4.1 Basic Equation

Before we start modelling, we look at the summary of investment return rates.

table 4.1.1 : 5 x 5 : Return of annually investment summary table.33 Kindly refer to the list of colors via Dark yellow with hexadecimal color code #9B870C for plot the stylist table.

\[\Re = \sum_{i=1}^{n}\rho_{i}^{EM}/\sum_{i=1}^{n}\rho_{i}^{BK} \cdots equation 4.1.1\]

\(\Re\) is the return rates of investment. The \(\rho_i^{EM}\) is the estimated probabilities which is the calculated by firm A from match 1,2… until \(n\) matches while \(\rho_{i}^{BK}\) is the net/pure probability (real odds) offer by bookmakers after we fit the equation 4.1.2 into equation 4.1.1.

\[\rho_i = P_i^{Lay} / (P_i^{Back} + P_i^{Lay}) \cdots equation 4.1.2\]

\(P_i^{Back}\) and \(P_i^{Lay}\) is the backed and layed fair price offer by bookmakers.

We can simply apply equation above to get the value \(\Re\). From the table above we know that the EMPrice calculated by firm A invested at a threshold edge (price greater) 1.0769894, 1.1072203, 1.0781056, 1.1148426, 1.0671108 than the prices offer by bookmakers. There are some description about \(\Re\) on Dixon and Coles (1996)44 Kindly refer to 25th paper in Reference for industry knowdelege and academic research portion for the paper. under 7.4 References. The optimal value of \(\rho_{i}\) (rEMProbB) will be calculated based on bootstrapping/resampling method in section 4.3 Kelly Ⓜodel.

table 4.1.2 : 48640 x 45 : Odds price and probabilities sample table.

Above table list a part of sample odds prices and probabilities of soccer match \(i\) while \(n\) indicates the number of soccer matches. We can know the values rEMProbB, netProbB and so forth.

graph 4.1.1 : A sample graph about the relationship between the investmental probabilities -vs- bookmakers’ probabilities.

Graph above shows the probabilities calculated by firm A to back against real probabilities offered by bookmakers over 48640 soccer matches.

Now we look at the result of the soccer matches.

table 4.1.3 : 7 x 8 : Summary of betting results.

The table above summarize the stakes and return on soccer matches result. Well, below table list the handicaps placed by firm A on agency A. I list the handicap prior to test the coefficient according to the handicap in next section 4.2 Linear Ⓜodel.

table 4.1.4 : 6 x 8 : The handicap in sample data.

4.2 Linear Ⓜodel

From our understanding of staking, the covariates we need to consider should be only odds price since the handicap’s covariate has settled according to different handicap of EMOdds.

Again, I don’t pretend to know the correct Ⓜodel, here I simply apply linear model to retrieve the value of EMOdds derived from stakes. The purpose of measure the edge overcame bookmakers’ vigorish is to know the levarage of the staking activities onto 1 unit edge of odds price by firm A to agency A. By refer to figure 4.4.1, I includes the models which split the pre-match and in-play ito comparison.

When I used to work in 188Bet and Singbet as well as AS3388, we know from the experience which is the odds price of favorite team win will be the standard reference and the draw odds will adjust a little bit while the underdog team will be ignore.

Steven Xu (2013)55 Kindly refer to 16th paper in Reference for industry knowdelege and academic research portion for the paper. has do a case study on the comparison of the efficiency of opening and closing price of NFL and College American Football Leagues and get to know the closing price is more efficient and accurate compare to opening price nowadays compare to years 1980~1990. It might be due to multi-million dollars of stakes from informed traders or smart punters to tune up the closing price to be likelihood.

