Thursday, 6 June 2024

Oilers vs Panthers 2024 - True Odds Calculation

 Oilers vs Panthers 2024 - True Odds Calculation

Ok, so, arguably, the title of the blog is a bit of click-bait.  The 'true odds' of any situation is too complicated for mere mortals to determine.  However, this is a head-to-head comparison of 20 (or 23) statistical categories, that should correlate with success in hockey.

The columns show the scores for each team, in the categories, over the 2023-24 regular season.  The weighing factors come from a long time-trend of Stanley Cup playoffs for each category.  They show the win percentage for each category, over this period, for the team with a better score in that category.  Note that these win percentages are on a game-by-game basis for all playoff levels.  

So, for example, home teams won 54% of games over the visitor.  Similarly, the higher ranked team in the regular season won 55% of playoff games over the lower ranked team.  The team with the higher goals per game in the regular season won 54% of their playoff games.  And so on, for all the rest of the categories.  The final three categories are ratios, based on some of the variables listed above them.  One could argue that doing this just repeats information already in the comparisons.  Or one could argue that the ratios actually do give additional insight into the situation.  So, I gave both alternatives.  A fully worked-out multivariate analysis would shed light on the matter, but that is for another time and blog.

Seq Category Name Edm Oilers FLA Panthers Weight (Win%) Pct Edge Edge Winner
1 Home Games vs Visitor 3 4 0.54 0.04 FLA
2 Rank (points) 104 110 0.55 0.05 FLA
3 Goals For per Game 3.56 3.23 0.54 0.04 EDM
4 Goals Against per Game 2.88 2.41 0.54 0.04 FLA
5 Power Play (PP) Goals For 64 63 0.53 0.03 EDM
6 PP Opportunities For 243 268 0.51 0.01 FLA
7 PP Success Pct 0.2634 0.2351 0.51 0.01 EDM
8 PP Against 53 51 0.53 0.03 FLA
9 PP Opp Against 258 291 0.49 -0.01 EDM
10 Penalty Kill 0.7946 0.8247 0.52 0.02 FLA
11 SH Goals For 7 8 0.51 0.01 FLA
12 SH Goals Against 5 9 0.49 -0.01 EDM
13 Pen Min Against Team/Game 9.5 13.6 0.51 0.01 EDM
14 Pen Min Against Opp/Game 8.5 13.5 0.51 0.01 FLA
15 Shots on Goal (Team) 2768 2764 0.53 0.03 EDM
16 Shot Pct (Goals Scored) 0.105 0.096 0.51 0.01 EDM
17 Shots on Goal (Opponent) 2569 2496 0.48 -0.02 EDM
18 Total Saves 2307 2279 0.48 -0.02 FLA
19 Save Pct (Goals Prevented) 0.898 0.913 0.53 0.03 FLA
20 Avg Age 29.4 29.5 0.53 0.03 EDM







21 Shots Ratio: Team/Opp 1.08 1.11 0.53 0.03 FLA
22 Goals Ratio: For Against 1.24 1.34 0.54 0.04 FLA
23 Ratio: PP/(1-PK) 1.28 1.34 0.52 0.02 FLA

 

Next are some relatively simple prediction models, based on the above data.

Model 1 - Simple Category Winner Models

The method below totals the number of categories won outright by each team and determines overall win probabilities based on those totals.  With the 20 variables, each team wins 10 categories, resulting in an even chance of winning for each of the teams.  Using the 23 categories (i.e. including the ratios), Florida Panthers win 13 categories compared to the Edmonton Oilers 10, for a 56 to 43 advantage.  So, the 20 variable method results in the series being a toss-up, while the 23 variable model shows the Panthers to be approximately a  2 to 3 favorite (using racetrack tote board figuring).  The last rows show the payoff needed on a 10 dollar bet, in order to even the odds.  Of course, this doesn't include the government (or bookie, same thing) take-out.  So, I wouldn't bet the Oilers as a favorite, but as a moderate underdog, they seem like a good bet.  But you shouldn't gamble, this is just for fun.


