Have you just been really unlucky, or does your betting strategy need some work? Methods to Estimate Prediction Error
Everyone has gotten unlucky on a seemingly sure bet that backfired. We hate losing that nail biter. It hurts a lot more than that blowout loss where you weren’t even close. The question is: should each loss (and alternatively each win) be treated equally? Margin of Victory If most of your wins are by a single point and you’re getting blown out in your losses, it might be a sign that your Win/Loss performance is due for a regression. Alternatively, if your only losses are of the nail biter variety, you might just be on the wrong side of variance. As an assessment, it might be helpful to measure your margin of victory on your wagers. Themargin of victory (“MOV”) measurement is a simple but useful measurement of how well your bets are performing. Since bets are generally binary outcomes (win or loss) there is a quite a bit of variance when it comes to measurement by simply wins and losses. Using the MOV measurement can give you a more precise measurement that isn’t as influenced by the binary nature of wager outcomes. This is identical to evaluating team performance using net differential as opposed to W-L. MOV Example: Say you placed the 15 NBA ATS bets below, winning 7 and losing 8 during the first week of March:
Date
Wager
Odds
Win/Loss
3/1/2020
Kings -7.5
-110
L
3/1/2020
Nuggets -2.5
-110
W
3/2/2020
Cavaliers +10
-110
L
3/3/2020
76ers +12.5
-110
L
3/3/2020
Warriors +15
-110
W
3/4/2020
Pacers +11.5
-110
L
3/4/2020
Thunder -8
-110
L
3/4/2020
Blazers -7.5
-110
W
3/5/2020
Raptors -9
-110
L
3/6/2020
Bulls +2
-110
L
3/6/2020
Celtics -1.5
-110
L
3/6/2020
Mavericks -7.5
-110
W
3/7/2020
Grizzlies -6.5
-110
W
3/8/2020
Pacers +6.5
-110
W
3/8/2020
Magic +8
-110
W
Wins
7
Losses
8
Win %
46.7%
A 46.7% winning percentage at -110 is certainly not a profitable record when betting the same amount every time. We could just assume that these weren’t very good bets. What we’d rather do, however, is examine our margin of victory for these games. The first wager of Kings -7.5, for example, was a game that the favorite failed to cover by 1.5 points, winning the game by 6 points when favorite bettors had to lay 7.5. Your wager (Kings -7.5) would have a MOV of -1.5 since your bet lost by 1.5 points.
Date
Wager
Pts
Opp Pts
Result
Line
W/L
MOV
3/1/2020
Kings -7.5
106
100
-6
-7.5
L
-1.5
We can do this same analysis for each wager and find that your MOV averaged 17.5 points in your wins and -3.1 in your losing wagers. Thus despite a losing record, your wagers had a total MOV of 6.5 points.
Date
Wager
Odds
Win/Loss
MOV
3/1/2020
Kings -7.5
-110
L
-1.5
3/1/2020
Nuggets -2.5
-110
W
12.5
3/2/2020
Cavaliers +10
-110
L
-3
3/3/2020
76ers +12.5
-110
L
-0.5
3/3/2020
Warriors +15
-110
W
31
3/4/2020
Pacers +11.5
-110
L
-7.5
3/4/2020
Thunder -8
-110
L
-1
3/4/2020
Blazers -7.5
-110
W
13.5
3/5/2020
Raptors -9
-110
L
-1
3/6/2020
Bulls +2
-110
L
-4
3/6/2020
Celtics -1.5
-110
L
-6.5
3/6/2020
Mavericks -7.5
-110
W
17.5
3/7/2020
Grizzlies -6.5
-110
W
10.5
3/8/2020
Pacers +6.5
-110
W
9.5
3/8/2020
Magic +8
-110
W
28
Wins
7
17.5
Losses
8
-3.1
Average MOV
6.5
This certainly indicates that variance was not on your side as you were on the losing side of several one-possession games and most of your wins occurred at pretty comfortable MOVs. Now certainly there are limitations to an MOV analysis. First, since it is an “average” measurement, it can be influenced by outliers. You might consider capping the MOV (say a 10 or 15-point maximum MOV) to reduce the impact of outliers. Second, different sports have different key numbers and a simple MOV analysis does not account for key numbers or non-normal distributions. Lastly, this type of analysis doesn’t translate as easily for moneyline wagers. To make an apples to apples comparison, you would need to assess the average score differential at various moneylines. We computed the average run differential of away teams in the MLB based on the breakeven win probability of their moneyline odds in the graph linked below. Normalizing Run Differentials Based on Implied Win Probability More Granular Measurements For sports that have lumpy scoring (NFL, NHL, MLB) you might perform a similar analysis using even more granular data than scoring. For example, to remove cluster luck from baseball scoring, you might do an analysis of net base production or in football you might analyze yards per play or play success rates. Grading Your Own Predictions Now let’s say you’ve made a model to come up with your own predictions for games (we’ll cover several ways to do this in our model building section) and you want to assess your predictions vs the market (or someone else). In statistics and machine learning, two common ways of assessing performance are by the mean absolute error (“MAE”) and the root mean squared error (“RMSE”) of various models. Mean Absolute Error The great thing about these terms is that their names so accurately describe their