The ‘Miracle of the Saints’
Three weeks ago, Carrara played host to a remarkable result, in what may have easily been scripted as an unremarkable match-up between 15th-placed Gold Coast and 16th-placed St Kilda at Metricon Stadium.
The off-Broadway match was one that may have easily slipped into the ether, with two no-hopers of 2018 playing in front of just over 10,000 spectators on the Gold Coast, and hardly demanding a television audience with a Saturday twilight time slot ahead of the Socceroos’ 2018 FIFA World Cup campaign launch against France.
Journalists were no doubt starting to sharpen the knives to finish off embattled coach Alan Richardson as the Saints trailed by 39 points with 26 minutes played in the third quarter. About 35 minutes – and 6.5 (41) to 0.0 (0) later – the Saints had completed the miracle with a dramatic two-point victory. It was the first match this season where a team had come back to win from a deficit of 30 points or greater.
‘Footballistics’ context
One of the 15 chapters in James Coventry’s new book ‘Footballistics’, named Win Probabilities, assesses various ‘heuristics’ or rules of thumb which are commonly adopted by the footy fan, pundit or commentator as a way to ‘call’ a victory for a particular team during a game. Thinking about it another way, this is when the individual believes that the in-game chance of victory for a particular team approaches close to 100 per cent.
In particular, the chapter considers the winning chances of teams meeting the criteria for three heuristics:
- Teams reaching 100 points before to their opposition (which considers only points scored)
- Teams with at least a 30-point lead (which considers points scored and points conceded)
- Teams leading by more goals than minutes remaining (which considers points scored, points conceded and time remaining – but typically relates only to the dying minutes of a match)
The winning rates of all these situations are discussed in some depth within the chapter.
The natural extension to these themes is the creation of a model which can provide an approximation to a probability of victory given point in a match – taking into consideration both scoring factors as well as time remaining. Left on the cutting room floor of the chapter were a list of the most unlikely comebacks, based on a simple logistic regression model I created at the time.
Coincidentally, the same topic was raised on Twitter over the following weekend following various throwbacks to the Bombers’ victory over the Kangaroos from a 69-point deficit in 2001.
So yeah it’s one of the great urban myths of footy IMHO, and plays purely to a big club narrative.
Possible task for @HPNfooty or @MatterOfStats … comeback margin vs time available to see best comeback ever.
— 𝔽𝕄𝕀 (@The_FMI) July 1, 2018
I had dragged together much of this content following the St Kilda win over Gold Coast, but this Twitter conversation was the catalyst to (eventually) finishing the post (two weeks later).
A simple in-game model for win probabilities
Recently I have slightly updated the model to create a number of variations. One simpler but stronger combination, which I’ve named WinProb2, takes into account:
- Percentage of game time duration remaining
- In-game running margin of the chosen team
- In-game running combined score (points) of both teams
- In-game running combined scoring shots of both teams
- In-game running difference in scoring shots of the chosen team relative to the opposition
- Home team
For simplicity, estimate probabilities have been calculated at the time of each score, and a second prior to each score, for all in-game scoring events since 2008. In practice, what this means is that probabilities have been estimated as the ball has effectively carried through for a score but before the score has been officially recorded. It is an important point to note: the model doesn’t know where the play is situated, or what may have happened and is yet to be signalled – it only considers the simple attributes above.
The most unlikely successful comebacks since 2008
Using WinProb2 as the basis for estimate in-game win probabilities, the following lists the top 100 most unlikely successful comebacks across all AFL Premiership Season matches between Round 1 2008 and Round 16 2018 inclusive.
