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NRL S2016 R11 Results

NRL S2016 R11 Results

Summary

This round we didn’t lay any stakes due to poor expected return and low probability scores.

Despite this, the model performed slightly better than the bookmakers and predicted 6 of 8 games (75%). The bookmakers (at time of previous post) actually had the Eels as favorites over the Storm, although leading up to and just before this match the the Storm became market favorites

As a point of interest, assuming I had staked $100 on each game at the odds I posted in the round 11 staking and predictions guide, we would have won a total of $140. We would have had $800 in bet risk and therefore would have made a 17% return on this risk. But as stated previously we currently have a very conservative bet strategy and therefore chose not to bet this round.

Predictive Results

Given:

mTP = Models true positives

mFP = Models False positives

mPrec = Models precision (equivalent to accuracy in this case)

bTP = Bookmakers true positives

bFP = Bookmakers False positives

bPrec = Bookmakers precision (equivalent to accuracy in this case)

Table of results

Predictive model vs bookmaker precision by round
round_no season mTP mFP bTP bFP mPrec bPrec
11 2016 6 2 5 3 0.75 0.625
round_no game_no tip_text perceived_odds implied_odds result
11 1 South Sydney Rabbitohs to win against St George Illawarra Dragons while Home 1.96 1.45 Correctly picked
11 2 North Queensland Cowboys to win against Brisbane Broncos while Home 1.84 1.73 Correctly picked
11 3 Wests Tigers to win against Newcastle Knights while Home 1.63 1.35 Correctly picked
11 4 New Zealand Warriors to win against Canberra Raiders while Home 1.82 1.73 Incorreclty picked
11 5 Cronulla Sharks to win against Manly Sea Eagles while Home 1.42 1.32 Correctly picked
11 6 Penrith Panthers to win against Gold Coast Titans while Home 1.65 1.28 Incorreclty picked
11 7 Canterbury Bulldogs to win against Sydney Roosters while Home 1.63 1.55 Correctly picked
11 8 Melbourne Storm to win against Parramatta Eels while Away 1.76 2.00 Correctly picked

Staking results

Initial bank = $2,200

Previous Round Bank = $2,263.03

Current bank = $2,335.00

Total round profit/loss = $71.97

Total profit/loss to date = $135.00

Round Staking results = 4 out of 5 bets correct

Staking results to date = 11 out of 19 bets correct

ROI (Total profit / Initial Bank) = 6.1%

Table of staking results to date
round game_no BET.STATUS BET.DETAILS STAKE RETURN PROFIT BANK
2 6 5 Win Penrith Panthers v Nth Queensland Cowboys / Head To Head / Nth Queensland Cowboys @ 1.67 50 84 34 2234
3 6 5 Win Penrith Panthers v Nth Queensland Cowboys / Head To Head / Nth Queensland Cowboys @ 1.67 60 100 74 2274
4 7 4 Lose Canterbury Bulldogs v New Zealand Warriors / Head To Head / Canterbury Bulldogs @ 1.90 114 0 -40 2160
5 7 7 Win Wests Tigers v Melbourne Storm / Head To Head / Melbourne Storm @ 1.52 107 163 15 2215
6 7 8 Lose Sydney Roosters v Penrith Panthers / Head To Head / Sydney Roosters @ 2.45 110 0 -95 2105
7 8 4 Win Nth Queensland Cowboys v Parramatta Eels / Head To Head / Nth Queensland Cowboys @ 1.38 100 138 -57 2143
8 8 5 Win Cronulla Sharks v Penrith Panthers / Head To Head / Cronulla Sharks @ 1.60 100 160 3 2203
9 8 7 Lose St George Illawarra Dragons v Sydney Roosters / Head To Head / Sydney Roosters @ 1.70 50 0 3 2203
10 8 8 Win Melbourne Storm v New Zealand Warriors / Head To Head / Melbourne Storm @ 1.67 100 167 70 2270
11 8 1,2,3,5,8 Win Brisbane Broncos / Canterbury Bulldogs / Canberra Raiders / Cronulla Sharks / Melbourne Storm @ 5.85 50 293 313 2513
12 9 1 Lose South Sydney Rabbitohs v Wests Tigers / Head To Head / South Sydney Rabbitohs @ 1.45 100 0 213 2413
13 9 2 Lose Parramatta Eels v Canterbury Bulldogs / Head To Head / Canterbury Bulldogs @ 1.90 100 0 113 2313
15 9 6 Lose New Zealand Warriors v St George Illawarra Dragons / Head To Head / St George Illawarra Dragons @ 2.45 100 0 13 2213
16 9 7 Win Gold Coast Titans v Melbourne Storm / Head To Head / Melbourne Storm @ 1.50 100 150 63 2263
17 10 1 Win St George Illawarra Dragons v Canberra Raiders / Head To Head / St George Illawarra Dragons @ 2.07 100 207 170 2370
19 10 4 Lose Melbourne Storm v Nth Queensland Cowboys / Head To Head / Nth Queensland Cowboys @ 1.42 100 0 70 2270
20 10 5 Win Manly Sea Eagles v Brisbane Broncos / Head To Head / Brisbane Broncos @ 1.19 100 119 89 2289
21 10 6 Win Newcastle Knights v Cronulla Sharks / Head To Head / Cronulla Sharks @ 1.18 100 118 107 2307
22 10 7 Win Wests Tigers v Canterbury Bulldogs / Head To Head / Canterbury Bulldogs @ 1.28 100 128 135 2335

For those who have contributed to the initial bank, the break down of your contribution and what you are currently entitled to is below. It’s pretty self explanatory with the main column being ‘entitlement’. This is how much you are entitled given your initial contribution. The gain (in dollars) is the amount of profit/loss you have currently made on your investment

Contributors investment entitlements

ID initial_bank current_bank cont_amount entitlement gain
1 2200 2335.03 1000 1061.377 61.377
2 2200 2335.03 500 530.689 30.689
3 2200 2335.03 200 212.275 12.275
4 2200 2335.03 100 106.138 6.138
5 2200 2335.03 100 106.138 6.138
6 2200 2335.03 200 212.275 12.275
7 2200 2335.03 100 106.138 6.138

Results to date

Predictive model vs bookmaker precision by round
round_no season mTP mFP bTP bFP mPrec bPrec
1 2016 5 3 5 3 0.625 0.625
2 2016 7 1 6 2 0.875 0.750
3 2016 4 3 2 5 0.571 0.286
4 2016 3 5 7 1 0.375 0.875
5 2016 3 5 6 2 0.375 0.750
6 2016 7 1 4 4 0.875 0.500
7 2016 5 3 5 2 0.625 0.714
8 2016 7 1 7 1 0.875 0.875
9 2016 3 5 4 4 0.375 0.500
10 2016 5 3 4 4 0.625 0.500
11 2016 6 2 5 3 0.750 0.625

NB these are results as posted - remodelling of round 4 and 5 considerably improved these results as explained in Results to date

Conclude

OK, lets hope for a good round 12!

Introduction to Hedging and Arbitrage

Introduction to Hedging and Arbitrage

Introduction

There are already some really great articles ([1], [2], [3]) which explain (sports bet) hedging and arbitrage in detail, and the point of this post is not to re-write these articles, but rather to:

  • briefly introduce the concept/s and provide example/s of opportunities I have had for hedging in my own bet placement this year

  • demonstrate what opportunities have existed (for hedging) in the 2016 NRL season to date and how to identify them

  • calculate (maximum) theoretical profit which could have been made by taking advantage of hedging

This post will focus more so on hedging over arbitrage, however the calculations/concepts are very similar.

Sports bet Hedging and Arbitrage

Hedging

Definition

Sports bet hedging is the process of placing multiple non-similtanuoes bets in the opposite direction on dependent events to guarantee profits (or mitigate loss) [4]. Opportunity for hedging usually arises in the event of odds shifting over time. An example is initially placing a bet on a team to win an NRL match at long odds, and after an odds shift, subsequently placing a bet on the opposing team to also win. Dependent on the size of the odds shift hedging can guarantee a profit no matter the outcome because at least one of the teams must win.

The main point of difference to arbitrage is that odds shifts are assumed or unknown and an initial stake may already be placed on one outcome. In arbitrage similtaneous or near similtaneous stakes are placed to guarantee profits.

Real world example

The most basic (and real) example follows:

In round 9 of the 2016 NRL season, I put a $100 stake on St George (at 2.45 odds) to defeat the Warriors (who were $1.65 favorites). At the time I placed the bet it was about four days before the actual match was to take place. Two days before the match took place, the Warriors coach announced that he was dropping six players from the squad and replacements would only be announced immediately before the match. This caused the odds for Warriors to shift dramatically and the odds (just before the game commenced) were 1.65 for St George and 2.39 for the Warriors. So in this case the odds almost completely flipped and St George became favorites.

This presented me with a hedging opportunity. This is because if I now placed a specified stake on the Warriors to win I would be gaurenteed profit no matter who actually won.

Lets just do the quick calculation. First I staked $100 on St George to win at 2.45 odds. Now I see that just before the match, the Warriors are paying $2.39. I know this is a hedging opportunity and so lets just say I also stake $100 on Warriors to win. This means we have staked $200 in total.

