Wednesday, 7 August 2013

The problem with predicting football results - you cannot rely on the data


Bloomberg Sports have published their predictions for the forthcoming Premiership season (****see update below for actual results) in the form of the predicted end of season table. Here are some key snippets from their press release:
The table indicates that this season will be a three horse race between Chelsea, Manchester City and Manchester United .... The Bloomberg Sports forecast expects Arsenal to claim the final Champions League place ahead of North London rivals Tottenham Hotspur.... At the bottom of the table, all three newly promoted teams are expected to face the drop...
There is just one problem with this set of 'predictions'. The final table - with very minor adjustments - essentially replicates last season's final positions.  The top seven remain the same (with the only positional changes being Chelsea and Man Utd switch positions 1 and 3, and Liverpool and Everton switch positions 6 and 7). And the bottom three are the three promoted teams so they also 'retain' their positions.

Bloomberg say they are using "mathematically-derived predictions" using "vast amounts of objective data". But herein lies the problem. As we argue in our book, relying on data alone is the classical statistical  approach to this kind of prediction. And classical statistics is great at 'predicting the past'. The problem is that we actually want to predict the future not the past!

Along with my PhD student Anthony Constantinou we have been applying Bayesian networks and related methods to the problem of football prediction for a number of years. The great thing about Bayesian networks is that they enable you to combine the standard statistical data (most obviously historical and recent match results) with subjective factors. And it is the incorporation of the subjective (expert) factors that is the key to improved prediction that 'classical' statisticians just do not seem to get.
 
This combination of data and expert judgement has enabled us to get more accurate predictions then any other published system and has even enabled us to 'beat the bookies' consistently (based on a simple betting strategy) despite the bookies' built-in profit margin. Unlike Bloomberg (and others) we have made our methods, models and results very public (a list of published papers in scholarly journals is below). In fact for the last two years Anthony has posted the predictions for all matches the day before they take place on his website pi-football. The prediction for each match is summarised as a very simple set of probabilities, namely the probability of a home win, draw and away win. Good betting opportunities occur when one of the probabilities is significantly higher than the the equivalent probability from the bookies odds.
Example: Suppose Liverpool are playing at home to Stoke. Because of the historical data the bookies would regard Liverpool as strong favourites. They would typically rate the chances of Stoke winning to be very low - say 10% (which in 'odds terms equates to '9 to 1 against'). They add their 'mark-up' and publish odds of, say, 8 to 1 against a Stoke win (which in probability terms is 1/9 or 11%). But suppose there are specific factors that lead our model to predict that the probability of a Stoke win is 20%. Then the model is saying that the bookmakers odds - even given their mark-up - have significantly underestimated the probability of a Stoke win. Although our model still only gives Stoke a 20% chance of winning it is worth placing a bet. Imagine 10 match scenarios like this. If our predictions are correct then you will win on 2 of the 10 occasions. Assuming you bet £1 each time you will end up spending £10 and getting £18 back - a very healthy 80% profit margin.
Thanks to Alex on the Spurs-list for the tip-off on the Bloomberg report.

****Update: The actual results for the 2013-14 season were very different from the Bloomberg predictions. The title was a two-horse race between Man City and Liverpool with the rest far behind. Liverpool had been predicted to come 6th and would have won the title but for a late collapse. Man Utd finished 7th. Only one of the newly promoted club (Cardiff) was relegated.

References:
  • Constantinou, A., N. E. Fenton and M. Neil (2013) "Profiting from an Inefficient Association Football Gambling Market: Prediction, Risk and Uncertainty Using Bayesian Networks". Knowledge-Based Systems. http://dx.doi.org/10.1016/j.knosys.2013.05.008
  • Constantinou, A. C. and N. E. Fenton (2013). "Determining the level of ability of football teams by dynamic ratings based on the relative discrepancies in scores between adversaries." Journal of Quantitative Analysis in Sports 9(1): 37-50. http://dx.doi.org/10.1515/jqas-2012-0036
  • Constantinou, A., N. E. Fenton and M. Neil (2012). ""pi-football: A Bayesian network model for forecasting Association Football match outcomes." Knowledge Based Systems, 36, 322-339,  http://dx.doi.org/10.1016/j.knosys.2012.07.008
  • Constantinou, A. , Fenton, N.E., "Solving the problem of inadequate scoring rules for assessing probabilistic football forecasting models", Journal of Quantitative Analysis in Sports, Vol. 8 (1), Article 1, 2012. http://dx.doi.org/10.1515/1559-0410.1418