Model 1 (20 Var) Model 2 (23 Var)
Using Category Wins EDM FLA EDM FLA
Category Wins by Team 10 10 10 13
Probabilities 50% 50% 43.5% 56.5%
Odds 1.00 1.00 0.77 1.30
Racetrack Odds (X to Y) 1 to 1 1 to 1 13 to 8 8 to 13
Payoff needed on a $10 Bet 10.00 10.00 13.00 7.69
Payoff including initial bet 20.00 20.00 23.00 17.69

 Model 2 - Using Weighted Scores for Categories

The next model uses the weightings in the data, which are based on win percentages for the better team in each category.   This method totals the weighted scores of categories for each team and determines overall win probabilities from those totals.  Both the 20 variable and 23 variable models show the series to be very evenly matched, with a slight advantage to Florida.  Since the edge in each category is slight, they generally offset each other.  Again, the Oilers seem like a good bet if they are underdogs, even if only slight underdogs.  Again, however the government will take a large bite, so finding good odds will be difficult, to say the least.

Method 1 Model 1 (20 Var) Model 2 (23 Var)
Using Weighted Points EDM FLA EDM FLA
Category Wins by Team 9.9 10.1 11.315 11.685
Probabilities 49.5% 50.5% 49.2% 50.8%
Odds 0.98 1.02 0.97 1.03
Racetrack Odds (X to Y) 98 to 102 102 to 98 97 to 103 103 to 97
Payoff on a $10 Bet 10.20 9.80 10.33 9.68
Payoff including initial bet 20.20 19.80 20.33 19.68

 

Model 3 - Using Weighted Scores for Categories but Giving all Weighted Points to the Category Winner

This model is a compromise between the other two.  It also uses the weighted scores, but gives 0 points to the team with the inferior score in that category.  The results are very similar to the first model, though evening up the predictions very slightly.

Method 2 Method 2 (20 Var) Method 2 (23 Var)
Using Weighted Points EDM FLA EDM FLA
Category Wins by Team 5.12 5.22 5.12 6.805
Probabilities 49.5% 50.5% 42.9% 57.1%
Odds 0.98 1.02 0.75 1.33
Racetrack Odds (X to Y) 97 to 103 103 to 97 3 to 2 2 to 3
Payoff on a $10 Bet 10.20 9.81 13.29 7.52
Payoff including initial bet 20.20 19.81 23.29 17.52

 So, my conclusion based on these admittedly simplistic methods, is that the series should be very close, probably 7 games.  Florida has an edge, but Edmonton is only behind by a bit.  So, if you see good odds for the Oilers, they would be a good bet, but don't bet, this is just for laughs.  Conversely, if you see Florida being the underdog, go for that.  But don't really, because gambling is bad.

And here's a picture of the Stanley Cup.


 

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So now you should read a short story to find out just how bad gambling is.  It is only 99 cents, and will be a good investment if it convinces you not to bet on horses or hockey games.   :)

A Dark Horse

In “A Dark Horse”, a gambler’s desire to hit a big win seems to lead him to make a Faustian bargain with a supernatural evil.  Or is it all just a string of unnaturally good luck?

The story is just $0.99 U.S. (equivalent in other currencies) and about 8000 words. It is also available on Kindle Unlimited and is occasionally on free promotion.