The return I will get if St George win = odds x initial stake - total stake

Which is: 2.45 x $100 - $200 = $45

The return I will get if Warriors win is = 2.39 x $100 - $200 = $39

So you can see if I did this I would have been guaranteed to either get a $45 profit if St George won, or a $39 profit if Warriors won!!

Of course the actual stake I put on the Warriors does matter which is why I said we need to put a specified stake on the Warriors. If you want to guarantee you get the exact same profit no matter who wins, the calculation to determine how much I should stake (called an unbiased stake) on Warriors is:

Stake on St George x (odds for St George/odds for Warriors )

100 x (2.45/2.39) = $102.51

If we just re-do the return calculation/s above using a stake of $102.51 for the Warriors and $202.51 as the total stake you will notice that the result is $42.49 for each. So now I have a gaurenteed profit of $42.49 no matter who wins!!

You might think this is pretty incredible and a no brainier to take the guaranteed profit, however in this case I did not!. Again you need to way up the risk vs reward. In this example my predictive model indicated St George had a 73% chance of winning, Warriors were down 6 players and I stood to profit $145 as opposed to the gaurenteed profit of $42.49. What would have you done???

Determining hedging oppertunities and formulas

I thought I would start with a real world example before I jumped into the formulas, but if you want to determine if an opportunity for hedging exists, we need to determine the margin and/or profit margin of the outcome/s. Intuitively if the profit margin is positive then a hedging opportunity exists and additionally indicates how much guaranteed profit you will make.

Given:

o1 = Decimal odds of initial stake

o2 = Decimal odds of the dependent outcome to compare

The margin (m) = 1/o1 + 1/o2

The profit margin (p) = 1/m - 1

If the margin is less than 1 or (more intuitively), if the profit margin is greater than zero, then a hedging opportunity exists. The profit margin is the amount of profit you will receive if you place an unbiased stake on the dependent outcome. We can check this by again using our real world example.

o1 = 2.45 (odds of initial stake on St George)

o2 = 2.39 (odds of Warriors at odds close (IE just before the game))

m = 1/2.45 + 1/2.39 = 0.83

p = 1/0.83 - 1 = 0.21

We observe that the margin is less than 1 and the profit margin is positive. We observe that a hedging opportunity exists and we expect a 21% profit on our total stake if we choose to take the hedging opportunity. Lets confirm with our real example:

Recall if I stake $100 on St George at 2.45 and 102.51 on Warriors at 2.39 I stand to profit $42.49 no matter the outcome. $42.49 as a percentage of the total stake (t) ($202.51) = 0.21 which is the same as our calculated profit margin!

For completeness the formula for determining the amount to stake on the dependent outcome is:

Given

s1 = initial stake

s2 = amount to stake on the dependent outcome

o1 = Decimal odds of initial stake

o2 = Decimal odds of the dependent outcome to compare

s2 = s1 x (o1/o2)

In our real world example:

s1 = initial stake = $100

s2 = amount to stake on the Warriors

o1 = 2.45 (odds of initial stake on St George)

o2 = 2.39 (odds of Warriors at odds close (IE just before the game))

s2 = 100*(2.45/2.39) = 102.51

Hedging oppertunities in the 2016 NRL season to date

Before I go on I must stress that hedging opportunities are not known (although might be predicted) at the time of initial stake. This is the point of difference to arbitrage. If an odds difference exists in which you can simultaneously place bets (say at different bookmakers) to guarantee profit this is arbitrage bet placement. If the opportunity to guarantee profit arises due to odds shift over time by placing opposing bets (for example placing a bet that both team/s will win) on dependent events, then this is hedging. Therefore when I determine the hedging opportunities which have existed in the NRL this year, it doesn’t mean that we were aware of these opportunities, it just highlights how many have existed and how large the opportunities were.

If you are placing a bet on a match in the hope that you will get a hedging opportunity then you still have to have some way of forecasting (predicting) the probability that this will happen!!

OK, so lets take a look at the hedging opportunities (and their profit margin size) which have existed this year. To do this we need to have a data set which contains odds shift details (such as min max, open close odds) of each match.

You can compile this yourself (from historic odds websites) or refer to some pre-processed generally available data sets. I am going to utilize a pretty decent (and generally maintained) data set which is posted on Aussportsbetting.com. In accordance to the terms of use of this data-set I can only provide a link to the website and cannot provide or supply this data-set directly.

The data-set contains basic match details such as the home/away team, the scores, and importantly (averaged) opening and closing odds, and min/max odds. The odds details are mainly compiled from the OddsPortal.

We are reviewing matches up to round 9 which represents 72 matches.

To use this data set what I am going to do is assume a couple of scenarios:

The first scenario assumes that we have staked on a team as soon as odds have opened up and see how often a hedging opportunity has come up at odds close (just before match start). This represents my real world example.

The second scenario takes the best (maximum) odds for a team and compares the opposing teams odds at close. This represents a scenario when you have been ‘lucky’ enough to grab the odds for a team when they have been highest and should represent the theoretical maximum hedging profit margin.

To analyse these scenarios we need to:

  • Determine the margin and profit margin of the opening odds of home teams and the closing odds of away teams

  • Determine the margin and profit margin of the opening odds of away teams and the closing odds of home teams

  • Subset the data on any matches where the profit margin was >0

  • Identify the best historic hedging opportunities and determine the total potential profit

  • Complete the same exercise using maximum odds

There is one final scenario which would potentially present more hedging opportunities - that is odds movement during live matches. Since I don’t have the details of in-game odds movement for all matches I could not present these results but suspect that there may be more (and higher profit margin) opportunities.

OK, lets take a look at all matches where the profit margin was positive when comparing home team opening odds against away team closing odds (ordered by highest to lowest profit margin):

Date Home.Team Away.Team Home.Score Away.Score Home.Odds.Open Away.Odds.Close Profit.Margin
2016-03-12 Canberra Raiders Sydney Roosters 21 20 2.03 2.15 0.044
2016-03-19 Gold Coast Titans Wests Tigers 30 18 2.16 2.02 0.044
2016-03-06 Sydney Roosters South Sydney Rabbitohs 10 42 2.16 1.95 0.025
2016-03-12 Parramatta Eels North QLD Cowboys 20 16 2.47 1.74 0.021
2016-05-01 Gold Coast Titans Melbourne Storm 0 38 2.31 1.81 0.015
2016-04-02 Wests Tigers Cronulla Sharks 26 34 2.30 1.81 0.013
2016-03-26 Sydney Roosters Manly Sea Eagles 20 22 2.40 1.75 0.012
2016-03-06 Gold Coast Titans Newcastle Knights 30 12 2.10 1.95 0.011
2016-03-14 Wests Tigers Manly Sea Eagles 36 22 2.58 1.66 0.010
2016-04-28 South Sydney Rabbitohs Wests Tigers 22 30 1.40 3.52 0.002

We observe that there are 10 instances where if we placed a stake on the home team when odds first opened we would have been presented with a hedging opportunity. We notice though that aside from the top two hedging opportunists (4.4%), the majority of present a potential profit margin of less than 2% or close to break even.

Using the top match (Canberra v Roosters) as an example, the way to read this result is; If I placed a stake on Canberra (home) to win when the odds first opened at 2.03, and then placed a subsequent specified stake on the Roosters at odds close (2.15), I could guarantee myself a profit of 4.4%.

Lets quickly check the math. I know the profit margin is 4.4% and so this is the amount I expect on top of my total stake (t):

The profit margin (p) = 1/m - 1

= 1/(1/2.03+ 1/2.15) - 1

=0.044

To guarantee the 4.4% profit I need to determine the amount to stake on Roosters. Lets assume I have already staked $100 on Canberra, the amount I will need to stake on Roosters to get the 4.4% profit margin is $94.42:

s2 = s1 x (o1/o2)

= 100 * (2.03/2.15)

= $94.42

Now now matter if Canberra or Roosters win I get a return of $8.58:

If Canberra win: 2.03*100 - 194.42= 8.58

If Roosters win: 2.15*94.42 - 194.42 = 8.58

8.58 as a percentage of 194.42 (8.58/194.42) equals 4.4%

Now lets take a look at all matches where the profit margin was positive comparing away team opening odds and home team closing odds.