In order to test the empirical clichés, I used to conduct a research thoroughly through ®γσ, Eng Lian Hu (2016)66 Kindly refer to 3rd paper in Reference for industry knowdelege and academic research portion for the paper. under 7.4 References, I completed the research on year 2010 but write the thesis in year 2016. and concludes that the opening price of Asian Handicap and also Goal Lines of 29 bookmakers are efficient than mine. However in my later ®γσ, Eng Lian Hu (2014)77 Kindly refer to 4th paper in Reference for industry knowdelege and academic research portion for the paper. under 7.4 References applied Kelly staking model where made a return of more than 30% per sesson. Meanwhile, the Dixon and Coles (1996) and Crowder, Dixon, Ledford and Robinson (2001)88 Kindly refer to 27th paper in Reference for industry knowdelege and academic research portion for the paper. under 7.4 References has built two models which compare the accuracy of home win, draw and away win. From a normal Poison model reported the home win is more accurate and therefore an add-hoc inflated parameter required in order to increase the accuracy of prediction. You are feel free to learn about the Dixon and Coles (1996) in section 4.4 Poisson Ⓜodel.

Based on table 2.2.1 we know about the net bookies probabilities and EM probabilities, here I simply apply linear regression model99 You can learn from Linear Regression in R (R Tutorial 5.1 to 5.11). You can also refer to Getting Started with Mixed Effect Models in R, A very basic tutorial for performing linear mixed effects analyses and Fitting Linear Mixed-Effects Models using lme4. Otherwise you can read Linear Models with R and somemore details about regression models via Extending the Linear Model with R : Generalized Linear, Mixed Effects and Nonparametric Regression Models. Besides, What statistical analysis should I use? summarise a table for test analysis and data validation. Fit models to data provides examples for application of linear regression and model selection, the main model-fitting commands covered lm (linear models for fixed effects), lme (linear models for mixed effects), glm (generalized linear models), nls (nonlinear least squares), gam (generalized additive models) and also visreg (to visualize model fits). The answer from How to use R anova() results to select best model? eleborates the use of ANOVA and AIC criterion to choose the best fit model. How to Choose the Best Regression Model describes how to find the best regresion model to fit and applicable to the real world. ANOVA - Model Selection summarised a lecture notes in slideshow while Model Selection in R conducts a research on model selection for non-nested linear and polynomial models. and also anova to compare among the models.

shinyapp 4.2.1 : WDW-AH convertion and summary and anova of linear models. Kindly click on regressionApps1010 You might select Y response variable and X explanatory variable(s) to measure your model (Refer to Shiny height-weight example for further information about shinyapp for linear models.) or existing models. to use the ShinyApp.

Here I simply attached with a Fixed Odds to Asian Handicap’s calculator which refer to my ex-colleague William Chen’s1111 My ex-colleague and best friend in sportsbook industry which known since join sportsbook industry year 2005 —— Telebiz and later Caspo Inc. spreadsheet version 1.1 in year 2006. You can simply input the home win, draw, away win (in decimal format) as well as the overround to get the conversion result from the simple an basic equation.1212 Kindly refer to my previous research to know the vigorish / overround.

From the summary of shinyapp 4.2.1, we know the comparison among the models to get the best fitted model.

table 4.2.1 : Application of linear regression models to test the effects on staking.

table 4.2.2A : Best model to test the effects of staking on all soccer matches (includes both pre-match and in-play).

table 4.2.2B : Best model to test the effects of staking on pre-match soccer matches.

table 4.2.2C : Best model to test the effects of staking on in-play soccer matches.

table 4.2.3 : Best model to test the effects of staking soccer matches.

Base on above few tables and also summarised table 4.2.3, we can compare both lm5 and lm5ip + lm0pm and decide that the model lm51313 BIC will be primary reference while AIC is the secondary reference. The smallest value is the best model. all = 381955.593187122 and mixed = 447655.156177823 is the best fit to determine the factors and effects to place stakes for all matches1414 mixed InPlay + Pre-match, all observations are 48640 soccer matches which has placed bets.. The timing of InPlay and the stakes amount is the major effects to the return of investment.