U.S.: https://www.amazon.com/dp/B01M9BS3Y5

U.K.: https://www.amazon.co.uk/dp/B01M9BS3Y5

Germany: https://www.amazon.de/dp/B01M9BS3Y5

France: https://www.amazon.fr/dp/B01M9BS3Y5

Italy: https://www.amazon.it/dp/B01M9BS3Y5

Netherlands: https://www.amazon.nl/dp/B01M9BS3Y5

Spain:https://www.amazon.es/dp/B01M9BS3Y5

Japan: https://www.amazon.co.jp/dp/B01M9BS3Y5

India: https://www.amazon.in/dp/B01M9BS3Y5

Mexico: https://www.amazon.com.mx/dp/B01M9BS3Y5

Brazil: https://www.amazon.com.br/dp/B01M9BS3Y5

Canada: https://www.amazon.ca/dp/B01MDMY2BR

Australia: https://www.amazon.com.au/dp/B01M9BS3Y5


 

 

 

 

Saturday, 1 June 2024

Sappers on D-Day (as Experienced by the 18th Fld Coy RCE)

Sappers on D-Day (as Experienced by the 18th Fld Coy RCE)

The Sappers’ War focuses on 12 Fld Coy RCE, who were primarily in Italy during 1943 and 1944 and later in Belgium/Holland/Germany during 1945. Thus, they didn’t participate in the D-Day landings, though they saw plenty of action in those Italian and Northwestern Europe battles. But here is an excerpt describing D-Day, from an account about one of their sister companies, who did land on the beaches of Normandy, taken from The Sappers’ War.

 


“L/Sgt. Semple and party of 23 ORs plus 4 armoured D7s landed at approximately 0800 hours. The party worked in at least 4 feet of water clearing beach obstacles which in many cases were mined…gap was cleared in approximately 30 minutes…The party, unable to continue work assembled under cover of the dunes and assisted in removing wounded infantry from the beach as well as assisting in taking 19 prisoners from a pill box…Casualties – 2 ORs wounded.” (War History, 18th Field Company Royal Canadian Engineers 1944-1945, John Sliz).

The source listed above (by John Sliz) has more about that unit’s WW2 history.  It is available from Amazon and other outlets.

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And here are some links to The Sapper’s War, along with a description of the contents of the book.

The Sappers' War: 12th Field Company Royal Canadian Engineers, Oct 1943 to Sept 1945

What follows is a review of the history of the 12th Field Company, Royal Canadian Engineers, primarily relating to the time that the company was in the Italian and Northwestern European theatres during World War II. Though the book focuses on the experiences of a particular company of Canadian military engineers, it also discusses some of the wider issues of the second world war and how it affected the people who lived through the era, civilian and military. Among those are my father (a sapper or military engineer) and mother (a war worker in wartime Britain and ultimately a war bride).


Thus, this is meant to be an informal and unofficial history of the company, written by an interested party in an effort to understand what these men went through during this period, and how that experience affected them and other people who lived through the war. The military aspects of the company's history are there (e.g. fighting, building bridges, detecting mines, maintaining routes), as are the cultural factors that influenced them and their times (e.g. the movies that they watched, the drinking they did, the many diseases they faced, their interactions with the Italian, British and other civilians that they lived among, their worries for the future). Some focus on life on the British home front is also given, via the experiences of my mother and her family.

Since many people had family and relations that lived during this time, it is my hope that the account will be of general interest to them, and to any that have a particular interest in this critical interval in history. Also, though the text relates specifically to Canadian sappers, I believe that many of the experiences will be common to the soldiers and loved ones of other nations who lived through the war, especially Americans and those from Britain and the British Commonwealth.

The primary sources of this document are the 12th Field Company War Diaries and related orders, with some material from The History of the Corps of Royal Canadian Engineers, Volume 2 as well as various official histories by the Department of National Defence. Various other published sources are used as well, especially when discussing the wider issues of the war or the army experience (e.g. Churchill’s history of the war) , or conversely when relating very specific episodes of the war (e.g. Popski’s Private Army in late 1944). Personal accounts of my father’s or mother’s stories also augment the narrative. I have tried to fit those in during appropriate time periods, though some stories are more general and have therefore don’t necessarily relate to the time period being discussed. Nonetheless, they do help capture the essence of “being there” during the war years.

