With the World Cup having finished in the most dramatic of circumstances, England fans could perhaps be forgiven for wanting a little break from cricket to allow themselves time to fully digest the events of Sunday 14th July 2019. There is, however, the little matter of the Ashes just around the corner, with the England team's preparations already well under way, with several players having the opportunity to impress with a test match against Ireland, which starts this Wednesday.





So what exactly are England's chances of regaining the Ashes? This article uses the Bradley-Terry model - an adaptation of the logistic regression that we used for our ranking system - to examine the likely outcomes of the series. As part of this, we examine the extent to which two factors might influence the results. First of these is home advantage, which is the primary reason that England are widely seen as favourites for the series, and the return of Steve Smith and David Warner to the Australian test team after their involvement in the sandpaper controversy last year .





Firstly, it's worth examining what the bookies are saying. Below are the implied outcome probabilities based on the Bet365 odds at the time of writing (Sunday 21st July).













Our predictive model is based around finding outcome probabilities for a single test, and then running ten thousand simulations of five tests with these probabilities. For simplicity, we'll consider that the outcome probabilities of each test is equal - no attempt is made to account for the different grounds and other varying factors between each game. This is, admittedly, a limitation of the model, but keeping it simple allows us to focus on the impact of the factors that we are examining.





The basic Bradley-Terry model only allows us to predict a winner, and does not allow us to predict the likelihood of a draw. There are extensions of the model that make an attempt to account for this, but the nature of draws in test cricket mean these are inappropriate to use here. These extensions tend to base the likelihood of a draw on how closely matched the two teams are, which makes sense in something like football, but in test cricket this makes no sense - the probability of a draw is effectively independent of the teams' respective abilities, and is much more heavily influenced by external factors such as pitch and weather conditions.





Unfortunately, predicting the English weather is an infinitely more complex challenge than we dare take on, but we do have a couple of options to get a figure that we can work with. The easiest option would just be to use the bookies odds - which gives the probability at 17.1%. Looking at the data, however, this value seems far too high. The last 18 test matches in England have finished in a result, and just 1 out of the last 32 have finished in a draw. If we go back a few years further we do get a few draws creeping in - in the last 6 English summers we have seen 5 draws out of 42 tests - this gives us a value of 11.9% which seems appropriate, so we'll go with that.





Now we've got a draw probability, it's time to figure out what happens in those 88.1% of games where we'll see a result. To do this we apply the Bradley-Terry model, accounting for home advantage, on all test matches that ended in a result in the past three years. This gives us estimates for the respective abilities of the teams and the effect of home advantage:





This shows us that, based on results from the past three years, Australia are the slightly better side. The difference is small however, and if we add the home advantage coefficient on to England's, then they become the favourites. Calculating the win probabilities based on these figures, and then simulating the five match series 10,000 times, gives us the following probabilities for the series:





Looks good for England, right? A 54.3% chance of winning any given test, which translates to a 63% chance of regaining the Ashes. Bet365 only give England a 53% chance of a series win, so this looks very promising indeed.





There is, however, a crucial factor that we haven't yet accounted for. In March of 2018, Australian batters Steve Smith and David Warner were banned for a year for their involvement in the ball-tampering controversy in a test match against South Africa. Since then, they have played nine tests and only won three, which include two home wins against a relatively weak Sri Lanka side. By comparison, their previous twenty test matches saw eleven victories, including four victories over England, a couple of wins over South Africa, and an impressive win away in India - albeit in a series they ultimately lost.

The initial model takes no account for this, and thus Australia's estimated ability was damaged by this bad run of form during Smith and Warner's absence. Given that they will be back in the side for the Ashes, and their return is widely expected to boost their team's chances, it makes sense to re-run the model to look at how the presence of Smith and Warner influences Australia's chances.





The model effectively treats the presence of Smith and Warner as an external factor attributed to Australia in the games that they were playing in. This is applied in the same manner as we did for home advantage in the previous version. We've also kept home advantage in as a predictor here:





Here we can see that without Smith and Warner, Australia are a much weaker team than England. Smith and Warner's presence, however, boosts Australia's quality by 0.8944, a figure we'll dub as the Smith-Warner coefficient. Adding the Smith-Warner coefficient to Australia's ability rating pushes them well over England - the difference is now over 0.4 compared to just 0.2 when we had not accounted for their ban in the previous model. Whilst this is obviously an improvement for Australia, it should be noted that with home advantage on their side, England still retain their status as favourites.





In order to truly assess their contribution to their team's chances, we've run two separate simulations - one that looks at what would happen if they weren't playing, and one that looks at if they are. Firstly, let's look at how things might turn out if Warner and Smith were still banned:

And now again, with the Smith-Warner coefficient factored in - these can be considered our final estimated probabilities:





The differences here are fairly dramatic. Smith and Warner's presence nearly quadruple Australia's chances of winning the series - from around 8% to 31% - and they roughly triple their team's chances of at least retaining the urn - from 16% to 45%.





England are still the favourites though, with a 55% chance of bringing the Ashes home. This is only a slightly better chance than the bookies give them, and the difference can largely be attributed to the difference in opinion on the likelihood of a draw. If we had run our model using the draw probability of 17.1% as predicted by Bet365, the predicted outcomes for the series would be more or less identical.





Now that we've established that, even with Smith and Warner playing, England are definitely going to win the Ashes, the next question is how much they will win by. The table below shows the breakdown of the results from each of our 10,000 simulations:









The most likely outcome here is a 3-2 series win for England, with a probability of 17.8%. Next most likely is the reverse - a 3-2 series win for Australia, although that is only marginally more likely than a 2-2 draw or a 4-1 win for England. For the optimistic/pessimistic amongst you, England have a 3.4% chance of a series whitewash, with a 5-0 win for the away side coming in at 0.8%.





Overall, the series looks finely poised and it will be fascinating to see how it all unfolds. Smith and Warner will be determined to drag their side to victory and win back the support of the Australian public, and the likes of Jofra Archer and Jason Roy will be looking to make a big impact in their first Ashes series - assuming they make the side. Any number of influencing factors that haven't been considered here could emerge as decisive factors - the fitness of James Anderson, the weather conditions, and the performance of England's frail looking top order but to name a few - and there's sure to be a number of interesting narratives developing throughout.





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