| WP2 | Season | Round | Quarter | Time | Team | Opponent | In_game_margin | Eventual_margin |
|---|---|---|---|---|---|---|---|---|
| 0.3% | 2013 | R13 | 3 | 25:08 | Brisbane Lions | Geelong | -51 | +5 |
| 0.4% | 2008 | R4 | 3 | 24:13 | Brisbane Lions | Port Adelaide | -47 | +20 |
| 0.5% | 2013 | R9 | 4 | 15:13 | Adelaide | North Melbourne | -30 | +1 |
| 0.6% | 2015 | R6 | 3 | 04:31 | St Kilda | Western Bulldogs | -55 | +7 |
| 0.7% | 2011 | R5 | 3 | 29:33 | Gold Coast | Port Adelaide | -40 | +3 |
| 0.7% | 2011 | R23 | 4 | 10:17 | Essendon | Port Adelaide | -34 | +7 |
| 0.8% | 2018 | R13 | 3 | 26:06 | St Kilda | Gold Coast | -39 | +2 |
| 0.8% | 2008 | R21 | 4 | 01:51 | Carlton | Brisbane Lions | -32 | +6 |
| 1.1% | 2013 | R23 | 3 | 21:30 | Carlton | Port Adelaide | -38 | +1 |
| 1.2% | 2013 | R5 | 3 | 20:00 | Port Adelaide | West Coast | -41 | +5 |
| 1.2% | 2012 | R8 | 4 | 13:42 | Port Adelaide | North Melbourne | -32 | +2 |
| 1.3% | 2008 | R7 | 4 | 02:15 | Melbourne | Fremantle | -32 | +6 |
| 1.5% | 2016 | R21 | 4 | 00:19 | Geelong | Richmond | -35 | +4 |
| 1.5% | 2008 | R11 | 3 | 19:06 | Carlton | Port Adelaide | -38 | +12 |
| 1.8% | 2017 | R15 | 4 | 05:10 | Brisbane Lions | Essendon | -27 | +8 |
| 1.9% | 2008 | R17 | 3 | 29:46 | Richmond | Brisbane Lions | -31 | +3 |
| 1.9% | 2015 | R1 | 3 | 25:42 | Sydney | Essendon | -41 | +12 |
| 2.1% | 2017 | R2 | 3 | 34:03 | Geelong | North Melbourne | -31 | +1 |
| 2.2% | 2009 | EF | 4 | 05:23 | Brisbane Lions | Carlton | -29 | +7 |
| 2.3% | 2008 | R17 | 3 | 23:44 | Carlton | Western Bulldogs | -31 | +28 |
| 2.4% | 2013 | R19 | 4 | 22:01 | Port Adelaide | Adelaide | -20 | +4 |
| 2.6% | 2010 | R14 | 3 | 22:25 | Richmond | Sydney | -33 | +4 |
| 2.6% | 2009 | R17 | 4 | 04:07 | Geelong | Hawthorn | -28 | +1 |
| 2.7% | 2011 | R20 | 4 | 13:48 | Adelaide | Brisbane Lions | -22 | +5 |
| 2.7% | 2014 | R6 | 4 | 14:26 | Carlton | West Coast | -24 | +3 |
| 3.1% | 2011 | R23 | 3 | 19:53 | West Coast | Brisbane Lions | -29 | +8 |
| 3.1% | 2014 | R13 | 3 | 05:06 | Melbourne | Essendon | -33 | +1 |
| 3.2% | 2008 | R6 | 4 | 02:08 | Geelong | Fremantle | -25 | +1 |
| 3.2% | 2008 | R5 | 4 | 12:51 | North Melbourne | Collingwood | -21 | +7 |
| 3.3% | 2011 | R17 | 3 | 15:38 | Essendon | Adelaide | -34 | +11 |
| 3.3% | 2008 | R11 | 3 | 04:31 | Sydney | West Coast | -37 | +5 |
| 3.3% | 2013 | R16 | 3 | 25:02 | Brisbane Lions | North Melbourne | -33 | +12 |
| 3.4% | 2017 | R9 | 4 | 05:30 | Greater Western Sydney | Richmond | -27 | +3 |
| 3.6% | 2013 | R22 | 4 | 05:05 | Essendon | Carlton | -19 | +6 |
| 3.6% | 2013 | R2 | 2 | 29:50 | Geelong | North Melbourne | -41 | +4 |
