This post was initially intended to be a short little thing about using in-play odds to show how the 2019 Allsvenskan title race dramatically climaxed on the last day of the season, but with the current Corona situation delaying and drastically changing the new upcoming season, the synopsis grew and eventually came to focus more on my own path leading up to that glorious afternoon in Norrköping.

If you only want the short version or look at the graphs you can scroll down. And if you want a more technical explanation on the calculations behind the graphs it’s available at the bottom of this post.

Background: 1988-2018

Supporting a football club can sometimes be hard to justify. When things, as they often do, go wrong and you’ve spent a lot of time, energy and money to support your team and all you get is disappointment, embarrassment and ridicule, you sometimes start to question your decisions. Through the years I’ve done just that more times than I can remember, often on the way back home from yet another away defeat. I’ve always come to the same conclusion: that it’s really not much of a decision as the club is such an integral part of who I am. Together with my family it’s been the only constant in my life, it’s how I engage with most of my friends and it has actually brought a lot of joy with all the pain. So you pick yourself up one more time, allow yourself to start dreaming again, thinking about that one day that is sure to come if you just keep on carrying on…

Djurgården came into my life at an early stage. My father supported the club, and so naturally I had to as well. In the early and mid 90’s when I grew up Ice Hockey was the main sport in Sweden, and while my dad’s interest had long since declined to a level of watching a match on TV now and then to be able to keep up with the banter at work, my own interest skyrocketed throughout the decade. Dad’s low interest meant we didn’t go to many matches so I was instead stuck to the radio whenever Djurgården played, usually a couple of nights a week during the Ice Hockey season. The coverage was limited so you never got to hear a full match, instead you’d have to patiently wait for something interesting to happen in your match and then the radio operator would switch to the commentator on scene. I think most Swedes interested in sports back then still remember the famous goal jingle played by the Swedish Public Service radio whenever they’d switch matches to report on a new goal. Suddenly hearing it you always froze, hoping it was Djurgården who’d scored. 

Matches on TV were rare then, at least in our house as we only had the three standard channels (yes kids, that’s right) – so actually going to see the team play live was an unreal experience. I still have the flag my dad bought me on one of those days, back in November 1995 when Djurgården mounted a third period comeback to beat Modo 6-3 after being down 0-2 and 1-3. A priceless memory for a 7 year old boy.

Djurgården won back-to-back ice hockey trophies during the 1999/2000 and 2000/2001 seasons – with the latter a sweet revenge on Färjestad for the 1998 Final defeat in overtime of the deciding match – but since the 1998 World Cup, football had taken over as my main focus. Djurgården were pretty much shit then but promoted back to Allsvenskan for the 2001 season things were starting to fall into place. After an impressing second place that year, a ‘golden generation’ lead by Kim Källström, Andreas Isaksson, Johan Elmander and many more, came to dominate Swedish football with league titles in 2002, 2003 and 2005 and cup titles in 2002, 2004 and 2005 – and I was of course hooked for life.

My dad had taken me to my first football matches but by 2005 I had started going more regularly with friends. Having seen the club line up title after title (including the 2005 double) on TV I was of course very anxious to experience the ‘real deal’ myself, to climb down the stands and run onto the pitch in celebration of yet another triumph. Little did I know how long I would have to wait and the amount of suffering I would have to endure.

After those double titles in 2005 things rapidly fell apart. The following 13 years consisted mostly of pain, embarrassment and constant worries. Losing 6-0 away to IFK Göteborg, 5-1 away to Kalmar FF, and 5-1 away to Åtvidaberg brings up many ‘fond’ memories of long, quiet trips back home. So too does the horrid 2009 season when the threat of relegation hung low over the club. Nearing the end of a disastrous season, three wins were needed from the last three matches – and that only to reach the relegation play-off spot. Getting there, only to lose 2-0 away to Assyriska in the first leg, a miraculous 116th minute 3-0 winner from Mattias Jonson finally shut the relegation trapdoor without us going down through it. The last couple of minutes and the ensuing pitch invasion are some of my best memories looking back, nearly beating the trophies that would come much later on. There’s something special about a comeback like that, snatching victory from the jaws of defeat at the very last moment after having been ruled out for an entire season.

Crowd troubles were common for a couple of seasons when everything looked as darkest. Pitch invasions and abandoned matches, assaulted referees and opposition players, threats (real and perceived) against players and club officials, riots against the police and violence amongst supporters were a constant threat, it seemed all hell could break loose at any given moment. It all culminated very sadly on March 30th 2014 when a supporter lost his life just minutes before the away match against Helsingborg kicked off. Me and my friends stayed in the stands for well over an hour after the match had been abandoned, with riots on the streets outside the stadium. I will never forget the feeling of meaninglessness and emptiness. After a sleepless night train back to Stockholm I tied my scarf to the fence of the 1912 Olympic Stadium where a memorial site had been organized.

The club’s finances were for a period a constant worry and at one point bankruptcy looked likely until Daniel Amartey could be sold to Copenhagen. From then on results were slowly getting better but soon a new source of pain emerged: failing to win any of the most important matches – the Stockholm derbies – for a long time of course drew massive amounts of ridicule from our rivals. It didn’t seem to matter how much things looked to be in our favor before kickoff, or how many goals we were up – we just couldn’t win.

But all this only strengthened me and my friends. Having traveled up and down the country during the darkest years we were starting to dream of new victories again, although quietly so at first. Amidst the chaotic first part of the 2013 season, with the manager and chairman having just abandoned ship after a series of losses and some ’hard words’ from supporters, we had suddenly been given a surprise chance. Playing IFK Göteborg in the cup final we again had our eyes on a title, but eventually losing in a penalty shootout we would have to wait 5 more years until we got another chance. By then the club had been almost transformed.