John Fingleton & Patrick Waldron (1999) apply Shin’s model and finally conclude suggests that bookmakers in Ireland are infinitely risk-averse and balance their books. The authors cannot distinguish between inside information and operating costs, merely concluding that combined they account for up to 3.7% of turnover while normally Asian bookmakers made less than 1% and a anonymous company has made around 2%. However the revenue or the stakes are farly more than European bookmakers.1515 You can refer to my another project Analyse the Finance and Stocks Price of Bookmakers which analysis the financial report of public listed companies and also profitable products’ revenue and profit & loss of anonymous company..

They compare different versions of our model, using data from races in Ireland in 1993. The authors’ empirical results can be summarised as follows:

• They reject the hypothesis that bookmakers behave in a risk neutral manner;
• They cannot reject the hypothesis that they are infinitely riskaverse;
• They estimate gross margins to be up to 4 per cent of total oncourse turnover; and
• They estimate that 3.1 to 3.7% (by value) of all bets are placed by punters with inside information.

Due to the Shin model inside the paper research for the sake of bookmakers and this sportsbook consultancy firm is indeed the informed trading (means smart punters or actuarial hedge fund but not ordinary gambler place bets with luck). Here I think of test our previous data in paper ®γσ, Eng Lian Hu (2016)1616 Kindly refer to 3rd paper in Reference for industry knowdelege and academic research portion for the paper. under 7.4 References which collect the dataset of opening and also closing odds price of 40 bookmakers and 29 among them with Asian Handicap and Goal Line. Meanwhile, there has another research on smart punters (Punters Account Review (Agenda).xlsx) which make million dollars profit from Ladbrokes. You are feel free to browse over the dataset for the paper. and also the anonymous companies’s revenue and P&L to analyse the portion of smart punters among the customers in Analyse the Finance and Stocks Price of Bookmakers. However the betslip of every single bet require to analyse it. The sparkR amd RHadoop as well as noSQL require in order to analyse the multiple millions bets. It is interesting to analyse the threaten of hedge fund1717 Kindly refer to 富传奇色彩的博彩狙击公司EM2 to know the history and the threaten of EM2 sportsbook consultancy company to World wide known bankers. since there has a anonymous brand among the brands under Caspo Inc had closed due to a lot of smart punters’ stakes and made loss. Well, here I leave it for future research1818 Here I put in 6.2 Future Works. if the dataset is available.

4.3 Kelly Ⓜodel

From the papers Niko Marttinen (2001)1919 Kindly refer to 1th paper in Reference for industry knowdelege and academic research portion for the paper. and Jeffrey Alan Logan Snyder (2013)2020 Kindly refer to 2nd paper in Reference for industry knowdelege and academic research portion for the paper. under 7.4 References both applying Full-Kelly,Half-Kelly and also Quarter-Kelly models which similar with my previous Kelly-Criterion model ®γσ, Eng Lian Hu 20142121 Kindly refer to 4th paper in Reference for industry knowdelege and academic research portion for the paper. in 7.4 References but enhanced.

To achieve the level of profitable betting, one must develop a correct money management procedure. The aim for a punter is to maximize the winnings and minimize the losses. If the punter is capable of predicting accurate probabilities for each match, the Edward O. Thorp (2006)2222 Kindly refer to 6th paper in Reference for industry knowdelege and academic research portion for the paper. in 7.4 References has proven to work effectively in betting. It was named after an American economist John Kelly (1956)2323 Kindly refer to 26th paper in Reference for industry knowdelege and academic research portion for the paper. in 7.4 References and originally designed for information transmission. The Kelly criterion is described below:

\[S=(\rho*\sigma-1)/(\sigma-1) \cdots equation 4.3.1\]

Where S = the stake expressed as a fraction of one’s total bankroll, \(\rho\) = probability of an event to take place, \(\sigma\) = odds for an event offered by the bookmaker. Three important properties, mentioned by Hausch and Ziemba (1994) (Efficiency of Racetrack Betting Markets (2008Edition)), arise when using this criterion to determine a proper stake for each bet:

• It maximizes the asymptotic growth rate of capital
• Asymptotically, it minimizes the expected time to reach a specified goal
• It outperforms in the long run any other essentially different strategy almost surely

The criterion is known to economists and financial theorists by names such as the geometric mean maximizing portfolio strategy, the growth-optimal strategy, the capital growth criterion, etc. We will now show that Kelly betting will maximize the expected log utility for sports-book betting.