| 3.7% | 2011 | R11 | 4 | 03:58 | Hawthorn | Fremantle | -26 | +22 |
| 3.7% | 2017 | R13 | 3 | 13:10 | Sydney | Richmond | -31 | +9 |
| 3.8% | 2015 | R9 | 3 | 01:16 | Collingwood | North Melbourne | -39 | +17 |
| 3.8% | 2013 | R14 | 3 | 30:36 | Essendon | West Coast | -23 | +7 |
| 3.9% | 2016 | R21 | 4 | 23:57 | West Coast | Greater Western Sydney | -18 | +1 |
| 3.9% | 2013 | R3 | 3 | 02:23 | Essendon | Fremantle | -36 | +4 |
| 3.9% | 2015 | R15 | 3 | 11:48 | Western Bulldogs | Gold Coast | -37 | +22 |
| 4.0% | 2015 | R13 | 3 | 04:12 | Richmond | Sydney | -33 | +18 |
| 4.0% | 2017 | R14 | 4 | 25:13 | Sydney | Essendon | -19 | +1 |
| 4.1% | 2009 | R21 | 1 | 31:48 | Brisbane Lions | Port Adelaide | -47 | +15 |
| 4.4% | 2012 | R16 | 4 | 18:31 | Gold Coast | Richmond | -18 | +2 |
| 4.4% | 2017 | R9 | 2 | 11:54 | Collingwood | Hawthorn | -43 | +18 |
| 4.5% | 2008 | R8 | 4 | 14:00 | Western Bulldogs | Fremantle | -18 | +3 |
| 4.5% | 2012 | R22 | 2 | 14:29 | Hawthorn | Sydney | -38 | +7 |
| 4.5% | 2012 | R15 | 2 | 19:31 | West Coast | North Melbourne | -35 | +2 |
| 4.5% | 2016 | R12 | 3 | 16:36 | Adelaide | West Coast | -26 | +29 |
| 4.6% | 2014 | R18 | 4 | 06:38 | Essendon | Western Bulldogs | -20 | +7 |
| 4.8% | 2015 | R13 | 4 | 01:34 | Adelaide | Brisbane Lions | -24 | +13 |
| 5.1% | 2010 | R22 | 4 | 17:30 | Hawthorn | Collingwood | -19 | +3 |
| 5.1% | 2017 | R14 | 4 | 19:08 | Melbourne | West Coast | -16 | +3 |
| 5.3% | 2012 | R23 | 4 | 15:57 | St Kilda | Carlton | -15 | +15 |
| 5.4% | 2008 | R13 | 3 | 19:15 | Western Bulldogs | Collingwood | -23 | +10 |
| 5.5% | 2008 | R16 | 2 | 28:39 | Sydney | Carlton | -29 | +2 |
| 5.5% | 2011 | R9 | 4 | 08:52 | Collingwood | Adelaide | -23 | +43 |
| 5.6% | 2014 | R21 | 3 | 10:35 | Essendon | West Coast | -34 | +3 |
| 5.6% | 2008 | R16 | 2 | 29:47 | St Kilda | Hawthorn | -34 | +30 |
| 5.6% | 2013 | R11 | 3 | 15:47 | Essendon | Carlton | -31 | +5 |
| 5.6% | 2018 | R6 | 4 | 01:56 | Sydney | Geelong | -22 | +17 |
| 5.6% | 2010 | R15 | 2 | 10:17 | Collingwood | Port Adelaide | -36 | +26 |
| 5.8% | 2008 | R9 | 3 | 14:53 | North Melbourne | Western Bulldogs | -24 | +3 |
| 5.9% | 2016 | R8 | 4 | 16:15 | Carlton | Port Adelaide | -18 | +2 |
| 5.9% | 2011 | R17 | 2 | 00:44 | Gold Coast | Richmond | -36 | +15 |
| 6.0% | 2010 | R6 | 3 | 20:31 | St Kilda | Western Bulldogs | -23 | +3 |
| 6.2% | 2009 | R6 | 3 | 02:34 | Fremantle | West Coast | -23 | +13 |
| 6.2% | 2012 | R22 | 3 | 31:58 | Brisbane Lions | Port Adelaide | -19 | +11 |
| 6.2% | 2016 | R1 | 3 | 28:26 | Melbourne | Greater Western Sydney | -22 | +2 |
| 6.2% | 2009 | R1 | 2 | 10:06 | Brisbane Lions | West Coast | -38 | +9 |
