Vendire-Ludorum Excel Add-In

Treat yourself to an Excel Add-In (32-bit and 64-bit [Windows] that includes some of the standard functions on which we have come to rely in our daily sports trading. Among the functions available are the following:

• Edge,
• Expected Value,
• Time Value,
• Kelly Single Stake,
• Kelly Mutually-Exclusive Stakes,
• Kelly Simultaneous Independent Events (5),
• Mark-To-Market,
• Risk-Of-Ruin, and
• Wisdom-Of-Crowd Market Index (WCMI).

In addition, there is a sample spreadsheet highlighting the various functions through worked examples from Haigh, Paulos, and Yao.

Mark-To-Market And Hedging

Following careful analysis of the next race, your assessment of the odds is 4/1(5.00) - a 20% edge on the market price of 5/1 (6.00) - with respect to your selection. Flushed with confidence, you place a $250 (4%) win bet on InTheMoney at 5/1 (6.00). Time to sit back and wait for the profit to roll in? Maybe!
Consider for a moment -  what is the current market value of your investment?. When you place the initial trade, its market value is $250=[($250*6.00)*(1/6.00)]. Roll tape and the market turns in-play as InTheMoney sets the early pace with measured fractions. Turning into the stretch it looks an even-money chance at worst to win. Freeze frame and consider once again - what is the current market value of your investment?. Assuming the market is now efficient with respect to InTheMoney’s win probability, the updated market value is $750=[(($250*6.00)*(1/2.00)]. In other words, at this point in the race, you have already won $500=[$750-$250]. Fast forward to the finish-line and InTheMoney is beaten by a late closer, JustInTime. Now, the really interesting question is - how much have you lost? If you had no choice but to only back your selection before the race, then you have lost $250. But, if you also had the option in-play to hedge the win bet at even-money, then you lost $750! (see Weighing the Odds in Sports Betting (Ch.4)).
In summary, no trade is complete without both a back and a lay bet or, in other terminology, an opening and a closing position.

Using our knowledge of time averages, we can select a lay price and calculate a hedging stake to maximize our median bankroll over time.

Horse-Racing Overlays

Sports traders sometimes conflate AvB events with AvK (K = N-1) events (N = number of entrants). The prototypical AvB game is a football match and the equivalent AvK example is horse-racing. Some experts encourage traders to identify a single overlay in both events and bet accordingly. Whereas this advice is generally correct for AvB events, it is not correct for AvK events.
In horse-racing, you should only select those races with at least one overlay for further examination. But, as Ravi Phatarfod points out in his excellent 1996 paper Betting Strategies In Horse Races, a gambler is more likely to correctly assess that the winner will be one of three horses than being able to correctly assign win probabilities to each individual horse. And, as John Haigh illustrates in Taking Chances, Kelly betting on horse races also encourages us to spread our risk across multiple entrants including, on occasion, those from all three categories of bets, favorable (positive expected value), fair (zero expected value), and unfavorable (negative expected value) bets. This approach guarantees over time that you will minimize your risk of ruin (total loss of capital).

Note: You must enter horse details in descending e.v. order only.

Engineer, Physicist, And Statistician

Many years ago, as a young postgraduate student, two colleagues (an engineer (E) and a physicist (P)) and I would meet every Saturday for an early lunch to discuss the week’s events in our respective disciplines and to give our differing perspectives on world events. It was an innocent and idealistic exercise driven by youthful enthusiasm and naivete. Naturally, our discussions ranged from the sublime to the ridiculous and everything in between.

Time passed and as our careers evolved we drifted apart and lost contact. Then a few years ago, I unexpectedly ran into E at Royal Ascot. After we engaged in some good-natured banter about the humbling nature of the aging process and introduced our respective wives, our attention turned to the Group 2, 6f, Coventry Stakes (2yo). I asked E what he liked in the race and how he made his selections. He turned to me in disbelief and said, “For 2yo races, I use the method you recommended to me back in the day to identify a select band of unexposed horses to exploit throughout the season.” Completely bewildered I said, “Remind me”. He then proceeded to outline an adaptation of the Bayesian Bandit (Thompson Sampling) “explore-exploit” strategy as used in the multi-armed bandit problem. To which, I blurted out, “You mean, it works!”. I quickly pointed out that I must have thought at the time it was a strategy worth exploring but that all the kudos should go to him for exploiting it so successfully. Engineers rule by defeasible reasoning.