The War Diary is a day by day account of the primary activities of a given unit, as recorded by personnel in the headquarters staff of that unit, and signed off by the commander of the unit. As such, it is an official record, though the writers often brought a bit of their own character into the document. Naturally, as a relatively brief document it can’t hope to capture the complexity of the individual stories of 280 or so men, so the family lore generally has no corresponding entry in the War Diary, though there are sometimes tantalizing hints and near-verifications of these personal accounts.

There are a number of other sources for the book, from official histories to popular history books. I include quotations and references from these works (an eclectic mix), as I believe that they also shed light on different aspects of this period of time, and besides that, are just interesting accounts, in and of themselves.

U.S.: https://www.amazon.com/dp/B09HSXN6Q2

U.K.: https://www.amazon.co.uk/dp/B09HSXN6Q2

Germany: https://www.amazon.de/dp/B09HSXN6Q2

France: https://www.amazon.fr/dp/B09HSXN6Q2

Spain: https://www.amazon.es/dp/B09HSXN6Q2

Italy: https://www.amazon.it/dp/B09HSXN6Q2

Netherlands: https://www.amazon.nl/dp/B09HSXN6Q2

Japan: https://www.amazon.co.jp/dp/B09HSXN6Q2

Brazil: https://www.amazon.com.br/dp/B09HSXN6Q2

Canada: https://www.amazon.ca/dp/B09HSXN6Q2

Mexico: https://www.amazon.com.mx/dp/B09HSXN6Q2

Australia: https://www.amazon.com.au/dp/B09HSXN6Q2

India: https://www.amazon.in/dp/B09HSXN6Q2

Friday, 17 May 2024

Neighbourhood Cat and the Magpies

Neighbourhood Cat and the Magpies

We have a couple of magpie nests in some trees in our backyard. My wife refers to one of them as “the condominium”, as it is pretty big. It isn’t all that obvious whether it is being used as an actual egg-hatching place, from year to year, as these birds can be surprisingly secretive. However, this year I am quite sure that I spotted a magpie sitting in the nest. Plus, there has been a fair bit of magpie activity around it.

Anyway, a neighbourhood cat also seemed rather inquisitive about the matter, the other day. It was walking on a neighbour's fence, which is near the condominium tree. I saw it from the bedroom window, as it paced tentatively along the fence, seeming to be not sure of what to do. At first I thought it might just be having trouble getting down from the fence, but then rejected that idea, as cats are excellent jumpers. But, I observed that the cat was taking quite an interest in this tree.

Then it started climbing up the tree.

I didn’t want it to get to the nest, as I actually like magpies and don’t mind them raising a brood in our tree. Plus, I have seen magpies go after cats that are heading for a bird nest. They are smart birds and work in a team, so the cat is usually in trouble. So these situations are not great for the cat, either.

I rapped on the window to get its attention, but it mostly ignored me. I quickly went outside, to try to shoo it away, but by that time I got there, the cat was gone and the magpies were being pretty vocal about the affair. I suppose that they chased it off, and it left before I had a chance to see which way it went.

The day before, the magpies were giving neighbourhood squirrel a hard time, as well. So I hope we will be seeing and hearing baby birds soon.

Thursday, 2 May 2024

Some Analysis of Stanley Cup Winners since 1993-94

I wrote the post below as a response to a Quora question.  I was planning to do some blogging about Stanley Cup data that I am analyzing, so I will kick that off with reprinting this on the blog.

 

Can statistics and data analysis be used to predict the results of cricket matches?

Yes, obviously you can use statistics and data analysis to predict the results of cricket matches. You can do this for any game that has a consistent set of rules and a reasonably large collection of data on games, teams, players, results of matches, etc…

I haven’t followed cricket personally (though it seems like an interesting game), but I have used statistics to predict horse races (made some money for a few years) and am currently looking at ice hockey (Stanley Cup playoffs history) both for prediction purposes and for understanding of some aspects of the game. Specifically, I want to explain why Canadian teams haven’t won a Stanley Cup in over 30 years. I have found a very reasonable, evidence-based answer to that question, but am holding that back for now. I will eventually use all this data to do a book on Amazon.