| 6.2% | 2013 | EF | 3 | 08:16 | Carlton | Richmond | -31 | +20 |
| 6.2% | 2014 | R22 | 3 | 12:04 | Hawthorn | Geelong | -33 | +23 |
| 6.3% | 2011 | R1 | 4 | 16:07 | Fremantle | Brisbane Lions | -17 | +2 |
| 6.3% | 2017 | R4 | 2 | 31:12 | Fremantle | Melbourne | -27 | +2 |
| 6.3% | 2018 | R1 | 4 | 08:38 | Essendon | Adelaide | -20 | +12 |
| 6.3% | 2017 | R18 | 4 | 04:07 | Collingwood | West Coast | -24 | +8 |
| 6.3% | 2017 | R14 | 3 | 27:01 | Geelong | Fremantle | -27 | +2 |
| 6.3% | 2016 | R2 | 4 | 23:12 | Collingwood | Richmond | -17 | +1 |
| 6.4% | 2018 | R15 | 3 | 27:29 | Adelaide | West Coast | -27 | +10 |
| 6.4% | 2014 | R12 | 3 | 03:15 | North Melbourne | Richmond | -35 | +28 |
| 6.5% | 2010 | R3 | 3 | 30:25 | Fremantle | Geelong | -21 | +7 |
| 6.5% | 2011 | R23 | 3 | 15:00 | Richmond | Adelaide | -24 | +22 |
| 6.5% | 2014 | EF | 3 | 06:05 | North Melbourne | Essendon | -33 | +12 |
| 6.6% | 2009 | R11 | 3 | 15:55 | Adelaide | Essendon | -21 | +16 |
| 6.7% | 2008 | R14 | 2 | 09:36 | St Kilda | North Melbourne | -33 | +15 |
| 6.8% | 2013 | R21 | 2 | 10:00 | Carlton | Richmond | -30 | +10 |
| 6.8% | 2009 | R14 | 2 | 06:03 | Carlton | Fremantle | -36 | +15 |
| 6.9% | 2017 | R4 | 3 | 07:17 | Western Bulldogs | North Melbourne | -29 | +3 |
| 7.0% | 2017 | R10 | 3 | 12:21 | Melbourne | Gold Coast | -30 | +35 |
| 7.0% | 2014 | R4 | 3 | 24:01 | Western Bulldogs | Greater Western Sydney | -20 | +27 |
| 7.0% | 2017 | R8 | 2 | 19:37 | Melbourne | Adelaide | -28 | +41 |
| 7.0% | 2012 | R16 | 3 | 22:29 | Fremantle | Melbourne | -20 | +34 |
| 7.0% | 2016 | R3 | 4 | 01:28 | Hawthorn | Western Bulldogs | -19 | +3 |
| 7.1% | 2008 | R19 | 4 | 22:38 | Sydney | Fremantle | -14 | +4 |
| 7.1% | 2012 | R10 | 4 | 07:09 | Brisbane Lions | West Coast | -21 | +2 |
| 7.2% | 2013 | R21 | 3 | 25:09 | Western Bulldogs | Adelaide | -22 | +17 |
| 7.2% | 2013 | R1 | 2 | 26:52 | Geelong | Hawthorn | -30 | +7 |
| 7.3% | 2008 | R12 | 3 | 15:45 | Carlton | Collingwood | -24 | +30 |
The most unlikely victory across ten years was the ‘miracle on grass’ by Brisbane against Geelong once again in 2013. The Lions trailed 5.6 (36) to 13.10 (88) into time-on in the third quarter, with our model giving them just an estimated 0.3 per cent chance of victory. In what really was a remarkable result, Brisbane managed 10.7 (67) to 1.4 (10) in just over a quarter to pinch the game – and even then still needed a kick after a siren, thanks to Ashley McGrath’s effort from about 50 metres in a fairytale 200th game. Clearly an unlikely result, whether you are talking in layman’s terms or mathematically.
