Polish / Inverted Middling the new NRL rules
By David Barrett
Analyst for the NRL Tips service
This article discusses the concept of Polish/Inverted Middling, and how there currently appears an opportunity to take advantage of this betting concept due to the new NRL rules.
A ‘standard middle’ profits if the total or line falls inside a certain range.
A ‘Polish/Inverted middle’ profits if the total or line falls outside a specific range. It is two separate bets placed at different lines or totals so that it profits if the line or total falls outside the range in-between them.
Standard middles have limited downside risk because you’re guaranteed that at least one line wager will win. However Polish/Inverted middles carry total downside risk because there is the possibility that both wagers will lose.
Given the recent rule changes there is now a bit of an inefficiency in the NRL betting market. These rule changes have had more of an impact on the game than the six-again rule from last year, and have made scoring more volatile. As has been discovered, totals have risen due to the greater scoring chances teams have when opposing teams are down a player, but this is not the only change that has occurred.
Historically, margins of victory can be modelled off of a bell curve (normal distribution). Some changes need to be made to fit it to the NRL, but it loosely fits quite well. This works out for game outcomes where there is a proportional chance for one team to win and a reciprocal probability for the opposition to win shown by H2H/Line odds. This can be seen through looking at historical lines or through a bookmaker’s ‘pick your own line’ odds.
The upcoming Round 12 Tigers v Dragons game has been used for example where I have estimated a total of 50.5 points (totals markets aren’t up yet), and the market has posted up a -5.5 line in favour of the Tigers. This approximates to the Dragons scoring 22 and the Tigers scoring 28 on average, which can be seen in the chart below. The H2H odds of $1.50 for the Tigers implies a 66.6% probability for a Tigers win and the $2.55 odds for the Dragons implies a 39.2% probability of a Dragons win. Removing overround/vig the probabilities will approximate to 63% Tigers win and 37% Dragons win.
The following chart implies the game outcomes with the yellow line indicating the point where the two teams draw, and in this example yields a 0.04 chance (4% probability of golden point) and has been forecast between the Dragons winning by 6 and the Tigers winning by 16 (not all outcomes have been run through for simplicity). The green line represents the average of all outcomes that has been determined for the game (-5.5 from the market), wherein 50% of all outcomes are to the left and 50% are to the right on the chart. The orange part represents about 2/3 of the chart area, which approximates to the 63% implied win probability from the H2H odds. The red part of the chart represents the other part of the chart which is approximately 1/3 of the chart which approximates to the 37% win probability from the H2H odds.
One can use the cumulative density function to determine the area under the line (coloured area) or fit a polynomial and use integration to determine the area which leads to the total probability of each team winning. Whilst the individual NRL teams strengths and weaknesses haven’t changed since the rule changes (although some have been fared better than others), the distribution of points has changed such that the curve, whilst still normally distributed, has changed. The variance and in turn standard deviation for margin of victory has changed. The following chart has the blue curve representing the historical data and the orange is indicative of the game post rule changes.
This chart still has a mean margin of victory of 5.5 points to the Tigers, however areas under the curve and henceforth the probabilities of outcomes have changed. So, what does this mean for the outcomes of games? In the following chart the grey area represents the part of the curve that no longer exists given the changes to the game and the purple area represents the portion of the game outcomes that have moved to a greater margin of victory for the Tigers and the pink to a greater margin of victory for the Dragons.
The grey area represents portions of the game that won’t happen anymore.
What does all this mean in relation to betting?
Given the rule changes, we have seen a growth in the margin of victory of teams in NRL games for favourites and a few upsets of favourites that will happen week to week (we will see fewer close games). The growth in game scoring has impacted more than just the total points scored markets.
How can one profit from this?
Given that we know that there is a reduction in game margins of victory around the average (where the market has set the line at) one can use Inverse/Polish middling to take advantage of the current market situation, whereby the Dragons at $2.55 (representing 39.2% of outcomes) and Tigers by 13+ at $2.90 (representing 34.5%). If one bet wins then the payoff covers the loss of the other bet and still provides some profit. Given that the market has stipulated that there is a 27.3% (1 - 39.2% - 34.5%) chance of the Tigers winning by 1 to 12 we want to lay this bet, because the change in the rules has led to there being less likelihood of this occurring (grey area in the chart). This can be visualised with the following chart.
At this stage there is no way of quickly determining how much value is present, but in the near term there is the opportunity to take advantage before the market fully adjusts to the new rules.
N.B. These charts have been put together for educational purposes and the tail values are not representative of actual outcomes as we do not yet have enough data to ascertain the new distribution.
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