair's rating at matchpoint. It just needs to replace IMP score with matchpoint score and using a different formula to calculate expected performance for matchpoint. So a pair could have two ratings: one for IMP and one for MP.

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