Here is a quick lesson in how to use data to predict sports:

  • First, make sure you actually know how to analyze data. That means a reasonable grounding in math, statistics, data science and computer programming (or spreadsheet manipulation). That is usually obtained via schooling, but an intelligent motivated person can probably pick up a lot of the essentials with time and self-study.

  • Next, find a source of data for your analysis. When I did the horse races, decades ago, that meant obtaining a paper copy of The Daily Racing Form, then hand-entering the data into a computer. For my hockey study, there are now numerous websites with data. So, if you have the time and knowledge, you can often scrape a lot of data from those sites.

  • Next, analyze the data. It helps to have at least a general idea of what you are looking for (a “research question”). However, this isn’t an academic study (not usually anyway), so you can relax a lot of the methodological niceties. So, explore widely, for interesting insights that you may not have expected when you got into the study.

  • Do a lot of descriptives. They are always helpful. Here is an example from my hockey analysis, where you can see that the home team that has an advantage in the playoffs, though it isn’t huge (about 54%). But it is consistent, which is important.


    Here's another one, where you can see that the team that has a higher ranking in the regular season does have an advantage in the playoffs, though it isn’t huge (averaging about 55%, but the best-fit trend-line shows it going from about 60% at the beginning of the period to about 50% by the end).


  • But then do a deeper dive. Being higher ranked is important, but how much higher ranked is even more important. You can see that the win pct of the better ranked team goes up, as the difference between that team and the lesser ranked team increases. This is also quite consistent, though there are some interesting outliers.


  • The second graph shows the size of the data grouping for each rank difference (i.e. the number of games where there was that difference in ranks). Now those outliers don’t look so scary - they only accounted for a small percentage of games overall. The main sequence of the data is consistent and has large numbers of games, so probably very reliable.


  • Then, you might do some more inferential and/or multivariate statistics. You might also do subgroup analysis, to understand your data at a more granular level. As you can see below, the relationship between team success in the playoffs vs the regular season seems to break down as you get further into playoff rounds (the red line is for all playoff games, and the blue line is for semi-final games only).


  • Anyway, you can obviously carry on with this type of analysis, looking at various other factors (e.g. home game vs away game, offensive team style vs defensive team style, etc.). I am doing that with my hockey analysis. All this could be done for cricket, too, though obviously the factors that you will study will be unique to the game (e.g. for cricket, you might be interested in batting averages or runs scored).

Naturally, a big question for this sort of activity is “what is the purpose?” It might be for:

  1. a better understanding of the game

  2. to improve team management or coaching

  3. win money gambling.

If your purpose is to win money gambling, that is a high hurdle to jump, unless you are just betting with friends. If you are up against government-sponsored gambling, you face a very high “take-out”. That’s the part of the pool that the government keeps for itself. If that number is high, you need a very big edge to win, so you have to discover something important about predicting results, that nobody else knows, especially the government odds-maker.

If your purposes are general understanding or managing a team (like the movie Moneyball or my quest to find out why Canada can’t seem to win the Stanley Cup), then the situation is different. The advantages that you can discover from your analysis are less tangible, but perhaps more enjoyable.

One last thing about cricket and math/statistics. The famous English mathematician Hardy was quite a fanatic about cricket and kept meticulous statistics on the game. I believe that some people thought that a waste of time, when he could do real math. His famous colleague Ramunajin was from India, so it is likely that he liked cricket too, though I don’t know that for sure. In North America, many economists and the like, seem to be drawn to baseball statistics, according to my reading.