Date Home.Team Away.Team Home.Score Away.Score Away.Odds.Open Home.Odds.Close Profit.Margin
2016-05-01 New Zealand Warriors St George Dragons 26 10 2.31 2.39 0.175
2016-04-29 Parramatta Eels Canterbury Bulldogs 20 12 1.98 2.36 0.077
2016-04-17 Wests Tigers Melbourne Storm 18 19 1.77 2.74 0.075
2016-03-20 New Zealand Warriors Melbourne Storm 14 21 2.05 2.11 0.040
2016-04-04 Canterbury Bulldogs Canberra Raiders 8 22 3.03 1.56 0.030
2016-03-13 Melbourne Storm Gold Coast Titans 34 16 5.33 1.26 0.019
2016-04-17 Canberra Raiders Cronulla Sharks 16 40 2.09 1.97 0.014
2016-03-13 Cronulla Sharks St George Dragons 30 2 2.63 1.65 0.014
2016-04-30 Penrith Panthers Canberra Raiders 19 18 2.58 1.67 0.014
2016-04-09 New Zealand Warriors Manly Sea Eagles 18 34 3.02 1.52 0.011
2016-03-26 Canberra Raiders Gold Coast Titans 20 24 2.97 1.53 0.010
2016-03-27 St George Dragons Penrith Panthers 14 12 2.07 1.97 0.009
2016-04-03 Parramatta Eels Penrith Panthers 18 20 2.79 1.58 0.009
2016-04-25 Newcastle Knights Manly Sea Eagles 10 26 1.50 3.08 0.009
2016-04-02 Melbourne Storm Newcastle Knights 18 14 6.31 1.20 0.008
2016-04-09 Penrith Panthers North QLD Cowboys 18 23 1.68 2.52 0.008
2016-04-30 Manly Sea Eagles North QLD Cowboys 18 34 1.34 4.05 0.007
2016-04-10 Newcastle Knights Wests Tigers 18 16 1.81 2.25 0.003
2016-04-02 North QLD Cowboys St George Dragons 36 0 4.59 1.28 0.001

This list of opportunities is a bit longer (19) purely because away teams tend to start a longer odds. You can see that The St George v Warriors game is by far and away the largest hedging opportunity and has been for the entire season. The profit margin (17.5%) is slightly lower than in my real world example simply because I had higher odds at time of stake, where-as the odds in the table represent the average across bookmakers. We can also see a couple of matches in would have returned 7.7% and 7.5% respective while the remainder would have returned < 4%.

Finally lets just have a quick look at the maximum theoretical hedging opportunity/s. To do this we are just running the same exercise as above but we are looking at the maximum odds of a home/away team as compared to the closing closing odds of the home/away team. This represents our maximum hedging opportunity assuming we are going to hedge on a game just before it starts:

First the maximum odds of a home team vs the close odds of an away team:

Date Home.Team Away.Team Home.Score Away.Score Home.Odds.Max Away.Odds.Close Profit.Margin
2016-04-29 Parramatta Eels Canterbury Bulldogs 20 12 2.79 1.67 0.045
2016-03-12 Canberra Raiders Sydney Roosters 21 20 2.03 2.15 0.044
2016-03-19 Gold Coast Titans Wests Tigers 30 18 2.16 2.02 0.044
2016-03-31 Manly Sea Eagles South Sydney Rabbitohs 12 16 2.98 1.59 0.037
2016-04-17 Canberra Raiders Cronulla Sharks 16 40 2.24 1.93 0.037
2016-05-01 Gold Coast Titans Melbourne Storm 0 38 2.42 1.81 0.036
2016-03-19 Newcastle Knights Canberra Raiders 24 24 2.67 1.69 0.035
2016-03-20 St George Dragons South Sydney Rabbitohs 8 6 3.45 1.47 0.031
2016-03-12 Parramatta Eels North QLD Cowboys 20 16 2.50 1.74 0.026
2016-03-06 Sydney Roosters South Sydney Rabbitohs 10 42 2.16 1.95 0.025
2016-03-26 Sydney Roosters Manly Sea Eagles 20 22 2.45 1.75 0.021
2016-03-05 North QLD Cowboys Cronulla Sharks 20 14 1.47 3.31 0.018
2016-03-21 Manly Sea Eagles Cronulla Sharks 22 12 2.11 1.96 0.016
2016-04-07 Brisbane Broncos St George Dragons 26 0 1.20 6.52 0.013
2016-03-10 Penrith Panthers Canterbury Bulldogs 16 18 2.53 1.69 0.013
2016-04-02 Wests Tigers Cronulla Sharks 26 34 2.30 1.81 0.013
2016-03-04 Manly Sea Eagles Canterbury Bulldogs 6 28 1.67 2.57 0.012
2016-04-28 South Sydney Rabbitohs Wests Tigers 22 30 1.42 3.52 0.012
2016-03-06 Gold Coast Titans Newcastle Knights 30 12 2.10 1.95 0.011
2016-03-14 Wests Tigers Manly Sea Eagles 36 22 2.58 1.66 0.010
2016-04-08 South Sydney Rabbitohs Sydney Roosters 10 17 1.54 2.93 0.009
2016-04-17 Wests Tigers Melbourne Storm 18 19 2.97 1.52 0.005

And finally the maximum odds of an away team vs the closing odds of a home team:

Date Home.Team Away.Team Home.Score Away.Score Away.Odds.Max Home.Odds.Close Profit.Margin
2016-05-01 New Zealand Warriors St George Dragons 26 10 2.33 2.39 0.180
2016-04-29 Parramatta Eels Canterbury Bulldogs 20 12 2.05 2.36 0.097
2016-04-17 Wests Tigers Melbourne Storm 18 19 1.77 2.74 0.075
2016-03-25 South Sydney Rabbitohs Canterbury Bulldogs 12 42 1.75 2.78 0.074
2016-03-27 St George Dragons Penrith Panthers 14 12 2.32 1.97 0.065
2016-04-10 Newcastle Knights Wests Tigers 18 16 2.01 2.25 0.062
2016-03-20 New Zealand Warriors Melbourne Storm 14 21 2.11 2.11 0.055
2016-04-25 Newcastle Knights Manly Sea Eagles 10 26 1.58 3.08 0.044
2016-04-09 Penrith Panthers North QLD Cowboys 18 23 1.77 2.52 0.040
2016-03-20 St George Dragons South Sydney Rabbitohs 8 6 1.61 2.91 0.037
2016-04-25 Melbourne Storm New Zealand Warriors 42 0 2.63 1.70 0.033
2016-04-04 Canterbury Bulldogs Canberra Raiders 8 22 3.03 1.56 0.030
2016-04-30 Manly Sea Eagles North QLD Cowboys 18 34 1.38 4.05 0.029
2016-04-23 Canberra Raiders Wests Tigers 60 6 3.35 1.48 0.027
2016-04-30 Penrith Panthers Canberra Raiders 19 18 2.66 1.67 0.026
2016-03-17 North QLD Cowboys Sydney Roosters 40 0 5.02 1.28 0.020
2016-03-13 Cronulla Sharks St George Dragons 30 2 2.67 1.65 0.020
2016-03-13 Melbourne Storm Gold Coast Titans 34 16 5.33 1.26 0.019
2016-04-17 Canberra Raiders Cronulla Sharks 16 40 2.11 1.97 0.019
2016-03-28 Wests Tigers Parramatta Eels 0 8 1.70 2.54 0.018
2016-03-18 Canterbury Bulldogs Parramatta Eels 6 20 2.66 1.65 0.018
2016-04-09 New Zealand Warriors Manly Sea Eagles 18 34 3.04 1.52 0.013
2016-04-01 Gold Coast Titans Brisbane Broncos 16 24 1.26 5.16 0.013
2016-03-26 Canberra Raiders Gold Coast Titans 20 24 2.97 1.53 0.010
2016-03-06 Gold Coast Titans Newcastle Knights 30 12 2.09 1.95 0.009
2016-04-03 Parramatta Eels Penrith Panthers 18 20 2.79 1.58 0.009
2016-04-02 Melbourne Storm Newcastle Knights 18 14 6.31 1.20 0.008
2016-04-24 Cronulla Sharks Penrith Panthers 20 18 3.05 1.50 0.005
2016-04-02 North QLD Cowboys St George Dragons 36 0 4.65 1.28 0.004
2016-03-28 Cronulla Sharks Melbourne Storm 14 6 2.27 1.79 0.001

As expected the hedging opportunities are a little more prevalent when we compare maximum odds against closing odds, and observe that maximum away team odds vs closing home team odds present the most opportunities (30).

Conclusion

Now that we have looked at the different scenarios we can conclude that:

  • Of 72 matches to date, the maximum theoretical number of (positive profit margin) hedging opportunities which were available was 30 (41% of matches).

  • The number of hedging opportunities which have arisen from comparing opening odds of away teams against closing odds of home teams is 19 (26% of matches).

  • Hedging opportunists rarely return more than 4% profit

  • St George vs Warriors has been the best hedging opportunity of the season at 18% profit margin (using bookmakers averages)

  • Hedging is opportunistic and while the opportunities do arise, they may still be unpredictable (but you can keep an eye out for them!)

Tables and graphs to assist in intepreting hedging oppertuities

OK, so now we have identified the opportunities which have existed and we understand how to calculate the potential profit margins; how do you easily keep an eye on any hedging opportunities after you have put down a stake?

Probably the easiest way to do this is to visualize in a graph and/or refer to a table rather than scribbling down calculations all the time. If you are code eccentric, I’ll show you how to quickly whip these visualizations up in R programming language (otherwise just keep my table/graph handy).