[1] 23.71528

\[K = \frac{(B + 1)p - 1} {B} \cdots equation 4.3.2\]

\[G: = \mathop {\lim }\limits_{N \to \infty } \frac{1/N}{\log}\left( {\frac{{{BR_N}}}{{{BR_0}}}} \right) \cdots equation 4.3.3\]

\[BR_N = (1 + K)^W(1 - K)^L BR_0 \cdots equation 4.3.4\]

Kelly K-value 凯利模式资金管理

## Bootstrapping to get the optimal value
#'@ llply(rEMProbB)

table 4.3.2

In order to get the optimal value, I apply the bootrapping and resampling method.

\[L(\rho) = \prod_{i=1}^{n} (x_{i}|\rho) \cdots equation 4.3.5\]

Now we look at abpve function from a different perspective by considering the observed values \(x1, x2, …, xn\) to be fixed parameters of this function, whereas \(\rho\) will be the function’s variable and allowed to vary freely; this function will be called the likelihood.

4.4 Poisson Ⓜodel

Niko Marttinen (2001)2424 Kindly refer to 1th paper in Reference for industry knowdelege and academic research portion for the paper. has enhanced the Dixon and Coles (1996) which are :

• Basic Poisson model : Independence Poisson model for both home and way teams with a constant home advantage parameter.
• Independent home advantages model : Seperate the home advantage parameter depends on the teams accordingly.
• Split season model : Split a soccer league season to be 1st half and 2nd half season.
• 5. Scores plus Poisson model.

From above models, the author has compare the efficiency and the best fit model for scores prediction as below.

figure 4.4.1 : Comparison of various Poison models.

From figure 4.4.1 above, the author compare the deviance of the models2525 Kindly refer to Generalized Linear Models in R, Part 2: Understanding Model Fit in Logistic Regression Output, devianceTest and Use of Deviance Statistics for Comparing Models to learn baout the method of comparison.

• Weighted model :

Here we introduce the Dixon and Coles (1996) model and its codes. You are freely learning from below links if interest.

• Dixon and Cole’s Poisson regression R Packages
• Dixon and Coles Poisson model
• Dixon Coles model - Python
• Predicting Football Using R

table 4.4.1 : Filtered multiple bets placed on same matches.

Due to the soccer matches randomly getting from different leagues, and also not Bernoulli win-lose result but half win-lose etc as we see from above. Besides, there were mixed Pre-Games and also In-Play soccer matches and I filter-up the sample data to be 20009 x 45. I don’t pretend to know the correct answer or the model from firm A. However I take a sample presentation Robert Johnson (2011)2626 Kindly refer to 23th paper in 7.4 References from one of consultancy firm which is Dixon-Coles model and omitted the scoring process section.

Here I cannot reverse computing from barely \(\rho_i^{EM}\) without know the \(\lambda_{ij}\) and \(\gamma\) values. Therefore I try to using both Home and Away Scores to simulate and test to get the maximum likelihood \(\rho_i^{EM}\).

\[X_{ij} = pois(\gamma \alpha_{ij} \beta_{ij} ); Y_{ij} = pois(\alpha_{ij} \beta_{ij}) \cdots equation 4.4.1\]

sample…

In order to minimzie the risk, I tried to validate the odds price range invested by firm A.2727 As I used to work in AS3388 which always take bets from Starlizard where they only placed bets within the odds price range from 0.70 ~ -0.70. They are not placed bets on all odds price in same edge. The sportbook consulatancy firms will not place same amount of stakes on same edge, lets take example as below :-