calculations. The mean absolute error is the average (mean) of the absolute value of your model’s prediction error. So if you forecasted a game to be -5 and the game ended in -3 the absolute value of the error of your model was 2 points. Do that for every prediction and take the average. Simple enough. Root Mean Squared Error The root mean squared error is conceptually very similar to MAE except that you first 1) square your error term, then 2) take the average (mean) of the squared error terms and finally 3) take the squared root of those squared errors. We’ve calculated the MAE and RMSE for the NBA ATS wagers that you made linked below. Naturally, since those wagers had a positive average MOV, we’re not surprised that the prediction error was less than the market. MAE and RMSE The difference between MAE and RMSE is that by squaring the error values, you are more heavily penalizing predictions with large errors. If large errors are significantly worse than smaller errors, then RMSE might be a better calculation for you to use. Otherwise MAE will work just fine.
Some Parlay Math from an idiot who thought he could beat the system, but might help others projects
So a couple of things to say from the beginning. I am smart enough to use excel and do some math, which is to say I am not that smart, and I am stupid enough to think that I could somehow figure out a way to use parlays to get free money. Secondly, for some this is going to be super trivial stuff, and for other this isn't going to be worth anything. Regardless, I am putting it out there because you really never know when some random piece of math, or a random discovery/idea you had and threw away is the last piece of a puzzle for someone else. I had never bet on sports using a book and I knew very little about sports betting before this summer. One of my best friends bets quite a bit and I would pick up tid-bits from him all the time. He talked to me about parlays and having no idea what it was I looked into it. After a quick search and him explaining it some more, I figured it would be worth it to see what would happen if you bet every "leg" of a combination of different parlays. ( That is what I have been calling it myself, what I mean by a leg is lets say you are betting on two moneylines for a basketball game, there are four possible parlays, or legs, win win, lose lose, win lose, and lose win, each parlay would be a leg as I am calling it in the overall system). This is probably already sounding stupid, which it is. I settled on combining soccer with any regular sport like basketball, because its not uncommon to find games where all the odds are positive for the two teams winning and a draw. This meant a total of 6 parlays. What I did in Excel was pretty rudimentary. I calculated the decimal odds for each parlay. Then I chose an arbitrary amount of money I split between the 6 parlays, say 200$. 200$/6 was 33.3$. (33.33*the odds for the parlay)-200$=profit. Minus 200 because thats the total amount you have spent across the 6 bets. that profit number will always be negative because you will always lose money if you do this. Take that profit and divide by the odds of the parlay. That is how much money you need to add to the original 33.3$ to "maximize" your gain (what you will really be doing is minimizing your losses across the board). Once you do this for each leg, the actual amount that you bet will be different, the lower odds will require more and the higher odds will require less. using the new bet amount, multiply again by the odds, and subtract the total the new betting amounts, for your "profit". All of the profits should be the same number, and they will all be negative. This number is something you can find just from looking at the odds, I called it the "Parlay Goodness" number. The Parlay Goodness number tells you the percentage of your principle you will lose if you bet all the legs of a parlay. The equation I made assumes that you are using soccer + a regular sport with no draws, and assumes all the soccer odds are positive. As I am looking at my spreadsheet it would take a little to long to describe, so I will link it somehow if you are interested. The next obvious step on this path was to determine if I could remove a leg, or two legs, and have the operation still be profitable. Remove meaning not bet, this would lower the amount of overhead, but now leaves the hole open for you to lose because you did not bet a certain outcome. I tested 4 different situations. Two where I removed only one leg (5/6), and two where I removed two legs( 4/6). In the first 5/6 I removed the favorite. I should say that for this part of the story, I converted each of the parlay decimal odds into percentage odds, or the odds it would hit/win. When I removed the "favorite" I removed the leg of the parlay with the highest percentage odds. I did a different scenario using the least likely parlay to happen. The give and take here is that the favorite requires the largest bet size, but is "favored", so while your taking out more overhead, your leaving yourself open to not having bet the most "likey" scenario. When you remove the least likely, you don't really remove much overhead, because it was the one that required the lowest bet size. The same sort of thing was done for the 4/6, the two favorites were removed and the two least favorite removed. In order to see if any of these would be profitable over the long term, meaning say if you bet 100 times. I said that (win $/loss$) > (% of the time you lost/ % of the time you won) then you would make money. Where win $ means how much you win if the parlay hits one of the legs you bet, and loss $ is how much you lose if the outcome is one of the leg(s) you didn't bet. The percentage of the time you won was found by adding up those percentages of each leg I talked about earlier, subtracting that from the total percentage of each leg added up, dividing by the total percentage. Then doing 1-that number so it was how often you won not how often you lost, then multiplying by 100 for a %. That is the % of the time you should win, and 100-that is the % of the time you should lose. Throwing all that information into the aforementioned equation should tell you if you have found something interesting or not. If your actually interested I uploaded my spreadsheets into google. Its a mess, but you may find something you want. For most people this was a stupid post to read, sorry bro. For people who are actually good at excel, sorry bro. For everyone who is a real sports bettor, sorry bro. TLDR; I did some math because I am stupid. https://drive.google.com/file/d/1DMzSSiwLurQGHTV8XAgXOaeDbHUk-n-view?usp=sharing https://drive.google.com/file/d/1KyWPmfE90yszfrRanJNFbUWsQQVb-l54/view?usp=sharing https://drive.google.com/file/d/1qJW9-Dox_62ytA8FBltO_2GHOHLol3WQ/view?usp=sharing https://drive.google.com/file/d/1QXO_FWEqUYgrPZ7ulShogJ5DID_pucm1/view?usp=sharing EDIT: I would like to add that if you could ever "insure" your bet so to speak, or bet against your self, as in bet a friend or your book that you would lose money, then you be able to use all this to make money.
Leveraging Optionality: Applying financial theory in the sportsbetting markets
Option Pricing Theory Stock options are equity derivatives that are frequently used for employee compensation or speculation within the finance realm. Anyone who spends more than 5 minutes on /wallstreetbets should know what I’m talking about. A typical plain vanilla call option provides the upside of capital appreciation with capped downside risk. The upside potential provided by options frequently holds considerable value. Stock option are frequently valued using the Black-Scholes option pricing method, using variables such as the price of the underlying asset, the exercise price of the option, time to expiration, volatility and a risk-free interest rate. For our purposes, we’re going to simplify things a bit by using a simple binomial option pricing model which determines option value by assuming the price of an asset can either increase or decrease by some estimated amount with some estimated probability. Quick example: let’s assume Tesla is trading at $700 per share and they report earnings tomorrow. We assume that depending on how many cars they sold, the price will either be $800 or $600 tomorrow with 50/50 probability. If one of your friends said “Hey, I’ll sell you my share for $700. Just let me know tomorrow if you want it” what should your reply be? My reply would be, “Sure I’ll let you know tomorrow.” And then I would wait to see how earnings went. If Elon sold a lot of cars (and the price increased to $800) I would go ahead and buy my friend’s share for $700. If earnings crap the bed, I would pass on my friend’s offer and not buy the share. Basically, you have no downside, only upside. To value this option that our friend gave us, we would simply multiply the payoff in each scenario by the probability of each one occurring:
Scenario
Option Value
A) $100 Increase
Max($800-$700, 0) = $100
B) $100 Decrease
Max($600-$700,0) = $0
Value of Option
50%*$100 + 50%*$0 = $50
In this hypothetical scenario, our friend gave us a free $50 worth of option value.[1] Optionality in Sports Betting A key advantage that sports bettors hold is deciding when to bet. We have covered this in a previous post, but it’s important to recognize that lines are dynamic and frequently vary across sportsbooks. Sometimes the lines differ considerably across books and sometimes they are very similar. In the former scenario, bettors can get tremendous value from shopping lines. In the latter, bettors might hold significant option value. Let me demonstrate with an example. This season, the New York Jets hosted the New England Patriots in a divisional clash on Monday Night Football. Let’s assume that your model suggests that there is value to betting the Jets on the moneyline (lol). You got your paycheck on Friday and you want to fire off your bet at one of your two sportsbook