The first table/graph we will look at is a break even hedging opportunity. This is our baseline. A break even hedging opportunity is one where; if you stake a specified amount on the opposing team you are gaurenteed to break even. You might want to do this if you fear that the team you placed (maybe a large) bet on really doesn’t stand a chance to win and so you are looking to ‘opt out’ without loosing money (if given the opportunity)

Lets quickly review a few formulas so we know how to calculate this. What we want to calculate is the o2 under a break even scenario (margin = 1, profit margin = 0)

We know that given:

o1 = Decimal odds of initial stake

o2 = Decimal odds of the dependent outcome to compare

The margin (m) = 1/o1 + 1/o2 and the profit margin (pm) = 1/m - 1

Therefore to calculate o2 for m=1 we re-arrange the formula/s so that:

o2 = o1/(o1*m-1)

Or if we want to know o2 given a desired profit margin:

o2 = o1/((1/pm+1)-1)

So for example if we have put down a stake at odds of 1.90 we would need to wait until the opposing teams odds are at least 2.11 to be able to hedge to break even

o2 = 1.90/(1.90*1-1) = 2.11

We can quickly and easily generate a reference table using this knowledge. All we will do is generate a table showing the odds ‘o1’ of the team we may have bet on and the corresponding value of the the opposing odds ‘o2’. The value of ‘o2’ is what the odds must be on the opposing team in order to break even when hedging:

o1 o2 m pm
1.3 4.33 1 0
1.4 3.50 1 0
1.5 3.00 1 0
1.6 2.67 1 0
1.7 2.43 1 0
1.8 2.25 1 0
1.9 2.11 1 0
2.0 2.00 1 0
2.1 1.91 1 0
2.2 1.83 1 0
2.3 1.77 1 0
2.4 1.71 1 0
2.5 1.67 1 0
2.6 1.62 1 0
2.7 1.59 1 0
2.8 1.56 1 0
2.9 1.53 1 0
3.0 1.50 1 0
3.1 1.48 1 0
3.2 1.45 1 0
3.3 1.43 1 0
3.4 1.42 1 0
3.5 1.40 1 0
3.6 1.38 1 0
3.7 1.37 1 0
3.8 1.36 1 0
3.9 1.34 1 0
4.0 1.33 1 0
4.1 1.32 1 0
4.2 1.31 1 0
4.3 1.30 1 0
4.4 1.29 1 0
4.5 1.29 1 0
4.6 1.28 1 0
4.7 1.27 1 0
4.8 1.26 1 0
4.9 1.26 1 0
5.0 1.25 1 0

The way to read the table is pretty simple. o1 represents the odds of the initial stake and o2 is the odds that the opposing team must reach in order to break even in hedging. So you can see that when o1 is 1.3 the opposing team odds must reach 4.33 before you have a hedging opportunity and so on. We also include ‘m’ which is the margin, and ‘p’ which is the profit margin. Since this is the break even odds, ’p is obviously 0.

An alternative way to visualize this is in a graph. You could plot o2 against o1 and read off the o2 value required directly from the graph:

As an example you can read from the graph that when ‘o1’ is 1.5, ‘o2’ must be 3.00:

Since we might want to do better than just break even, we can expand on the above and generate a table and graph with multiple options. Lets create a table showing the odds that o2 have to be in order to generate profit margins from 0-30%

Hedging opportunity table
o1 o2pm00 o2pm05 o2pm10 o2pm15 o2pm20 o2pm25 o2pm30
1.3 4.33 5.46 7.15 9.97 15.60 32.50 Inf
1.4 3.50 4.20 5.13 6.44 8.40 11.67 18.20
1.5 3.00 3.50 4.13 4.93 6.00 7.50 9.75
1.6 2.67 3.05 3.52 4.09 4.80 5.71 6.93
1.7 2.43 2.75 3.12 3.55 4.08 4.72 5.53
1.8 2.25 2.52 2.83 3.18 3.60 4.09 4.68
1.9 2.11 2.35 2.61 2.91 3.26 3.65 4.12
2.0 2.00 2.21 2.44 2.71 3.00 3.33 3.71
2.1 1.91 2.10 2.31 2.54 2.80 3.09 3.41
2.2 1.83 2.01 2.20 2.41 2.64 2.89 3.18
2.3 1.77 1.93 2.11 2.30 2.51 2.74 2.99
2.4 1.71 1.87 2.03 2.21 2.40 2.61 2.84
2.5 1.67 1.81 1.96 2.13 2.31 2.50 2.71
2.6 1.62 1.76 1.91 2.06 2.23 2.41 2.60
2.7 1.59 1.72 1.86 2.00 2.16 2.33 2.51
2.8 1.56 1.68 1.81 1.95 2.10 2.26 2.43
2.9 1.53 1.65 1.77 1.91 2.05 2.20 2.36
3.0 1.50 1.62 1.74 1.86 2.00 2.14 2.29
3.1 1.48 1.59 1.70 1.83 1.96 2.09 2.24
3.2 1.45 1.56 1.68 1.80 1.92 2.05 2.19
3.3 1.43 1.54 1.65 1.77 1.89 2.01 2.15
3.4 1.42 1.52 1.63 1.74 1.85 1.98 2.10
3.5 1.40 1.50 1.60 1.71 1.83 1.94 2.07
3.6 1.38 1.48 1.58 1.69 1.80 1.91 2.03
3.7 1.37 1.47 1.57 1.67 1.78 1.89 2.00
3.8 1.36 1.45 1.55 1.65 1.75 1.86 1.98
3.9 1.34 1.44 1.53 1.63 1.73 1.84 1.95
4.0 1.33 1.42 1.52 1.61 1.71 1.82 1.93

We observe that when our staking odds are 1.3 that to break even the odds of o2 have to be 4.33 to break even. To generate a profit margin of 30% the odds of o2 have to be impossibly high (infinite). For a more reasonable comparison, using starting odds (o1) of 2.0, we see that the odds range for a profit margin of 0-30 are 2.00-3.71.

Finally we can plot this table data if we want a visual graph to pick values from:

Again using o1 of 2.00, we can read across the y-axis and see that to break even we need an o2 of 2.00, to generate a profit of 20% we need an o2 of 3.00 etc.

Arbitrage

As I indicated in the introduction, this article focus’ more on Hedging, and if you want more detail on arbitrage I encourage you to read any of the articles I reference in the introduction. So briefly:

Arbitrage is very similar in concept to Hedging (and in fact you can determine the margin and profit margin of an arbitrage opportunity in the exact same way), however the difference is that arbitrage opportunities occur similtaniuosly or in very close space of time. As an example:

Lets just say that you observe that a bookmaker ‘A’ has the following (even) odds for two teams:

o1: 1.9

o2: 1.9

You also see that at the same time bookmaker ‘B’ has different odds for the same team/s:

o1: 1.6

o2: 2.35

Using the Hedging opportunity table, you see that when o1 is 1.9, then you can generate a profit margin of 5% when o2 = 2.35.

Knowing this, you will observe that if I placed a stake on ‘o1’ with bookmaker ‘A’ (at 1.9 odds), and immidiatly after/ similtaneuosly also stake on ‘o2’ at Bookmaker ‘B’ then I will guarantee myself a 5% profit. I have exploited the differing odds that bookmakers have offered and guaranteed myself a profit no matter the outcome of the match!

You can double check the math:

Assume a $100 stake on o1 at Bookmaker A.

Now calculate the stake I need to place on o2 at bookmaker ‘B’ to guarantee my 5% profit

Stake 2 = $100*(1.9/2.35) = $80.85

Now determine the guaranteed profit amount:

If o1 win: 1.9*100 - 180.85 = $9.15

If o2 win: 2.35*80.85 - 180.85 = $9.15

9.15 as a percentage of 180.85 (9.15/180.85) equals 5%

So we can see that the calculations are the same as for Hedging, and you can use the tables/graphs to also identify potential arbitrage opportunities. Fair warning however, Arbitrage opportunities are even less frequent then hedging opportunities and last for a very brief period of time. In order to take advantage of Arbitrage opportunities you need accounts with very many bookmakers, be able to place bets very quickly and additionally would need some sort of ‘automated’ notification system to alert you of any opportunity which arose.

Final words

This is by no means a comprehensive article on hedging/arbitrage, and as I alluded to in the introduction presents the most basic example of hedging/arbitrage. Specifically I have not explored hedging/arbitrage on events with multiple potential outcomes (such as horse racing where any one of 10+ horses can win) and have only given simplistic examples of head to head betting where two outcomes are assumed. Also for the purposes of simplicity I have ignored (assumed it is negligible) the potential for draws in NRL matches - and one reason is that draw odds are rarely offered for head to head NRL matches. So in reality hedging on NRL games is not absolute guaranteed profit because in the event of a draw you (at best) may get your money back (or at worst lose both bets). So make sure you check the terms of your bookmaker!! Generally if a draw event is not offered for a match, then you will get your money back in the event of a draw (dead heat). So be careful if your bookmaker actually offers odds for a draw occurring.

NRL S2016 R11 Predictions and Staking guide

NRL S2016 R11 predictions and staking guide

Summary

This round, (at current odds) no matches have been identified as good value bets! This is the first time across all rounds this has occurred owing to the models perceived closeness of match outcomes. All matches either have negative expected return or the perceived probability of a team winning is <66%. The model agrees with the bookmaker on all games except Storm vs Eels (the model predicts Storm to win). This match also represents the best ‘value’ (and is in fact the only match with indicated positive expected return), however does not pass our current probability cut off limit for staking.

Keep an eye on the odds for Cronalla Sharks, if this team gets to >1.42 odds then it will become a favorable bet. However I see this as unlikely (in fact the odds are probably more likely to shorten).