• \(Odds_{em}\) = 0.40 while \(Odds_{BK}\) = 0.50, The edge to firm will be 0.5 ÷ 0.4 = 1.25
• \(Odds_{em}\) = 0.64 while \(Odds_{BK}\) = 0.80, The edge to firm will be 0.8 ÷ 0.64 = 1.25

We know above edge is same but due to the probability of occurance an event/goal at 0.4 is smaller than 0.64. Here I try to bootstrap/resampling the scores of matches of the dataset and apply maximum likelihood on the poisson model to test the Kelly model and get the mean/likelihood value. Boostrapping the scores and staking model will be falling in the following sections [4.5 Staking Ⓜodel and Ⓜoney Management] and 4.6 Expectation Ⓜaximization and Staking Simulation.

4.5 Staking Ⓜodel and Ⓜoney Ⓜanagement

Section : reverse modelling to get the EMProb prior to calculate the coefficient of the staking model. Otherwise might rearrange the order of applied Poison model here by refer to international competitions.

Galema, Plantinga and Scholtens (2008)2828 You are feel free to refer to Reference for industry knowdelege and academic research portion for the paper. in 7.4 References for further details

draft : 
  - http://www.moneychimp.com/articles/risk/regression.htm
  - read *Galema, Plantinga and Scholtens (2008)* https://englianhu.files.wordpress.com/2016/06/the-stocks-at-stake-return-and-risk-in-socially-responsible-investment.pdf
  - reverse engineering on staking-profit linear regression model to get/retrieve EMProb value since now only get the coefficients figire of EMProb. Although incompleted soccer teams... 2ndly, reversed poison model from EMProb might is not workable on one-sided competition, need to refer to some international competition as references for incompleted dataset.

4.6 Expectation Ⓜaximization and Staking Simulation

sample…

5.1 Comparison of the ®esults

Chapter 4.2 Comparison of Different Feature Sets and Betting Strategies in

Dixon and Pope (2003) apply linear model to compare the efficiency of the odds prices offer by first three largest Firm A, B and C in UK.

5.2 Market Basket

By refer to ®γσ, Eng Lian Hu (2016)3030 Kindly refer to 28th paper in Reference for industry knowdelege and academic research portion for the paper. under 7.4 References, here I apply the arules and arulesViz packages to analyse the market basket of the bets.

6.1 Conclusion

Due to the data-sets I collected just one among all agents among couple sports-bookmakers 4lowin. Here I cannot determine if the sample data among the population…

JA : What skills and academic training (example: college courses) are valuable to sports statisticians?

KW : I would say there are three sets of skills you need to be a successful sports statistician:

• Quantitative skills - the statistical and mathematical techniques you’ll use to make sense of the data. Most kinds of coursework you’d find in an applied statistics program will be helpful. Regression methods, hypothesis testing, confidence intervals, inference, probability, ANOVA, multivariate analysis, linear and logistic models, clustering, time series, and data mining/machine learning would all be applicable. I’d include in this category designing charts, graphs, and other data visualizations to help present and communicate results.

• Technical skills - learning one or more statistical software systems such as R/S-PLUS, SAS, SPSS, Stata, Matlab, etc. will give you the tools to apply quantitative skills in practice. Beyond that, the more self-reliant you are at extracting and manipulating your data directly, the more quickly you can explore your data and test ideas. So being adept with the technology you’re likely to encounter will help tremendously. Most of the information you’d be dealing with in sports statistics would be in a database, so learning SQL or another query language is important. In addition, mastering advanced spreadsheet skills such as pivot tables, macros, scripting, and chart customization would be useful.