Here is a bit about G.H. Hardy from a math history site:

“There was only one passion in Hardy's life other than mathematics and that was cricket. In fact for most of his life his day, at least during the cricket season, would consist of breakfast during which he read The Times studying the cricket scores with great interest. After breakfast he would work on his own mathematical researches from 9 o'clock till 1 o'clock. Then, after a light lunch, he would walk down to the university cricket ground to watch a game. “

Here’s a link to my Stanley Cup analysis, of why Canada’s long Stanley Cup dry spell is not “just one of those things”, using some fundamental statistical reasoning:

Canada’s Long Stanley Cup Drought, 2023 Edition

And here’s a link to my blog, with more details about my horseracing/statistics project:

HORSE RACING DAYS - Part 1

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And here is a short story about the danger of mixing sports and gambling (horse racing).

A Dark Horse

In “A Dark Horse”, a gambler’s desire to hit a big win seems to lead him to make a Faustian bargain with a supernatural evil.  Or is it all just a string of unnaturally good luck?

The story is just $0.99 U.S. (equivalent in other currencies) and about 8000 words. It is also available on Kindle Unlimited and is occasionally on free promotion.

U.S.: https://www.amazon.com/dp/B01M9BS3Y5

U.K.: https://www.amazon.co.uk/dp/B01M9BS3Y5

Germany: https://www.amazon.de/dp/B01M9BS3Y5

France: https://www.amazon.fr/dp/B01M9BS3Y5

Italy: https://www.amazon.it/dp/B01M9BS3Y5

Netherlands: https://www.amazon.nl/dp/B01M9BS3Y5

Spain:https://www.amazon.es/dp/B01M9BS3Y5

Japan: https://www.amazon.co.jp/dp/B01M9BS3Y5

India: https://www.amazon.in/dp/B01M9BS3Y5

Mexico: https://www.amazon.com.mx/dp/B01M9BS3Y5

Brazil: https://www.amazon.com.br/dp/B01M9BS3Y5

Canada: https://www.amazon.ca/dp/B01MDMY2BR

Australia: https://www.amazon.com.au/dp/B01M9BS3Y5


 




Saturday, 13 April 2024

A Neighborhood Cat Mystery Solved

A Neighborhood Cat Mystery Solved

To quote from an earlier blog:

“Over the years we have had a number of neighborhood cats visit our house. These mystery creatures seem to belong to someone – they generally look well-fed (but not too well-fed) and healthy.”

Well, a few nights ago I was quietly reading in the bedroom, before retiring for the night, when I heard strange sounds from outside. At first I thought is was some rambunctious young people, walking down the alley, making the peculiar vocalizations that can pass for speech in such a situation. But then it carried on for longer than a group going down the alley could account for, and I thought “Aha, it must be a cat”.

I should note that we have a number of solar powered lights on the deck near the sidewalk, so it wasn’t very dark in that part of the yard. I went out to the back porch and looked out the small window of the outermost door to the outside. And there he (or she) was, about 10 feet down the sidewalk.

It had obviously heard me coming into the porch, though it is hard to say what it could see, as the porch was dark (I hadn’t put on an inside light). Under those circumstances, it might be hard to see into a window, with all the light from the solar lights reflecting off the glass.

I looked at him and he seemed to be looking right back back at me. It was an unusual meeting of the minds. The cat had what I could only deem to be a very defiant look. And it was a surprisingly big cat. It made me wonder if a lynx or a small bobcat might have come into the city. Skunks have come into the yard in the past, but it didn’t really look much like that. But in dim light, who knows? At any rate, it didn’t seem worth going to the trouble to shoo it away. Hopefully, its presence would frighten away some mice, if nothing else.

My wife then came into the porch to investigate, which quickly had a second, much smaller, cat go shooting down the sidewalk at high speed. It was immediately followed by the bigger cat. For the short amount of time that I could see them as they departed, the bigger cat didn’t catch up, though I didn’t sense that it was trying very hard.

So what was all the yowling about, I wondered. Was it a cat fight? Was one of them in heat? Were they afraid of some other animal (e.g. a coyote) and they had come near the house for protection? Were they strays? Were they feral? Or were they owned by someone who lets them come and go as they please?