Since all other perceived probabilities are <66%, even with odds shift the only game the model would recommend a bet on is the Sharks (assuming they move to >1.42 odds)

Predictions

game_no tip_text perceived_prob bookie_prob bookie_odds agree_with_bookie
1 South Sydney Rabbitohs to win against St George Illawarra Dragons while Home 0.511 0.690 1.45 Y
2 North Queensland Cowboys to win against Brisbane Broncos while Home 0.545 0.578 1.73 Y
3 Wests Tigers to win against Newcastle Knights while Home 0.613 0.741 1.35 Y
4 New Zealand Warriors to win against Canberra Raiders while Home 0.549 0.578 1.73 Y
5 Cronulla Sharks to win against Manly Sea Eagles while Home 0.705 0.758 1.32 Y
6 Penrith Panthers to win against Gold Coast Titans while Home 0.605 0.781 1.28 Y
7 Canterbury Bulldogs to win against Sydney Roosters while Home 0.614 0.645 1.55 Y
8 Melbourne Storm to win against Parramatta Eels while Away 0.569 0.500 2.00 N

NB Bookmaker odds (taken from www.Sportsbet.com.au) as at 19-May-2016

Stake recommendation/s

Recommended bets are those with a perceived probability of > ~0.66 and a positive expected return.

game_no tip_text perceived_prob bookie_odds expected_return recommend_stake
1 South Sydney Rabbitohs to win against St George Illawarra Dragons while Home 0.511 1.45 -0.259 N
2 North Queensland Cowboys to win against Brisbane Broncos while Home 0.545 1.73 -0.058 N
3 Wests Tigers to win against Newcastle Knights while Home 0.613 1.35 -0.172 N
4 New Zealand Warriors to win against Canberra Raiders while Home 0.549 1.73 -0.051 N
5 Cronulla Sharks to win against Manly Sea Eagles while Home 0.705 1.32 -0.069 N
6 Penrith Panthers to win against Gold Coast Titans while Home 0.605 1.28 -0.226 N
7 Canterbury Bulldogs to win against Sydney Roosters while Home 0.614 1.55 -0.049 N
8 Melbourne Storm to win against Parramatta Eels while Away 0.569 2.00 0.137 N

Conclude

Lets hope we have a good round. Good luck contributors!

NRL S2016 R10 Results

NRL S2016 R10 Results

Summary

This round was a better staking round with 4 of 5 bets paying off. The at risk amount for the round (amount of money staked) was $500, however due to the relatively short odds on the majority of games, the profit for the round was a modest $72. The model predicted 5 of 8 games (62.5%) doing better than the bookmaker/market who predicted on 4 of 8 games (50%).

Total profit to date rose to $135.00 which currently represents a 6% return on our initial bank

Predictive Results

Given:

mTP = Models true positives

mFP = Models False positives

mPrec = Models precision (equivalent to accuracy in this case)

bTP = Bookmakers true positives

bFP = Bookmakers False positives

bPrec = Bookmakers precision (equivalent to accuracy in this case)

Table of results

Predictive model vs bookmaker precision by round
round_no season mTP mFP bTP bFP mPrec bPrec
10 2016 5 3 4 4 0.625 0.5
round_no game_no tip_text perceived_odds implied_odds result
10 1 St George Illawarra Dragons to win against Canberra Raiders while Home 1.48 2.07 Correctly picked
10 2 South Sydney Rabbitohs to win against Parramatta Eels while Away 1.76 2.65 Correctly picked
10 3 New Zealand Warriors to win against Penrith Panthers while Away 1.53 2.45 Incorreclty picked
10 4 North Queensland Cowboys to win against Melbourne Storm while Away 1.38 1.42 Incorreclty picked
10 5 Brisbane Broncos to win against Manly Sea Eagles while Away 1.21 1.19 Correctly picked
10 6 Cronulla Sharks to win against Newcastle Knights while Away 1.07 1.18 Correctly picked
10 7 Canterbury Bulldogs to win against Wests Tigers while Away 1.25 1.28 Correctly picked
10 8 Sydney Roosters to win against Gold Coast Titans while Away 1.73 1.55 Incorreclty picked

Staking results

Initial bank = $2,200

Previous Round Bank = $2,263.03

Current bank = $2,335.00

Total round profit/loss = $71.97

Total profit/loss to date = $135.00

Round Staking results = 4 out of 5 bets correct

Staking results to date = 11 out of 19 bets correct

ROI (Total profit / Initial Bank) = 6.1%

Table of staking results to date
round game_no BET.STATUS BET.DETAILS STAKE RETURN PROFIT BANK
2 6 5 Win Penrith Panthers v Nth Queensland Cowboys / Head To Head / Nth Queensland Cowboys @ 1.67 50 84 34 2234
3 6 5 Win Penrith Panthers v Nth Queensland Cowboys / Head To Head / Nth Queensland Cowboys @ 1.67 60 100 74 2274
4 7 4 Lose Canterbury Bulldogs v New Zealand Warriors / Head To Head / Canterbury Bulldogs @ 1.90 114 0 -40 2160
5 7 7 Win Wests Tigers v Melbourne Storm / Head To Head / Melbourne Storm @ 1.52 107 163 15 2215
6 7 8 Lose Sydney Roosters v Penrith Panthers / Head To Head / Sydney Roosters @ 2.45 110 0 -95 2105
7 8 4 Win Nth Queensland Cowboys v Parramatta Eels / Head To Head / Nth Queensland Cowboys @ 1.38 100 138 -57 2143
8 8 5 Win Cronulla Sharks v Penrith Panthers / Head To Head / Cronulla Sharks @ 1.60 100 160 3 2203
9 8 7 Lose St George Illawarra Dragons v Sydney Roosters / Head To Head / Sydney Roosters @ 1.70 50 0 3 2203
10 8 8 Win Melbourne Storm v New Zealand Warriors / Head To Head / Melbourne Storm @ 1.67 100 167 70 2270
11 8 1,2,3,5,8 Win Brisbane Broncos / Canterbury Bulldogs / Canberra Raiders / Cronulla Sharks / Melbourne Storm @ 5.85 50 293 313 2513
12 9 1 Lose South Sydney Rabbitohs v Wests Tigers / Head To Head / South Sydney Rabbitohs @ 1.45 100 0 213 2413
13 9 2 Lose Parramatta Eels v Canterbury Bulldogs / Head To Head / Canterbury Bulldogs @ 1.90 100 0 113 2313
15 9 6 Lose New Zealand Warriors v St George Illawarra Dragons / Head To Head / St George Illawarra Dragons @ 2.45 100 0 13 2213
16 9 7 Win Gold Coast Titans v Melbourne Storm / Head To Head / Melbourne Storm @ 1.50 100 150 63 2263
17 10 1 Win St George Illawarra Dragons v Canberra Raiders / Head To Head / St George Illawarra Dragons @ 2.07 100 207 170 2370
19 10 4 Lose Melbourne Storm v Nth Queensland Cowboys / Head To Head / Nth Queensland Cowboys @ 1.42 100 0 70 2270
20 10 5 Win Manly Sea Eagles v Brisbane Broncos / Head To Head / Brisbane Broncos @ 1.19 100 119 89 2289
21 10 6 Win Newcastle Knights v Cronulla Sharks / Head To Head / Cronulla Sharks @ 1.18 100 118 107 2307
22 10 7 Win Wests Tigers v Canterbury Bulldogs / Head To Head / Canterbury Bulldogs @ 1.28 100 128 135 2335

For those who have contributed to the initial bank, the break down of your contribution and what you are currently entitled to is below. It’s pretty self explanatory with the main column being ‘entitlement’. This is how much you are entitled given your initial contribution. The gain (in dollars) is the amount of profit/loss you have currently made on your investment

Contributors investment entitlements

ID initial_bank current_bank cont_amount entitlement gain
1 2200 2335.03 1000 1061.377 61.377
2 2200 2335.03 500 530.689 30.689
3 2200 2335.03 200 212.275 12.275
4 2200 2335.03 100 106.138 6.138
5 2200 2335.03 100 106.138 6.138
6 2200 2335.03 200 212.275 12.275
7 2200 2335.03 100 106.138 6.138

Results to date

Predictive model vs bookmaker precision by round
round_no season mTP mFP bTP bFP mPrec bPrec
1 2016 5 3 5 3 0.625 0.625
2 2016 7 1 6 2 0.875 0.750
3 2016 4 3 2 5 0.571 0.286
4 2016 3 5 7 1 0.375 0.875
5 2016 3 5 6 2 0.375 0.750
6 2016 7 1 4 4 0.875 0.500
7 2016 5 3 5 2 0.625 0.714
8 2016 7 1 7 1 0.875 0.875
9 2016 3 5 4 4 0.375 0.500
10 2016 5 3 4 4 0.625 0.500

NB these are results as posted - remodelling of round 4 and 5 considerably improved these results as explained in Results to date

Conclude

OK, lets hope for a good round 11!

NRL S2016 R10 Predictions and staking guide

NRL S2016 R10 predictions and staking guide

Summary

We just had a round of representative games this weekend and matches are still 5 days away so these predictions are a bit preliminary, however are based on current knowledge. The odds currently offered are also likely to change because there hasn’t been a lot of bet placement on games for round 10 due to the rep games these weekend. I expect we will start to see a bit of odds movement soon as punters start to look towards this weeks round of games. Also I expect a bit of odds movement on Parramatta. For those unaware Parramatta has been hit with a range of diciplinary actions due to alleged salary cap breaches. This could mean the (forced) removal of some current team players before their match up with the Rabbits next week in addition to the (potential) psychological effects on the players. Interestingly Parramatta are still $1.48 favorites to beat the Rabbits and for my mind currently represents one of the best hedging opportunities for those odds. In fact my model currently indicates Rabbits as having a higher probability of winning than Parramatta putting aside results of disciplinary action.