• Domain knowledge - truly understanding the sport you want to analyze professionally is critical to being successful. Knowing the rules of the game; studying how front offices operate; finding out how players are recruited, developed, and evaluated; and even just learning the jargon used within the industry will help you integrate into the organization. You’ll come to understand what problems are important to the GM and other decisionmakers, as well as what information is available, how it’s collected, what it means, and what its limitations are. Also, I recommend keeping up with the discussions in your sport’s analytic community so you know about the latest developments and what’s considered the state of the art in the public sphere. One of the great things about being a sports statistician is getting to follow your favorite websites and blogs as a legitimate part of your job!

source : Preparing for a Career as a Sports Statistician: Two Interviews with People in the Field

… … …

6.2 Future Works

Niko Marttinen (2001) has conducted a very detail and useful but also applicable betting system in real life. There has a ordered probit model which shows a high accuracy predictive model compare to his Poisson (Escore) model. Well, the ®γσ, Lian Hu ENG (2016)3131 The research modelling with testing the efficiency of odds price which had completed in year 2010. Kindly refer to 3rd paper in Reference for industry knowdelege and academic research portion for the paper. under 7.4 References has build a weight inflated diagonal poisson model which is more complicated and shophitiscated and later ®γσ, Lian Hu ENG (2014)3232 Kindly refer to 4th paper inside Reference for industry knowdelege and academic research portion for the paper. under 7.4 References. However there has an automatically and systematically trading system which wrote in VBA + S-Plus + Excel + SQL3333 the betting system has stated in his paper. which is very useful as reference. The author use VBA to automac the algorithmic trading while there has no Asian Handicap and Goal Line odds price data to simulate compare to mine. While currently the shinyapps with RStudioConnect can also build an algorithmic trading system. However the session timeout issue3434 The connection timeout issue might be a big issue for real time algorithmic trading might need to consider. The shinydashboard example from ｮStudio might probably cope with the issue.

John Fingleton & Patrick Waldron (1999) applied Shin model to test the portion of hedge funds and smart punters. As I stated in 4.2 Linear Ⓜodel, the sparkR, RHadoop and noSQL require in order to analyse the high volume betslips dataset. Its interesting and will conduct the research if all betslips of bookmaker(s) is(are) available in the future.

From the 4.3 Kelly Ⓜodel we test the staking model, the table 4.2.1 we apply the linear models and choose the best fit model based on the edge of odds price. 4.4 Poisson Ⓜodel we try to reverse the odds price placed to get the probabilities of scoring different scores. Now we try to test the return of staking on different handicap (ex: 0, 0.25, 0.5, 0.75, 1 etc.) to know which handicap earn the most. Nowadays the hotest matches of four major leagues provides few handicaps market, there will be another case study and research to increase the profit base on same probabilities and also edge but staking on different handicap. The dataset will be collect for research beyond the future.

I will be apply Shiny to write a dynamic website to utilise the function as web based apps. I am currently conducting another research on Analyse the Finance and Stocks Price of Bookmakers which is an analysis on the public listed companies and also anonymous companies revenue and profit & loss. You are welcome to refer SHOW ME SHINY and build your own shinyapps.

I will also write as a package to easier load and log.

7.1 Documenting File Creation

It’s useful to record some information about how your file was created.

• File creation date: 2015-07-22
• File latest updated date: 2016-09-28
• R version 3.3.1 (2016-06-21)
• R version (short form): 3.3.1
• rmarkdown package version: 1.0.9014
• tufte package version: 0.2.2
• File version: 1.0.0
• Author Profile: ®γσ, Eng Lian Hu
• GitHub: Source Code
• Additional session information

[1] “2016-09-28 02:42:21 JST”