accounts that evening. Book 1 offers the Jets at +345 and Book 2 offers the Jets at +344. You should go ahead and place your bet at Book 1, right? Not necessarily. With odds that are nearly identical, your option value is worth more than the one penny in price difference (on a huge dog). If the line at either book moves up, you can get a better number. If the line at either book moves down, you bet at the book that didn’t move. This is option value. The value of that optionality depends on 1) if the books generally move in tandem, 2) the expected magnitude of the line movement and 3) the amount of time remaining until the game starts. With the historical lines of each book, you can determine the average discrepancy between the lines to figure out what the likely magnitude of a future line move. In the table below, you can see that there was often a considerable difference between the lines offered at these two books. Time Series of Odds between Two Books From line release until 6pm ET on Friday night, there was an average difference of 10 cents between the books. Let’s assume that a 10-cent move is a reasonable estimate for the expected magnitude of the next line movement. At this point, we don’t know if the next line movement will be in our favor or against us. Let’s assume that there is a 50% likelihood of the next line movement will be -10 cents and a 50% likelihood of the next line movement being +10 cents (on Book 2). [2] Optionality Example If the line at Book 2 moves down 10 cents, we bet Book 1 at +345. If the line at Book 2 moves up 10 cents, we bet at Book 2 at +354. By waiting for a line move, we can increase our expected odds from +345 to +349.5. Value of Optionality Now, we assume you are betting on the Jets ML because you believe there is an edge and that your expected win percentage exceeds the breakeven win percentage. As an example, let’s assume your expected win percentage is 24.0%. We can now determine your expected profit by 1) betting the odds at +345 or 2) waiting and getting expected odds of +349.5. As calculated below, the expected profit for a $100 bettor increases from $6.80 to $7.88 by preserving your optionality and waiting to bet. As a result, the indicated value of the optionality is $1.08. Option Value Calculation Now – a common critique might be that “hey, we can’t predict the future and there is a chance that both lines move down simultaneously” or that “the lines were volatile early in the week but since reached efficiency”. Certainly, it’s possible that lines move in lockstep, but given the historical spread between the lines, I wouldn’t count on it.[3] The argument that the lines have settled (and are thus less volatile) can be disproved by the line movement from 6pm ET on Friday until kickoff. If lines have settled, we would expect a negligible difference between the lines going forward. This, however, is not the case as the average difference between lines averaged 11 cents from 6pm ET Friday until kickoff, frequently exhibiting a 20-cent difference and peaking at a difference of 30 cents around midnight on Monday. Time Series of Odds between Two Books Continued So - what can we learn from this? Big picture: if you have multiple sportsbooks with the same line, you’re generally better off waiting for one of the lines to move rather than pull the trigger. This especially holds true when there is a considerable amount of time before kickoff/first pitch/etc. [1]We’ll ignore some of the technicalities of discounting that you would typically do with financial assets as the term (one day) is negligible and U.S. treasuries are yielding next to nothing. [2] Doesn’t matter which book we assume will move next. The math is the same. [3] Let’s also not forget that you’re contemplating placing a wager 72 hours before kickoff. If there are only 5 minutes to kickoff, that’s a different story(clearly not as much option value).
NBA 1st Half Fading Away B2B Revisited (real spreads!)
This is in regards to JTintheCity's proposed strategy of betting the 1st half home spread when playing a team on the second game of a back-to-back. In the previous analysis, people were unsatisfied with estimating lines. So thanks to INFPlayer's recommendation of a website that posts historical 1st half spread lines, I have scraped the past 5 seasons (and up to yesterday for this season) of the lines posted on sportsbookreview.com. This book posts lines and the exact moneyline from 10 books, so when scraping I took an optimistic line (the best of the 10 in regards to betting the home team, so which book being used changes from game-to-game), a constant line (Bovada, when not available set equal to the optimistic line), and a pessimistic line (the worst available for the home team). Using the threshold rule of only betting the home teams when the spread is >= -4 yields the following results over the past 5 seasons, including this seasons incredibly hot start, using the moneylines to calculate profit assuming 1 unit bets on all games.