For round 10 all of the predictions currently agree with the bookmaker with the exception of Parramatta vs Rabbits, which I indicated above. The model indicates 5 matches which represent good value (at current odds). Even given the currently short odds ($1.25) on Broncos and Sharks to win their respective games the model very strongly (>82% probability) suggests these teams will win.

We may have to re-visit the predictions and stake recommendations closer to match dates

Predictions

game_no tip_text perceived_prob bookie_prob bookie_odds agree_with_bookie
1 St George Illawarra Dragons to win against Canberra Raiders while Home 0.674 0.526 1.90 Y
2 South Sydney Rabbitohs to win against Parramatta Eels while Away 0.569 0.377 2.65 N
3 New Zealand Warriors to win against Penrith Panthers while Away 0.653 0.526 1.90 Y
4 North Queensland Cowboys to win against Melbourne Storm while Away 0.722 0.704 1.42 Y
5 Brisbane Broncos to win against Manly Sea Eagles while Away 0.828 0.800 1.25 Y
6 Cronulla Sharks to win against Newcastle Knights while Away 0.932 0.800 1.25 Y
7 Canterbury Bulldogs to win against Wests Tigers while Away 0.799 0.781 1.28 Y
8 Sydney Roosters to win against Gold Coast Titans while Away 0.577 0.645 1.55 Y

NB Bookmaker odds (taken from www.Sportsbet.com.au) as at 3-May-2016

Stake recommendation/s

Recommended bets are those with a perceived probability of > ~0.66 and a positive expected return.

game_no tip_text perceived_prob bookie_odds expected_return recommend_stake
1 St George Illawarra Dragons to win against Canberra Raiders while Home 0.674 1.90 0.280 Y
2 South Sydney Rabbitohs to win against Parramatta Eels while Away 0.569 2.65 0.508 N
3 New Zealand Warriors to win against Penrith Panthers while Away 0.653 1.90 0.242 N
4 North Queensland Cowboys to win against Melbourne Storm while Away 0.722 1.42 0.026 Y
5 Brisbane Broncos to win against Manly Sea Eagles while Away 0.828 1.25 0.034 Y
6 Cronulla Sharks to win against Newcastle Knights while Away 0.932 1.25 0.165 Y
7 Canterbury Bulldogs to win against Wests Tigers while Away 0.799 1.28 0.023 Y
8 Sydney Roosters to win against Gold Coast Titans while Away 0.577 1.55 -0.105 N

Conclude

Lets hope we have a good round. Good luck contributors!

NRL S2016 R09 Results

NRL S2016 R09 Results

Summary

This round was pretty interesting!!. The predictive accuracy was well below average with only 3 of 8 predictions being correct! There were some pretty big odds swings after my initial post (~3 days before start of the round) so I am comparing the closing odds (to demonstrate how poorly the ‘market’/bookmaker did on this round as well). Four strong favorites for the round ended up losing (50% bookmaker accuracy) which included 3 games we staked on. In particular:

  • St George lost to Warriors after becoming strong (1.65) favorites when it was announced Warriors dropped six players from the team. When we staked on this game we locked in odds on St George at 2.45 so it actually became a game which we had a high probability of a decent return, but alas St George couldn’t do it!!
    • As a side note, the opening and closing odds of St George represented one of the best hedging opportunities of the year which I will discuss in an upcoming post on arbitrage/hedging
  • Rabbits (strong 1.35 favorites) lost to West Tigers

  • Bulldogs (reasonably strong 1.65 favorites) lost to Parramatta

  • Brisbane lost to Sharks (28-30) after a strong (but not strong enough) come back in the second half

Aside from this we did have a win on Melbourne at odds of 1.50 ($50 profit).

Needless to say that the three staking losses made a reasonable impact on the overall bank taking a $250 chunk off our $2,513. This took our bank back down to $2,263, however this is still $63 above our initial bank so we are still in the black. Its just unfortunate that we “lost” an opportunity to increase our profit margins to sustain potential future losses.

Predictive Results

Given:

mTP = Models true positives

mFP = Models False positives

mPrec = Models precision (equivalent to accuracy in this case)

bTP = Bookmakers true positives

bFP = Bookmakers False positives

bPrec = Bookmakers precision (equivalent to accuracy in this case)

Table of results

Predictive model vs bookmaker precision by round
round_no season mTP mFP bTP bFP mPrec bPrec
9 2016 3 5 4 4 0.375 0.5
round_no game_no tip_text perceived_odds implied_odds result
9 1 South Sydney Rabbitohs to win against Wests Tigers while Home 1.26 1.35 Incorreclty picked
9 2 Canterbury Bulldogs to win against Parramatta Eels while Away 1.43 1.67 Incorreclty picked
9 3 Canberra Raiders to win against Penrith Panthers while Away 1.57 2.36 Incorreclty picked
9 4 Sydney Roosters to win against Newcastle Knights while Home 1.35 1.14 Correctly picked
9 5 North Queensland Cowboys to win against Manly Sea Eagles while Away 1.39 1.28 Correctly picked
9 6 St George Illawarra Dragons to win against New Zealand Warriors while Away 1.36 1.65 Incorreclty picked
9 7 Melbourne Storm to win against Gold Coast Titans while Away 1.47 1.81 Correctly picked
9 8 Brisbane Broncos to win against Cronulla Sharks while Away 1.60 1.88 Incorreclty picked

Staking results

Initial bank = $2,200

Previous Round Bank = $2,513.03

Current bank = $2,263.03

Total round profit/loss = -$250

Total profit/loss to date = 63.03

Round Staking results = 1 out of 4 bets correct

Staking results to date = 7 out of 14 bets correct

ROI (Total profit / Initial Bank) = 2.8%

Table of staking results to date
round game_no BET.STATUS BET.DETAILS STAKE RETURN PROFIT BANK
2 6 5 Win Penrith Panthers v Nth Queensland Cowboys / Head To Head / Nth Queensland Cowboys @ 1.67 50 84 34 2234
3 6 5 Win Penrith Panthers v Nth Queensland Cowboys / Head To Head / Nth Queensland Cowboys @ 1.67 60 100 74 2274
4 7 4 Lose Canterbury Bulldogs v New Zealand Warriors / Head To Head / Canterbury Bulldogs @ 1.90 114 0 -40 2160
5 7 7 Win Wests Tigers v Melbourne Storm / Head To Head / Melbourne Storm @ 1.52 107 163 15 2215
6 7 8 Lose Sydney Roosters v Penrith Panthers / Head To Head / Sydney Roosters @ 2.45 110 0 -95 2105
7 8 4 Win Nth Queensland Cowboys v Parramatta Eels / Head To Head / Nth Queensland Cowboys @ 1.38 100 138 -57 2143
8 8 5 Win Cronulla Sharks v Penrith Panthers / Head To Head / Cronulla Sharks @ 1.60 100 160 3 2203
9 8 7 Lose St George Illawarra Dragons v Sydney Roosters / Head To Head / Sydney Roosters @ 1.70 50 0 3 2203
10 8 8 Win Melbourne Storm v New Zealand Warriors / Head To Head / Melbourne Storm @ 1.67 100 167 70 2270
11 8 1,2,3,5,8 Win Brisbane Broncos / Canterbury Bulldogs / Canberra Raiders / Cronulla Sharks / Melbourne Storm @ 5.85 50 293 313 2513
12 9 1 Lose South Sydney Rabbitohs v Wests Tigers / Head To Head / South Sydney Rabbitohs @ 1.45 100 0 213 2413
13 9 2 Lose Parramatta Eels v Canterbury Bulldogs / Head To Head / Canterbury Bulldogs @ 1.90 100 0 113 2313
15 9 6 Lose New Zealand Warriors v St George Illawarra Dragons / Head To Head / St George Illawarra Dragons @ 2.45 100 0 13 2213
16 9 7 Win Gold Coast Titans v Melbourne Storm / Head To Head / Melbourne Storm @ 1.50 100 150 63 2263

For those who have contributed to the initial bank, the break down of your contribution and what you are currently entitled to is below. It’s pretty self explanatory with the main column being ‘entitlement’. This is how much you are entitled given your initial contribution. The gain (in dollars) is the amount of profit/loss you have currently made on your investment

Contributors investment entitlements

ID initial_bank current_bank cont_amount entitlement gain
1 2200 2263.03 1000 1028.650 28.650
2 2200 2263.03 500 514.325 14.325
3 2200 2263.03 200 205.730 5.730
4 2200 2263.03 100 102.865 2.865
5 2200 2263.03 100 102.865 2.865
6 2200 2263.03 200 205.730 5.730
7 2200 2263.03 100 102.865 2.865

Results to date

Predictive model vs bookmaker precision by round
round_no season mTP mFP bTP bFP mPrec bPrec
1 2016 5 3 5 3 0.625 0.625
2 2016 7 1 6 2 0.875 0.750
3 2016 4 3 2 5 0.571 0.286
4 2016 3 5 7 1 0.375 0.875
5 2016 3 5 6 2 0.375 0.750
6 2016 7 1 4 4 0.875 0.500
7 2016 5 3 5 2 0.625 0.714
8 2016 7 1 7 1 0.875 0.875
9 2016 3 5 4 4 0.375 0.500

NB these are results as posted - remodelling of round 4 and 5 considerably improved these results as explained in Results to date

Conclude

OK, lets hope for a good round 10!