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    สำหรับเกม The Great Icescape ที่มาพร้อมด้วยน้องเพนกวินน้อยสุดขนคิ้วท์จากแอนตาร์กติกา จะมากับพ้องเพื่อนฝูงสุดน่ารักน่าเอ็นดูที่ใช้เป็นเครื่องหมายรูปภาพในเกมสูงถึง 10 เครื่องหมายอย่างยิ่งจริงๆ ซึ่งจะมีอัตราการชำระเงินรางวัลที่ไม่เหมือนกันออกไปในแต่ละตัว ดังนี้ pgslot
    • นกน้อยหน้าโกรธ เมื่อภาพปรากฎ 3, 4 และก็ 5 รูป จะได้รับโบนัส 50, 200 แล้วก็ 500 เป็นลำดับ
    • แมวน้ำ เมื่อภาพปรากฎ 3, 4 รวมทั้ง 5 รูป จะได้รับโบนัส 30, 150 แล้วก็ 300 เป็นลำดับ
    • ปลาหมึก เมื่อภาพปรากฎ 3, 4 แล้วก็ 5 รูป จะได้รับโบนัส 25, 100 รวมทั้ง 250 เป็นลำดับ
    • ปลา เมื่อภาพปรากฎ 3, 4 และก็ 5 รูป จะได้รับโบนัส 20, 80 แล้วก็ 200 เป็นลำดับ
    • ตัวหนังสือ A เมื่อภาพปรากฎ 3, 4 และก็ 5 รูป จะได้รับโบนัส 15, 40 และก็ 50 เป็นลำดับ
    • ตัวหนังสือ K เมื่อภาพปรากฎ 3, 4 รวมทั้ง 5 รูป จะได้รับโบนัส 10, 30 รวมทั้ง 40 เป็นลำดับ
    • ตัวหนังสือ Q เมื่อภาพปรากฎ 3, 4 แล้วก็ 5 รูป จะได้รับโบนัส 8, 25 และก็ 35 เป็นลำดับ
    • ตัวหนังสือ J เมื่อภาพปรากฎ 3, 4 รวมทั้ง 5 รูป จะได้รับโบนัส 6, 20 รวมทั้ง 30 เป็นลำดับ
    • จำนวน 10 และก็ 9 เมื่อภาพปรากฎ 3, 4 และก็ 5 รูป จะได้รับโบนัส 5, 15 และก็ 20 เป็นลำดับ
    จะมองเห็นได้ว่าเกม The Great Icescape มีอัตราการชำระเงินรางวัลที่จัดว่าออกจะสูงขึ้นยิ่งกว่าเกมธรรมดา พลาดมิได้แล้วกับเกมบนโทรศัพท์เคลื่อนที่ทำเงินวันนี้ pgslot