7.2 Versions’ Log

• File pre-release version: 0.9.0
  • file created
  • Applied ggplot2, ggthemes, directlabels packages for ploting. For example, the graphs applied in Section [2. Data].
• File pre-release version: 0.9.1
  • Added Natural Language Analysis which is research for teams’ name filtering purpose.
  • Changed from knitr::kable to use datatble from DT::datatable to make the tables be dynamic.
  • Changed from ggplot2 relevant packages to googleVis package to make graph dynamic.
  • Completed chapter [3. Summarise the Staking Model].
• File pre-release version: 0.9.2 - “2016-02-20 09:41:49 JST”
  • Added Section 7.2 Versions’ Log and Section 7.3 Speech and Blooper since retest the coding
  • Added Section [4. Staking Model] .
• File pre-release version: 0.9.3 - “2016-02-05 05:24:35 EST”
  • Modified DT::datatable to make the documents can be save as xls/csv
  • Added log file for version upgraded
• File pre-release version: 0.9.3.1 - 2016-06-22 13:36:33 JST
  • Reviewed previous version, DT::datatable updated new version replaced Button extension from TableTools, removed sparkline and htmlwidget
  • Applied linear regression to test the efficiency of staking model by consultancy firm A
• File pre-release version 0.9.4 - 2016-09-28 00:15:24 JST
  • Add linear regression and shinyApp to test the effects on staking

7.3 Speech and Blooper

Firstly I do appreciate those who shade me a light on my research. Meanwhile I do happy and learn from the research.

Due to the rmarkdown file has quite some sections and titles, you might expand or collapse the codes by refer to Code Folding and Sections for easier reading.

There are quite some errors when I knit HTML:

• let say always stuck (which is not response and consider as completed) at 29%. I tried couple times while sometimes prompt me different errors (upgrade Droplet to larger RAM memory space doesn’t helps) and eventually apply rm() and gc() to remove the object after use and also clear the memory space.

• Need to reload the package suppressAll(library('networkD3')) which in chunk decission-tree-A prior to apply function simpleNetwork while I load it in chunk libs at the beginning of the section 1. Otherwise cannot found that particlar function.

• The rCharts::rPlot() works fine if run in chunk, but error when knit the rmarkdown file. Raised an issue : Error : rCharts::rPlot() in rmarkdown file.

• xtable always shows LaTeX output but not table. Raised a question in COS : 求助！knitr Rmd pdf 中文编译 2016年8月19日 下午9:56 7 楼.Here I try other packages like textreg and stargazer. You can refer to Test version to view the output of stargazer function and the source codes I reserved but added eval = FALSE in chunks named lm-summary and lm-anova to unexecute the codes.

• I refer to R Shiny: Rendering summary.ivreg output and tried to plot the output table, but there has no bottom statistical information like Residual standard error, Degree of Freedom, R-Squared, F-statistical value and also p-value, therefore I use R Shiny App for Linear Regression, Issue with Render Functions which simply renderPrint() the verbatimTextOutput() in shinyapp 4.2.1.

• I tried to raise an issue about post the shinyapps to RStudioConnect at Unable publish to RStudio Connect : Error in yaml::yaml.load(enc2utf8(string), …) : Reader error: control characters are not allowed: #81 at 276 #115. You might try to refer to the gif files in #issue 115 for further information. I tried couple times and find the solution but there has no an effective solution and only allowed post to ｮPubs.com where I finally decide to seperate the dynamic shinyApp into another web url.

• Remark : When I rewrite Report with ShinyApps : Linear Regression Analysis on Odds Price of Stakes and would like to post to ®StudioConnect, the wizard only allowed me post to rPubs.com (but everyone know rPubs only allow static document which is not effort to support Shinyapp). Therefore kindly refer to https://beta.rstudioconnect.com/content/1766/. You might download and run locally due to web base version always affected by wizards and sometimes only view datatable but sometimes only can view googleVis while sometimes unable access.

• Using formattable and plotly simultaneously and Possible namespace issue with plotly::last_plot() #41 solved the formattable issue.

• I am currently work as a customer service operator and self research as a smart punter. Hope to setup my sportsbook hedge fund company website Scibrokes® and running business and back to the sportsbook betting industry soon…

Terminator II

7.4 References