Calculating the value of multibets

How do you tell if a multibet if good value? How do you determine the odds and probability of multibets?

What about when a bookmaker has a ‘cash back’ promotional offer? How do I factor that in to my decision making process?

Find out below!

Calculating the value of multibets

Introduction

This is a quick post to explain how to identify if a head-to-head ‘multibet’ represents ‘good’ value or not. We will assume a good value bet is any bet where you think all teams (in your multibet) will win and expected return is positive (or more simply the perceived probability of an event/s occurring is higher than the bookmakers implied probability).

Calculating multibet odds & probability

Determining the value of a multibet is a simple exercise in which you multiply the implied odds of each match together (compute the product) and compare this to the product of your perceived odds. If your odds are shorter, then it would be a ‘good value’ (albeit long odds) bet. As an example, lets take the recent details of the multibet I placed for round 8 of the 2016 NRL season. In the table below, the team_descr is the team I tipped to win and the bookie_odds_stake were the odds at the time I placed the bet:

Round 8 multibet details
round_no game_no team_descr team_against_descr perceived_odds bookie_odds_stake
8 1 Brisbane Broncos South Sydney Rabbitohs 1.33 1.16
8 2 Canterbury Bulldogs Gold Coast Titans 1.42 1.33
8 3 Canberra Raiders Wests Tigers 1.51 1.42
8 5 Cronulla Sharks Penrith Panthers 1.37 1.60
8 8 Melbourne Storm New Zealand Warriors 1.31 1.67

If we calculate the product of the perceived odds we get 5.12 and if we calculate the product of the bookie odds we get 5.85. Because 5.12 is less than 5.85 it is a ‘good value’ bet. Just a reminder, the product of odds is simply all the odds multiplied together.

As an example the product of my perceived odds is:

1.33 x 1.42 x 1.51 x 1.37 x 1.31 = 5.12

If we look at it from a probability perspective, the perceived probability of this multibet paying off is 1/5.12 which is 19.5%. The bookmakers implied probability is 1/5.85 which is 17.1%. So I perceive that there is a greater chance of this event occurring than the bookmakers, therefore I deem it a good value bet. Of course we must also consider that the probability of it paying off (according to our own perceived probability) is only 19.5%.

Comparison of the precived odds/probabilty vs the bookmakers for the round 8 multibet
perceived_odds_prod perceived_prob bookie_odds_prod bookie_prob
5.118 0.195 5.854 0.171

Value of ‘cash back’ promotional offer/s

Now lets take a look at the scenario where a ‘cash back’ offer exists.

Specifically, for multibets, Sportsbet currently has a promotion whereby if you place a 5 leg multibet (on S2016 NRL matches) and only 4 of your tips actually win then you receive cash back (up to $50). So how do I tell if that’s good ‘value’ or not?

Well, I can tell you straight up that simply receiving your cash back on 4 of 5 legs is never good value because your perceived odds will be the product of 4 legs winning vs the cash back value which is equivalent to odds of 1.00. As an example the range of perceived odds for any 4 combinations of my 5 leg multi is between 3.39 and 3.9 and the odds offered (the cash back) is only 1.00. This is obviously negative expected return. So the ‘value’ of a cash back offer is really determined by your panchant for the overall risk of the multibet.

As an example in this 5 leg multi I can tell myself:

I perceive I have around (at best) a ~30% (1/3.39) chance of at least getting my cash back and about a 20% chance of a return of 5.8. So if I bet $50 I have around a 1 in 3 chance of getting my money back and about a 1 in 5 chance of a $290 return ($240 profit). In this case I took the ‘punt’ but at least I understood my chances. In this case it paid off!

As you can see multibets are high ‘risk’ high reward, and the promotional offer does not represent good value for the odds at time of potential cash back, however provides a ‘psychological’ buffer for the punter (which is why they offer them).

In all, given this sort of promotional offer it is worth understanding your chances of money back after 4 legs so you can put the multibet into perspective.

For example if you determine you have a 1 in 4 chance of money back and a 1 in 5 chance of a ‘big’ payout you might be less inclined to bet. Conversely if (in the case that one of your legs is very long odds) you might calculate you have a 1 in 2 chance of money back and a 1 in 4 chance of a big payout. In this case the higher chance of cash back might be enough for you to take a ‘punt’

Determing the odds of 4 of 5 betting legs

The odds of 4 of 5 of the multibet legs are simply calculated in the same way as previous (its just the product of the odds of 4 of the matches). If you assume that your top 4 ‘highest’ probability matches are most likely to win, just calculate the product of these odds and this is the (perceived) odds of cash back. For my multi, the highest probability games were games 1,2,3 and 8 and if I compute the product of these I get 3.3 which is equivalent to 29.5%. So I perceive I have a 29.5% chance of getting my money back.

It gets a little more tricky if you want to evaluate the range of odds for any four bets winning. To do this you have to compute the odds for every combination of odds for the 4 of 5 matches. Combination math is a little bit off topic (if your interested see http://stattrek.com/online-calculator/combinations-permutations.aspx#examples) but when you have 4 objects from a set of 5 objects there are 5 possible combinations of odds.

The 5 possible combinations of perceived odds odds expressed as a matrix looks like:

##      [,1] [,2] [,3] [,4] [,5]
## [1,] 1.33 1.33 1.33 1.33 1.42
## [2,] 1.42 1.42 1.42 1.51 1.51
## [3,] 1.51 1.51 1.37 1.37 1.37
## [4,] 1.37 1.31 1.31 1.31 1.31

Now If we compute the product of these combinations (re-ordered from lowest to highest) we observe the range of odds of getting our cash back after 4 legs:

## [1] 3.39 3.60 3.74 3.85 3.91

As probabilities this looks like:

## [1] 0.295 0.277 0.268 0.260 0.256

So if I assume that any combination of 4 legs is possible, the chances of getting my cash back is between 25.6% and 29.5%

Remember of course this all assumes my perceived probabilities are accurate 😉

Conclude

So now you know how to calculate the probability of a multibet based on your perceived odds and determine if its a good value bet. In the event of ‘cash back offer’, you will understand that the odds at time of cash back will never be favorable; however you will know its worth calculating the odds of to determine if the chances of cash back are favorable enough to factor into your psychology of bet placement. Finally you understand that multibets are high risk (long odds) high reward (high return) bets.

NRL S2016 R09 Predictions and staking guide

NRL S2016 R09 predictions and staking guide

Summary

We had a great round 8 with 4 of 5 bets paying off (and the 5th returning the stake due to a cash-back offer). The winnings from these bets returned the bank to profit (+14%).

This round there are two games which disagree with the bookmakers (current) predictions and four games have been identified as ‘good value’ bets. Lets take a look:

Predictions

game_no tip_text perceived_prob bookie_prob bookie_odds agree_with_bookie
1 South Sydney Rabbitohs to win against Wests Tigers while Home 0.794 0.704 1.42 Y
2 Canterbury Bulldogs to win against Parramatta Eels while Away 0.699 0.526 1.90 Y
3 Canberra Raiders to win against Penrith Panthers while Away 0.638 0.444 2.25 N
4 Sydney Roosters to win against Newcastle Knights while Home 0.741 0.769 1.30 Y
5 North Queensland Cowboys to win against Manly Sea Eagles while Away 0.719 0.741 1.35 Y
6 St George Illawarra Dragons to win against New Zealand Warriors while Away 0.736 0.408 2.45 N
7 Melbourne Storm to win against Gold Coast Titans while Away 0.678 0.667 1.50 Y
8 Brisbane Broncos to win against Cronulla Sharks while Away 0.624 0.581 1.72 Y

NB Bookmaker odds (taken from www.Sportsbet.com.au) as at 26-Apr-2016

Prediction observations

There are two games (game 3 and 6; Canberra Raiders v Penrith Panthers and St George Illawarra Dragons v New Zealand Warriors) which do not agree with the bookmakers predictions. There is very strong disagreement in game 6 where the model predicts St George as winning with a probability of 73.4% vs the bookmakers probability of 40.8%. This game represents very good value assuming the perceived probabilities are accurate. The overall probability of predictions is quite high; all being > 60%.

Stake recommendation/s

Recommended bets are those with a perceived probability of > ~0.66 and a positive expected return.

game_no tip_text perceived_prob bookie_odds expected_return recommend_stake
1 South Sydney Rabbitohs to win against Wests Tigers while Home 0.794 1.42 0.127 Y
2 Canterbury Bulldogs to win against Parramatta Eels while Away 0.699 1.90 0.329 Y
3 Canberra Raiders to win against Penrith Panthers while Away 0.638 2.25 0.435 N
4 Sydney Roosters to win against Newcastle Knights while Home 0.741 1.30 -0.036 N
5 North Queensland Cowboys to win against Manly Sea Eagles while Away 0.719 1.35 -0.029 N
6 St George Illawarra Dragons to win against New Zealand Warriors while Away 0.736 2.45 0.803 Y
7 Melbourne Storm to win against Gold Coast Titans while Away 0.678 1.50 0.017 Y
8 Brisbane Broncos to win against Cronulla Sharks while Away 0.624 1.72 0.073 N

NB bank and stake amounts are rounded to whole numbers

Four games are identified as being good value bets, and this round we will be staking level ($100) stakes on each game.