Anyway, a few days later I went on a lunchtime picnic with my wife and son in a small nearby park (it was a work-from-home day for everyone). On the way back I was relating the story of the two cats. Just about the time that I finished the story, we noticed a large cat in the yard that we were walking past. Further up in that yard was a smaller cat. The big cat then proceeded to chase the smaller cat, but not as if it really wanted to catch it.

“That’s them!” I said. “The very culprits!”

My son and I had a good laugh about it all. In the end, it was just a couple of neighbourhood cats playing tag. But it was as if they knew that they were the stars of the story, and wanted to perform an encore.

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The above account was all true, but if you want a nice cat story and kids, you can check out the books below, written by my wife quite some time ago.

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The Summer Cottage Mystery

Here's a nice children's story by Science Fiction and Romance writer Helena Puumala. Yes, she does kid's stories too. Read it to a younger child (pre-school, elementary or early junior-high), or read it yourself to bring back memories of those long, lazy childhood days at the lake, during summer vacation, when your biggest worry in life was a lost kitten. Note that this is a short story of about 8500 words.

It is just 99 cents U.S. (equivalent in other currencies) and is sometimes on free promotion. And, of course, it’s on Kindle Unlimited.

It is available on Amazon, at the following:


Amazon U.S.: https://www.amazon.com/dp/B00N0B4TYY

Amazon U.K.: https://www.amazon.co.uk/dp/B00N0B4TYY

Amazon Canada: https://www.amazon.ca/dp/B00N0B4TYY

Amazon Australia: https://www.amazon.com.au/dp/B00N0B4TYY

Amazon Germany: https://www.amazon.de/dp/B00N0B4TYY

Amazon France: https://www.amazon.fr/dp/B00N0B4TYY

Amazon Italy: https://www.amazon.it/dp/B00N0B4TYY

Amazon Spain: https://www.amazon.es/dp/B00N0B4TYY

Amazon Netherlands: https://www.amazon.nl/dp/B00N0B4TYY

Amazon Mexico: https://www.amazon.com.mx/dp/B00N0B4TYY

Amazon Brazil: https://www.amazon.com.br/dp/B00N0B4TYY

Amazon India: https://www.amazon.in/dp/B00N0B4TYY

Amazon Japan: https://www.amazon.co.jp/dp/B00N0B4TYY


Miranda and the Christmas Elf

The little pre-school girl, Miranda, is feeling unsafe because of bullies in the neighbourhood and family troubles between her mother and father. Can her friend, young elementary grade age Nathan, use his special powers to call on the North Pole for some Christmas Eve magic, to help her out?

The story is a heartwarming Christmas tale, suitable for children and adults, which will bring a little Christmas magic to us all. It is about 9000 words, or around 45 minutes or so, at typical reading speeds.

It is priced at only 99 cents (U.S. or equivalent in other currencies) and is sometimes on free promotion as well.

The book is available on Amazon, at the following links:

Amazon U.S.: https://www.amazon.com/dp/B019MCY3RM

Amazon U.K.: https://www.amazon.co.uk/dp/B019MCY3RM

Amazon Canada: https://www.amazon.ca/dp/B019MCY3RM

Amazon Australia: https://www.amazon.com.au/dp/B019MCY3RM

Amazon Germany: https://www.amazon.de/dp/B019MCY3RM

Amazon France: https://www.amazon.fr/dp/B019MCY3RM

Amazon Spain: https://www.amazon.es/dp/B019MCY3RM

Amazon Italy: https://www.amazon.it/dp/B019MCY3RM

Amazon Netherlands: https://www.amazon.nl/dp/B019MCY3RM

Amazon Japan: https://www.amazon.co.jp/dp/B019MCY3RM

Amazon Mexico: https://www.amazon.com.mx/dp/B019MCY3RM

Amazon Brazil: https://www.amazon.com.br/dp/B019MCY3RM

Amazon India: https://www.amazon.in/dp/B019MCY3RM

 

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