    ReplyDelete
  159. ทำความรู้จักและก็เรียนรู้เรื่องราวของ joker123 ไปพร้อมกัน
    joker123 เป็นอย่างไร
    ยินดีต้อนรับสู่แหล่งรวมของเกมออนไลน์ทำเงินที่เร่าร้อนที่สุดขณะนี้ ให้ท่านได่เจอกับเกมสล็อตออนไลน์ทุกจำพวกจากค่าย joker123! ตั้งแต่สล็อตใหม่ปัจจุบันไปจนกระทั่งเกมโปรดเก่าไปจนกระทั่ง Exclusive พวกเรามีเกมสล็อตออนไลน์ที่ครอบคลุมทั้งโลก พวกเราแน่ใจว่ามีบางสิ่งบางอย่างสำหรับทุกคนในหน้าสล็อตของพวกเรา ด้วยเกมยอดฮิตบางเกมของพวกเรา ตัวอย่างเช่น joker123 แม้คุณไม่ได้อยากต้องการเดินทางย้อนเวลากลับไปหรือเผชิญภัยใต้น้ำ พวกเราก็มีสล็อตที่อิงจากโทรทัศน์และก็ภาพยนตร์คลาสสิกให้เลือกล้นหลาม คุณจะเห็นด้วยคำแนะนำของนายแบงก์หรือเลือกที่จะทำทุกๆอย่าง? และก็แน่ๆว่าไม่มีคาสิโนที่ดีใดที่จะบริบูรณ์ได้ถ้าหากว่าไม่มีสล็อตจากคอลเลกชัน joker123 ที่สามารถเปิดใช้งานได้ตลอดระยะเวลาระหว่างการเล่นเกม โน่นเป็นเพียงแค่ส่วนเล็กๆของสิ่งที่พวกเราเสนอที่ joker123 สล็อตออนไลน์แม้กระนั้นอย่าพึ่งจะเชื่อคำพูดของพวกเรา เพราะเหตุไรไม่ทดลองเสี่ยงมองล่ะ
    ฉันจะเล่น joker123 ได้ยังไง?
    สำหรับเพื่อการเล่น joker123 สล็อตออนไลน์ สิ่งที่คุณจำเป็นต้องทำเป็นสมัครบัญชีแล้วก็ไปที่แท็บสล็อตของพวกเรา พวกเราอาจมอบข้อเสนอแนะต้อนรับให้ท่านเมื่อคุณทำ จากนั้นสิ่งที่คุณสร้างขึ้นอยู่กับคุณ คุณสามารถหมุนวงล้อบนหนึ่งในสล็อตเยอะแยะที่อยู่บนแท็บสล็อตของพวกเรา หรือตรวจสอบที่อื่นๆในคาสิโนของพวกเราด้วยบิงโก โป๊กเกอร์ คาสิโนสด และก็อีกเพียบเลยด้วยการสัมผัสเพียงแค่ไม่จำนวนกี่ครั้ง
    เกมส์ใหม่มาแรง
    พวกเรากำลังเพิ่มคอลเลกชันสล็อตของพวกเราอยู่ตลอดด้วยสล็อตใหม่ปัจจุบันและก็แจ๋วที่สุดจากผู้ให้บริการที่ใหญ่ที่สุดในธุรกิจ รวมทั้ง joker123 สล็อตออนไลน์ใหม่ชอบเป็นแถวคิดของสล็อตใหม่ทั้งปวง แม้กระนั้นยังสามารถปรับแก้เกมโปรดที่พวกเรามีอยู่บน joker123 สล็อตได้ อาทิเช่น เกมสล็อตเริ่มแรกของ Ted ทำให้มีการเกิดภาคต่อของ Ted Jackpot King แล้วก็ Ted Megaways ซึ่งมีความหมายว่าบางคราวสล็อตใหม่ๆก็เป็นเกมที่คุณรู้จักดีอยู่แล้ว
    สล็อตพิเศษ
    สล็อตพิเศษสำหรับผู้ใช้ joker123 แค่นั้น! คุณจะไม่เจอช่องพิเศษของพวกเราในคาสิโนออนไลน์ที่ชิงชัยกันอื่นๆซึ่งมีความหมายว่าสล็อตกลุ่มนี้ทำขึ้นโดยบริษัทแม่ของพวกเราอย่างสิ้นเชิง พวกเรามีสล็อตเอ็กซ์คลูซีฟเยอะมากทุกที่ที่ต้องการ รวมทั้งสล็อต joker123 เกมแจ็คพอต แล้วก็แม้กระทั้งเกมที่พวกเราผลิตเองข้างในบริษัท ด้วยเหตุนั้นไม่ว่าคุณอยากที่จะเดินทางไปยังโลกลึกลับ เสี่ยงอันตรายแบบสปอร์ต หรือออกล่าสัตว์ในธีมเพชรนิลจินดา อย่าลืมกลับมาตรวจตราที่ joker123 สล็อตของพวกเรา
    สล็อตแจ็คพอต
    สล็อตแจ็คพอตมอบโอกาสสำหรับการชนะแจ็คพอตแบบโปรเกรสซีฟสถานที่สำหรับทำงานพร้อมกันไปกับการเล่นเกมของคุณ แจ็คพอตแบบโปรเกรสซีฟมีขนาดมากยิ่งขึ้นจวบจนกระทั่งจะมีคนถูกล็อตเตอรี่แจ็คพอต โดยแจ็คพอตบางรายการจะมีมูลค่าหลายล้านปอนด์ Jackpot King เป็นแบบอย่างสล็อตแจ็คพอตยอดนิยมสูงที่สุด โดยมีสามแจ็คพอตแบบโปรเกรสซีฟรวมทั้งแจ็คพอต Royal, Regal รวมทั้ง Deluxe แจ๊คพ็อตกลุ่มนี้มีขนาดต่างกันทั้งหมดทั้งปวง แล้วก็สามารถสุ่มได้ตลอดเวลาด้วยการหมุนครั้งเดียวจากจำนวนเงินพนันใดๆก็ตามนอกเหนือจากนี้พวกเรายังมีสล็อตแจ็คพอตรายวันที่มีโปรเกรสซีฟรายชั่วโมง รายวัน แล้วก็เมกะแจ็คพอตที่จำเป็นต้องจ่ายข้างในกรอบตอนที่ระบุ