Conclude

Lets hope we have another good round. Good luck contributors!

NRL S2016 R08 Results

NRL S2016 R08 Results

Summary

We had a great round with 7/8 predictions correct. In addition to this, of the 5 bets placed, we profited from 4 and broke even on the 5th (due to cash back offer). Our initial bank for the round was $2,107.54 and after all concluded bets the bank sits at $2513.03 This represents a $313 profit to date (14% ROI)

We had a big win from a 5 game ‘multibet’, and profited from the 3 head to head bets recommended by the model.

Before I go on, in my last post I indicated I was staking on 3 head to head games (all of which profited), however after my post I actually placed two additional bet. One was a ‘multibet’ and the other was a head to head bet of which a there was a bookmakers promotion offering cash-back under certain conditions (margin <8 points).

I haven’t explained the math behind why I did this however I will outline in a future post explaining how Sportsbet’s head-to-head multibet odds are calculated. I also realize that I said in my original staking strategy that I wouldn’t place any ‘exotic’ bet types, however I hadn’t factored in the potential advantages which can be gained from various bookmaker promotions (which make some of these bet type more attractive). Again I will explain in a future post. Ok, now lets review how we did in detail:

Predictive Results

Given:

mTP = Models true positives

mFP = Models False positives

mPrec = Models precision (equivalent to accuracy in this case)

bTP = Bookmakers true positives

bFP = Bookmakers False positives

bPrec = Bookmakers precision (equivalent to accuracy in this case)

Table of results

Predictive model vs bookmaker precision by round
round_no season mTP mFP bTP bFP mPrec bPrec
8 2016 7 1 7 1 0.875 0.875
round_no game_no tip_text result
2921 8 1 Brisbane Broncos to win against South Sydney Rabbitohs while Home Correctly picked
2923 8 2 Canterbury Bulldogs to win against Gold Coast Titans while Home Correctly picked
2925 8 3 Canberra Raiders to win against Wests Tigers while Home Correctly picked
2927 8 4 North Queensland Cowboys to win against Parramatta Eels while Home Correctly picked
2929 8 5 Cronulla Sharks to win against Penrith Panthers while Home Correctly picked
2932 8 6 Manly Sea Eagles to win against Newcastle Knights while Away Correctly picked
2934 8 7 Sydney Roosters to win against St George Illawarra Dragons while Away Incorreclty picked
2935 8 8 Melbourne Storm to win against New Zealand Warriors while Home Correctly picked

Staking results to date

Initial bank = $2,200

Previous Round Bank = $2,107.54

Current bank = $2513.03

Total profit/loss = 331.03

Round Staking results = 4 out of 5 bets correct

Staking results to date = 6 out of 9 bets correct

ROI (Total profit / Initial Bank) = 14.2%

Table of staking results to date
BET.STATUS DATE.PLACED BET.DETAILS STAKE RETURN PROFIT BANK
1 Win 8-Apr-16 Penrith Panthers v Nth Queensland Cowboys / Head To Head / Nth Queensland Cowboys @ 1.67 50 84 34 2234
2 Win 9-Apr-16 Penrith Panthers v Nth Queensland Cowboys / Head To Head / Nth Queensland Cowboys @ 1.67 60 100 74 2274
4 Lose 16-Apr-16 Canterbury Bulldogs v New Zealand Warriors / Head To Head / Canterbury Bulldogs @ 1.90 114 0 -40 2160
5 Win 17-Apr-16 Wests Tigers v Melbourne Storm / Head To Head / Melbourne Storm @ 1.52 107 163 15 2215
6 Lose 18-Apr-16 Sydney Roosters v Penrith Panthers / Head To Head / Sydney Roosters @ 2.45 110 0 -95 2105
7 Win 20-Apr-16 Melbourne Storm v New Zealand Warriors / Head To Head / Melbourne Storm @ 1.67 100 167 -28 2172
8 Win 20-Apr-16 Cronulla Sharks v Penrith Panthers / Head To Head / Cronulla Sharks @ 1.60 100 160 32 2232
9 Win 20-Apr-16 Nth Queensland Cowboys v Parramatta Eels / Head To Head / Nth Queensland Cowboys @ 1.38 100 138 70 2270
10 Lose 20-Apr-16 St George Illawarra Dragons v Sydney Roosters / Head To Head / Sydney Roosters @ 1.70 50 0 70 2270
11 Win 20-Apr-16 Multibet (5 folds) 50 293 313 2513

For those who have contributed to the initial bank, the break down of your contribution and what you are currently entitled to is below. It’s pretty self explanatory with the main column being ‘entitlement’. This is how much you are entitled given your initial contribution. The gain (in dollars) is the amount of profit/loss you have currently made on your investment

Contributors investment entitlements

ID initial_bank current_bank cont_amount entitlement gain
1 2200 2513.03 1000 1142.286 142.286
2 2200 2513.03 500 571.143 71.143
3 2200 2513.03 200 228.457 28.457
4 2200 2513.03 100 114.229 14.229
5 2200 2513.03 100 114.229 14.229
6 2200 2513.03 200 228.457 28.457
7 2200 2513.03 100 114.229 14.229

Results to date

Predictive model vs bookmaker precision by round
round_no season mTP mFP bTP bFP mPrec bPrec
1 2016 5 3 5 3 0.625 0.625
2 2016 7 1 6 2 0.875 0.750
3 2016 4 3 2 5 0.571 0.286
4 2016 3 5 7 1 0.375 0.875
5 2016 3 5 6 2 0.375 0.750
6 2016 7 1 4 4 0.875 0.500
7 2016 5 3 5 2 0.625 0.714
8 2016 7 1 7 1 0.875 0.875

NB these are results as posted - remodelling of round 4 and 5 considerably improved these results as explained in Results to date

Conclude

Ok, lets hope we can can build on our great start to investing in following rounds!

NRL S2016 R08 Predictions and staking guide

NRL S2016 R08 predictions and staking guide

Summary

After a poor performing staking round in round 7 (1 of 3 bets correct) we will be looking for a stellar round!

This round, all of the models picks are (currently) in line with the bookmakers predictions and three games have been identified as being ‘good’ value.

These are:

  • Game 4: North Queensland Cowboys to win against Parramatta Eels while Home paying $1.35

  • Game 5: Cronulla Sharks to win against Penrith Panthers while Home paying $1.60

  • Game 8: Melbourne Storm to win against New Zealand Warriors while Home paying $1.67

All of the games are relatively short odds and we will need to watch odds movement to ensure that none of the games swing into ‘poor’ value territory (become negative expected return).

Ok, lets look at the predictions in detail:

Predictions

game_no tip_text perceived_prob bookie_prob bookie_odds agree_with_bookie
1 Brisbane Broncos to win against South Sydney Rabbitohs while Home 0.753 0.862 1.16 Y
2 Canterbury Bulldogs to win against Gold Coast Titans while Home 0.706 0.741 1.35 Y
3 Canberra Raiders to win against Wests Tigers while Home 0.662 0.704 1.42 Y
4 North Queensland Cowboys to win against Parramatta Eels while Home 0.797 0.741 1.35 Y
5 Cronulla Sharks to win against Penrith Panthers while Home 0.730 0.625 1.60 Y
6 Manly Sea Eagles to win against Newcastle Knights while Away 0.652 0.714 1.40 Y
7 Sydney Roosters to win against St George Illawarra Dragons while Away 0.581 0.571 1.75 Y
8 Melbourne Storm to win against New Zealand Warriors while Home 0.762 0.599 1.67 Y

NB Bookmaker odds (taken from www.Sportsbet.com.au) as at 19-Apr-2016

Prediction observations

We observe that all the predictions are (currently) in agreement with the bookmakers predictions and that probabilities (perceived and implied) are generally high (>60%).

Stake recommendation/s

Recommended bets are those with a perceived probability of > ~0.66 and a positive expected return.

game_no tip_text perceived_prob bookie_odds expected_return recommend_stake
1 Brisbane Broncos to win against South Sydney Rabbitohs while Home 0.753 1.16 -0.127 N
2 Canterbury Bulldogs to win against Gold Coast Titans while Home 0.706 1.35 -0.046 N
3 Canberra Raiders to win against Wests Tigers while Home 0.662 1.42 -0.060 N
4 North Queensland Cowboys to win against Parramatta Eels while Home 0.797 1.35 0.076 Y
5 Cronulla Sharks to win against Penrith Panthers while Home 0.730 1.60 0.169 Y
6 Manly Sea Eagles to win against Newcastle Knights while Away 0.652 1.40 -0.087 N
7 Sydney Roosters to win against St George Illawarra Dragons while Away 0.581 1.75 0.017 N
8 Melbourne Storm to win against New Zealand Warriors while Home 0.762 1.67 0.273 Y

Conclude

Lets hope we have a good round. Good luck contributors!