Later that evening, my wife teased me by asking if I had given mathematical advice to everyone I had ever met and when I looked surprised by the question she added wickedly, “My hero, so brave, so strong!”

True Talent Levels

It is easy to conflate Which team is number one? with Which team wins today? The former is decided over the course of a regular season and is primarily driven by skill (talent) but the latter changes on a daily basis and when there are two roughly equal opponents it is principally governed by luck!
With respect to being number one, the definitive review of the field is provided by Langville and Meyer (2012) in Who's #1?: The Science of Rating and Ranking. And, in terms of estimating true talent levels, Adam Dorhauer delivers two excellent articles worthy of publication, Elo vs. Regression to the Mean: A Theoretical Comparison and Regression with Changing Talent Levels: The Effects of Variance.

Cheltenham 2017: Supreme Novices Hurdle Handicapping

Once more unto the breach, dear friends, in our annual attempt to find live longshots to finish in the money in the Supreme Novices Hurdle (G1) at Cheltenham 2017. As ever, our approach is based on the following premises: 

• Supreme Novices Hurdle is similar to Kentucky Derby - young horses, many attempting graded stakes, championship race for first-time with little form in book.
• Eliminate non-contenders and whatever remains, no matter how improbable...
• Avoid horses with pedigree mismatch to former winners [Melon, Crack Mome].
• Avoid horses from small fields [Labaik], [Elgin].
• Late speed important [Magna Cartor, Glaring, Capitol Force].
• Poor Cheltenham Form [River Wylde].
• Poor FPR [Pingshou, High Bridge].
• Minimum price 10/1 [Ballyandy, Bunk Off Early].

This leaves Beyond Conceit 20/1 and Cilaos Emery 16/1 as our selections!
Note, given the limited exposure of all the runners, we are not saying that those we have eliminated are not going to win - simply that they did not meet our criteria for live longshots to run in the money. The key takeaway, as always, is using a process of elimination not selection for identifying contenders.
Footnote: In their respective next outings, Cilaos Emery won G1 (Punchestown) and Beyond Conceit finished second in G1 (Aintree).

Adaptive Boosting

Machine learning studies the design of automatic methods for making predictions about the future based on past experiences. In the context of classification problems, machine-learning methods attempt to learn to predict the correct grouping of unseen examples. In the mid-1990s, Freund and Schapire introduced the meta-heuristic, Adaptive Boosting (AdaBoost), “…an approach to machine learning based on the idea of creating a highly accurate prediction rule by combining many relatively weak and inaccurate rules… Indeed, at its core, boosting solves hard machine-learning problems by forming a very smart committee of grossly incompetent but carefully selected members…” (Boosting: Foundations And Algorithms). As context for how boosting might work, the authors introduce the following toy problem in the opening paragraph to A Short Introduction To Boosting: “A horse-racing gambler, hoping to maximize his winnings, decides to create a computer program that will accurately predict the winner of a horse race based on the usual information...” As discovered by the early pioneers of expert systems in the 70s and 80s and as acknowledged by the authors, the biggest stumbling block to using experts is that many of them are unable to detail their decision process or even to rank order the importance of key variables. In light of this issue, Freund and Schapire point out that the beauty of boosting is that it builds on what experts can do not on what they cannot do, namely, given a specific scenario they are usually able to make a judgment in favor or against a particular outcome. For instance, we can ask an expert handicapper if a specific scenario - course and distance winner in last outing a week ago - would lead him to believe that it was more likely to win again or to finish out of the money. Note the phrase “more likely to” – this is a key strength of boosting - it asks for the balance of probabilities and not for the highly probable. The boosting phase combines many such simple, scenario-based rules into an overall weighted decision for an upcoming event. In its original specification, the defining quality of boosting was that it aggregated an incomplete set of “if-then” rules (decision stumps) that recursively address unexplored regions (areas for which previously chosen rules would give incorrect predictions) of existing data sets. The inherent strength of this approach is that it automatically leverages the key dimensions of Wisdom Of Crowds, namely, diversity, independence, decentralization, and aggregation For a worked example applied to NFL prediction, see James McCaffrey’s Classification And Prediction Using Adaptive Boosting. For the underlying theory of why wisdom of crowds works, see Scott Page’s excellent The Difference. And finally, Malacaria And Smeraldi explore the relationship between the AdaBoost weight update procedure and Kelly’s theory of betting and also establish a connection between AdaBoost and Information theory in On AdaBoost And Optimal Betting Strategies.