System
Games
Wins
Losses
Pushes
Win%
Profit
Optimistic-All
1979
984
957
38
50.70
-44.2
Optimistic-Threshold
1399
699
675
25
50.87
-25.5
Bovada-All
1979
976
969
34
50.18
-105.4
Bovada-Threshold
1366
679
666
21
50.48
-68.2
Pessimistic-All
1979
961
980
38
49.51
-106.4
Pessimistic-Threshold
1331
653
658
20
49.81
-61.3
In order to provide full transparency, I encourage you to double check my methodology (CODE REPOSITORY HERE) and the data source (GOOGLE DRIVE WITH DATA AND PROFIT CHARTS OF EACH SEASON). Both line up very well with the data used for the previous analysis (which was scraped from a completely different source). Now, if we want to conduct some analysis beyond those presented in the table, consider the following. If we treat the win percentage of this strategy as a parameter theta, then each time we play the strategy is a Bernoulli random variable with parameter theta, and the number of wins in N total plays follows a Binomial distribution with parameters theta and N. In this case, we are interested in theta, we want to know what the win percentage of this strategy is, given the data that we have observed over the past 5 seasons and so far in this season. Since theta is a probability, it falls within the [0,1] range, and we can model theta with a Beta distribution. When we have no data (the prior), we set an uninformative prior, say Beta(1,1), which has an expected value of 0.5. Then using the likelihood function of the data (the Binomial), we can calculate the posterior distribution over theta, given the data which gives us the familiar Bayesian formula P(theta | data) = p(data | theta) p(theta). Since the Beta distribution is the conjugate prior here, we know analytically the posterior distribution will follow a Beta with parameters a = 1 + wins and b = 1 + losses (since we set the prior to be 1,1). Let us model the most optimistic scenario for the system, the Optimistic-Threshold row of the table. This means the posterior for theta will follow a Beta(700, 676). The benefit of using a Bayesian analysis is that it allows us to ask questions such as "What is the probability this system has a win percentage better than 0.5?" (remember in this context, win percentage = theta). The following table answers those questions. The R script that generates these probabilities (and the density of the posterior) can be found in the code repository linked previously. 0.528 is the minimum win percentage for profitability with -110 juice, 0.7 is the claimed win percentage of the strategy. Keep in mind, this uses the optimistic lines, meaning the best among 10 different books for every game analyzed.
X
P(theta > X)
0.5
74.13%
0.528
7.62%
0.7
0.00%
Its your money, do what you want with it, but historically this system has not been profitable and has a very low probability given the historical data of being a profitable system. I have seen no other proof to the contrary (besides the obviously hot start this season, but looking at the other profit charts shows how random processes can have similar good stretches), and anyone is free to download the data from the google drive and check the numbers for yourself. Edit: Including the December games of 2017
Now that the Falcon 9 is flying again, let's do some wagering!
Hey everyone! Long time lurker and first time poster. Now that SpaceX is flying again and will hopefully move through their backlog quickly this year, I thought it would be fun to put together a web app to let the community wager some internet points on the various aspects of the upcoming launches. If the community likes it, I will get some swag lined up to give away. I just published the skeleton version of bettingonrockets.com and would like to get some feedback from everyone, soft launch it for Jason 3 and then push it on SES-9. Check it out when you have some time. I will be adding to it and incorporating feedback over the next couple weeks. How it works Every launch, all users will get a set amount of credits which they can use to place bets on that launch. If the user doesn't make any bets before the launch, the points are lost and not added to your total. All the bets that you do win, adds up in your general fund that will place you on the leaderboard and can be used for any bets you want. Types of Bets Closest To - This is a winner take all bet where we guess some numerical value and whoever is closest to the actual would be the winner. Ex: Closest guess to the actual apogee of the payload. Sample Pool Bet - This is a bet where you wager a specific amount that something will or will not happen and you win a percentage of all the losing sides bets. This isn't a bet again the house but other people and doesn't have odds. This type of bet is best for situations we wouldn't be able to make an accurate moneyline on. Ex: NET Date of 1/17/2016 10:42 PST will be pushed back Sample Moneyline - This bet is just like a sports bet at a casino where we can calculate a moneyline based on past performance and you can bet the odds. Those are my ideas so let me know what you think! I hope we can have some fun with it and there is a link to suggest bets to make.