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  174. เกมใหม่จากค่าย pgslot เกม Wild Bandito pgslot889
    เกม Wild Bandito จังหรูหรากะโหลกเป็นเลิศในเกมพนันยอดนิยมของค่าย pgslot เป็นเกมที่มี 5 วงล้อ 4 แถวพร้อมกับระบบ Wild on the way พร้อมกับอัตราการชำระเงินรางวัลหรือค่า RTP อยู่ที่ 96.73% อัตราการจ่ายกำไรสูงสุดอยู่ที่ 25,000 เท่าของเงินที่ใช้ในการเดิมพันสามารถใช้งานบนระบบ Window, MAC, MacOS, iOS, Android แล้วก็ HTML5 ได้แบบสบายๆ

    ภาพรวมของเกม Wild Bandito จังโก้เก๋กะโหลก pg slot
    เกม pgslot Wild Bandito จังเก๋กะโหลกเป็นเกมสล็อตแบบ 5x4 นักเสี่ยงโชคสามารถเริ่มลงทุนได้ด้วยเงินที่ใช้ในการเดิมพันอย่างน้อยสุดอยู่ที่ 4 บาทต่อหนึ่งรอบเกม ด้านในเกมยังมีเครื่องหมายสำคัญที่นักการพนันอยากได้อาทิเช่นเครื่องหมาย Wild และก็ Wild on the way ซึ่งก็คือเครื่องหมายที่อยู่ภายใต้กรอบ “สีทองคำ” จะกลายเป็น Wild เมื่ออยู่ในตำแหน่งศูนย์รวมกับตัวอื่นๆส่วนเครื่องหมาย scatter โดยนักการพนันที่หมุนวงล้อแล้วสามารถได้ Scatter พร้อม 4 ตัวขึ้นไป ผู้เล่นจะเข้าสู่โหมดโบนัสหมุนวงล้อฟรีเริ่มที่ 12 รอบเกมพร้อมตัวคูณแบบสะสม
    จำนวนเงิน BET ในเกมสล็อตระบุได้แบบอิสระหรือเปล่า? Pg slot
    สำหรับเพื่อการระบุจำนวนเงินลงทุนในเกม Slot Online นักเสี่ยงดวงจะต้องรู้เรื่องให้ดีว่าแต่ว่าละเกมของแต่ละค่ายจะมีการระบุจำนวนเงินสำหรับเพื่อการลงทุนหรือที่เรียกว่า BET ไว้เป็นการเฉพาะแล้วจากระดับที่ถือว่าต่ำสุดจนกระทั่งจำนวนเงินพนันสูงสุดของเกม นักเสี่ยงดวงไม่อาจจะระบุจำนวนวงเงินพนันหรือวงเงิน BET ได้ด้วยตัวเอง ในตำแหน่งนี้ภาพของค่าย PG จะมีสัญลักษณ์ที่สำคัญ 2 สัญลักษณ์ให้นักการพนันกระทำเลือกระดับเงินที่ใช้ในการเดิมพันอย่างเช่น
    • สัญลักษณ์ (+)
    • สัญลักษณ์ (-)
    ทั้งคู่สัญลักษณ์นี้สามารถกดมากขึ้นหรือต่ำลงของจำนวนเงินพนันได้ นักเสี่ยงดวงพึงพอใจลงทุนจำนวนเงินมากแค่ไหนก็กดไปยังจำนวนนั้น ต่อจากนั้นก็กระทำหมุนวงล้อ ทุกรอบการหมุนนักเสี่ยงโชคสามารถตั้งค่า BET ได้ใหม่เสมอ
    อัตราการชำระเงินผลกำไรในเกม Wild Bandito จังโก้เก๋กะโหลก pgslot
    สำหรับเกม pg slot Wild Bandito จังหรูหรากะโหลก ด้านในเกมมีเครื่องหมายพิเศษซึ่งสามารถเพิ่มผลตอบแทนในอัตราที่สูงขึ้นอยู่กับ 2 เครื่องหมายอาทิเช่น
    • เครื่องหมายมือสังหารกระดูก รวมกับเครื่องหมายอื่นๆที่ไม่ใช่ Wild หรือ Scatter จะได้เงินรางวัลมากขึ้นตั้งแต่ x10 แล้วก็สูงสุดที่ x50 เท่าของเงินที่ใช้ในการเดิมพัน
    • เครื่องหมายกีตาร์ รวมกับเครื่องหมายอื่นๆที่ไม่ใช่ Wild หรือ Scatter จะได้เงินรางวัลมากขึ้นตั้งแต่ x8 รวมทั้งสูงสุดที่ x40 เท่าของเงินที่ใช้ในการเดิมพัน

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