It is of interest that even though only three of the top ten most bleak situations occurred in the final quarter, the going was that tight that all but one still only resulted in a winning margin of a seven point or fewer. It suggests that, even with well over a quarter of play remaining in the match, many of the wins were that tight that the trailing team needed every last minute remaining. The only match which ended in comfortable result was the remarkable 2008 match between Brisbane and Port Adelaide. In that game, the Power led by 47 points during time-on in the third quarter, before the Lions somehow found 11.8 (74) to 1.1 (7) from that point onwards to eventually win easily. Given nine of the top 31 results are from that season of 2008, I am conscious that the model perhaps is too well-calibrated to a modern, more-stodgier style of game play and may overstate the chances of a large comeback required in a higher-scoring game ten years ago.
But other comebacks came from particular dire circumstances are found late in final terms. In Round 9 of 2013, the Crows were 30 points down half way through the final quarter against the Kangaroos with an estimated chance of just 0.5 per cent, but managed to win by a point in a stunning result. At 21st position on the table, another game later in that season featured Adelaide finding itself on the other side of the ledger. The Crows this time led the Power in the Showdown by 20 points well into time on, with Port Adelaide given just a 2.4 per cent chance but still able to find a way to win by four points.
And lo and behold, well entrenched inside the top ten was the St Kilda performance against Gold Coast back in Round 13. The Saints may not have had too much to get excited about this season, but that result was one of the most unlikely in over a decade.
The ‘greatest comeback of all time’
Casting our minds back to the Bombers’ greatest comeback of all time against the Kangaroos, I applied the WinProb2 model according to the scores at the moment prior to Essendon’s goal eating into the then-69-point margin. Intriguingly, given the length of game duration remaining combined with the high scoring rate, the model estimated the Bombers still maintained a 2.4% chance of victory – placing 20 comebacks more unlikely in the past ten years alone. One thing I must note is that match was an outrageously high scoring game for the time, never mind for the dour matches of today. Because the model has only been trained on in-game score data since 2008, the model has had very little chance at being exposed to such extreme scoring , which may weaken the level of certainty around its estimate predictions.
Possible improvements
There were other various parameters I played with but they didn’t greatly improve the model, and I liked how well this model performed against one with many other combination of parameters given its simplicity. For example, I attempted trying to control for a ‘scoring end’ (based on wind or weather conditions), by taking into account the scoring rate at each end and the time teams had played to each end. This perhaps may pick up a stronger signal in a future improved model by factoring for various grounds (say, University of Tasmania Stadium in Launceston which seems to be often dominated by windy conditions).
One other definite improvement would be to understand contextualised chances of victory based on team quality and the pre-game estimate chance of victory. The only factor in the current models which takes into account any team context is a flag for the home team (which proves to be advantageous). This would come at the cost of moving the model away from its current simplicity, but would be a natural progression from considering factors based upon merely scoring, margin and time. To get a much better understanding of the chance of winning for a specific side against a specific opponent, a team- or player-based rating model would be required. I am yet to build one of these, but you will find team ratings at excellent sites like Matter of Stats, Squiggle, The Arc and a lovely player-based rating model at HPN.
Another element that needs to be modelled differently is the probability of victory within the last minutes of a match where the margin is small. The model is not well calibrated to deal with predicting results with margins tight in the last five per cent or so of matches. I’ve played with a few combinations but as yet I haven’t clocked this one, so I would hesitate to use the existing model to provide estimate probabilities on these types of matches.
Finally, the bias towards 2008 in the results may suggest that it is not adequately fitted to different modes of play across seasons earlier in the sample.
Further analysis
I am looking to build out these models and add more analysis on this topic in future weeks. To view every ScoreWorm since 2008, feel free to browse and play with my dynamic visualisation.
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Feedback
I am very open to feedback on this or any of my analysis. I expect many readers may have a deeper grounding in statistics than myself, and love to learn. If I have missed something, made an error, or if you have any suggestions or ideas, please feel free to comment below, shoot me a direct message or hit me up on Twitter.
All data provided for analysis on this page comes thanks to AFL Tables.