I'm working on an open source project that will allow checking bets for value
In order to gain experience of development in Meteor rapidly, I'm building two open source projects related to gambling. The first one will do what the title says. I have a plan mapped out for it and I've done more than 30% of the work. But I need to hear other people out: what checks do you want for your bets? I'm talking about the type of checks that would disconsider a bet in your eyes; I know from my own experience that sometimes it's hard to let go of them. But when you want to bet and the app will tell you "no" and offer valid reasons, maybe you'll actually listen. Here’s an example with the two most basic checks I can think about:
First thing, to get it out of the way and not have the user influenced by the subsequent tasks, ask for a percentage based probability on how often will the event occur. For example: do you want to bet that Real Madrid will win instead of drawing or losing in their next match? How often do you think that would happen? 85%. OK, let’s go to step 2.
Input the odds, calculate the bookmaker margin, compare it with the averages for that event and so on. The checks will get more complicated as it goes on. I have a certain flow in mind.
The interface is beautiful and it allows for events with any number of outcomes and odds expressed in these formats: fractional, decimal and moneyline. For this reason it will also be helpful to people that bet on things like 1x2 and horse races, not just for handicappers. TLDR: The online app is a checklist to go through before betting, in order to determine if the bet is indeed good. What checks do you want? What can you think of?
No-Vig Fair Odds Calculator; US Odds: No-Vig % No-Vig Odds: The tool to the left can be used to calculate no-vig odds and no-vig win probabilities. For example, if the moneylines of an NFL football game are NY Giants -160 / Atlanta Falcons +140 novice bettors often make the mistake of assuming the fair odds without juice are Giants -150 Mobile friendly moneyline calculator and sports betting calculators. Display payouts based on odds wagered. Money line calculator, Gambling calculator, Point spread calculator, Parlay calculator, Over/Under Calculator So when we see teams getting money line odds that far surpass or don’t meet the 60%/40% dynamic, we need to give that some thought. Look at it this way, even the best team in the league wins 60% of their games, which equates to a money line of -150. But when looking at the odds, we see favored teams far above -150 all the time. Fraction betting odds are easier to convert into an implied winning percentage. For fraction betting odds, the formula is: Denominator / (Denominator + Numerator) If the fraction betting odds are 11/10, the formula would look like this: 10 / (11+10) = 10 / 21 = 0.4761904. Multiply your end result (0.4761904) by 100 to get the percentage: 47.6% Calculating Payouts From Moneyline Odds. In the United States, most bookmakers use the moneyline format to express the odds they offer for wagers. Thus, moneyline odds are also commonly referred to as American odds. They can be either a positive number or a negative number. Moneyline (US) odds. For some events such as horse racing, US betting sites adopt fractional odds. However for many sports and markets such as American Football, Boxing etc. ‘moneyline’ odds are used. These moneyline odds are generally used for an event with two outcomes. Moneyline odds are worked out to a bet of $100. How to calculate odds. Our betting odds calculator takes a step further and calculates the percentage probability of winning and losing.The team would win 5 out of 6 games and lose 1 of them. By converting fraction to percent, we can say that the chances of winning are 5/6 = 83.33%, and of losing 1/6 = 16.67%.. Do you understand how we calculated this percentage? The spread converter / moneyline converter tool would then tell you that you should expect to find moneyline odds of -284.8 on the favorite and a moneyline price of +225.2 on the underdog, based Betting Odds Converter & Moneyline Calculator. Yes, our odds calculator shows the implied probability of winning your bet outright in an easy to read percentage. For example, a wager at +200 Win % – Percentage of wins required to show a profit at a given money line. For example, you would need to win 80% of all of your bets just to break even if you only bet on -400 money line favorites (over 80% to turn a profit). Moneyline Conversion: Odds to Percentage Chart
1X2 Home -- Draw -- Away: Expected Odds Calculation ...
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