With Bosse Andersson and Henrik Berggren back in the club, finances were slowly improving year after year, and with Kim Källström and Andreas Isaksson back in the lineup, a third place was secured in 2017. With it came a much awaited chance to travel abroad for the next season. Having spent 10 years regretting not going to Tallinn and Trondheim in 2008 I wouldn’t make the same mistake of waiting out ’better’ trips again. The 2018 European campaign began and ended in Odessa after a dodgy penalty for 2-1 in extra time and a 3-2 loss on aggregate, but the whole trip felt like a huge bonus after finally winning a trophy a couple of months earlier.

The 2018 cup win felt like a massive payoff after more than a decade of blood, sweat and tears and after sweeping Malmö 3-0 at home (and AIK 2-0 away in the semi, at last!) I was on a high for weeks and months. But despite finally standing triumphant the ultimate prize still haunted me. Winning the short and unpredictable cup was one thing, going the distance and competing over 30 rounds for the league title was something completely different.

The 2019 Season

Going into the 2019 season I didn’t expect much. New coaches Thomas Lagerlöf and Kim Bergstrand were known for their systematic approach at Sirius, but also for their long playing careers at AIK so they would have to work hard to convince me and many others. You could immediately see they’d done wonders to the team’s organization and discipline on the pitch though, and if it wasn’t for an extra time defeat to Häcken in the semi final, I’m sure they’d steer the team to repeat the cup triumph from the year before, with AFC Eskilstuna waiting in the final.

The team seemed to struggle due to injuries and sickness during the first part of the season but still managed to top the table after refusing to lose, most notably winning 1-0 away to Häcken where we had lost 5-0 the year before. The losses finally came against Hammarby and AIK and what had looked like a promising start now felt just like any season again. But the players stepped up and with the injury situation improving we were back at the top well after the half-season mark, only briefly surpassed by arch rivals AIK for two rounds. The table was starting to settle now, and it was getting clear that the four big clubs Djurgården, Malmö, Hammarby and AIK would battle it out for the title.

When it was time to face Malmö away we were three points clear and had a great chance to make ourselves strong favorites for the title just by avoiding a loss. I had run my simulations to investigate different scenarios and it was clear that this match was something of a crossroad. If we lost we would lose momentum and have a hard time to defend the lead, but a win or a draw would be a big step on the way. Unfortunately I couldn’t join my friends for the trip and had to watch the match at home, something I absolutely hate as I get so much more nervous when I can’t be in the stadium. Looking back this was definitely my most nervous day prior to the last one as I knew how crucial the match was. It’s the toughest away match in Sweden but the players stood up well and when Mohamed Buya Turay scored on a beautiful counter attack and Tommy Vaiho saved a penalty just minutes later, I nearly had a heart attack. We won that match and I was now starting to believe we could make it. Unfortunately we lost to both AIK and Hammarby after that but the Malmö win had given us room for errors and with just one match to go we were still on top of the table.

The title race up until the last match had been extreme. With one round still to be played there were now three teams above 60 points for only the third time ever, and it looked likely there’d be four teams above that threshold for the very first time when all was said and done. Usually you’d win by taking 60-62 points but now you would have to take home much more than that to lift the trophy. AIK had dropped out of the title race in the 29th round but the four biggest clubs in Sweden had really pushed each other to extremes this season, and it would all be decided in the very last round.

The conditions were clear going into the last round: Djurgården were on top and could afford to draw away to Norrköping as Malmö and Hammarby were three points behind. Having to look to Norrköping for help, Malmö played away to a Örebro with nothing to play for while Hammarby at home faced Häcken, also with nothing to play for. They both needed to win to take the title by goal difference, with Malmö having the upper hand there with +35 against Hammarby’s +34. If equal on goal difference Hammarby would take it all thanks to their superior goal record.

As indicated by betting odds and my own simulations, title chances looked close to 70%, 20% and 10% for Djurgården, Malmö and Hammarby respecively.

Match Day

Waking up much too early I spent the morning battling nervousness and when it was finally time to leave I apparently just grabbed a bottle of whiskey and mumbled some strange kind of goodbye to my very understanding girlfriend. The nervousness had to be countered with Irish Coffee’s for breakfast in the backseat of the car and some pre-kickoff beers once arrived, despite my intention of keeping the drinking to a minimum so I could stay sharp. It was just enough to calm my nerves and I was starting to feel very optimistic about the day, with a strange kind of euphoria kicking in.

Kickoff

By the time the referee blew the whistle I had made the mistake of trying to find a working toilet with just 30 minutes till kickoff. Naturally the away stand was jam-packed when I came back and I had no way of getting through to my friends. Walking round the stand to find some space in between it and the pitch, I just managed to take up position to the right of Norrköping’s goal before the ball was in play. According to the odds we had about a 70% chance for the title and I’d made the calculations myself the night before but my optimism now made it feel like 90% and I was anxious to get on with it.

8’ – 1-0

Just a couple of minutes in Norrköping got a corner at the far end of the pitch and after some minor crowd disturbance delaying it, the ball ended up in the net behind Tommi Vaiho. The away stand fell silent for a moment while the home fans exploded in taunting celebration. But singing soon picked up again and I was still confident we could make it, after all we only needed one goal and there was plenty of football left. Our chances had just dropped to about 40% but still optimistic, it felt more like 75% to me.

15’ – 2-0

If the first goal was a slap in the face, the second was a kick in the teeth. Just 7 minutes later we were suddenly 2-0 down and had a mountain to climb to take home the title. Optimistic as ever though, I had no room for negative thoughts. It was still early, we’d started to take control of the match despite conceding again, and eventually the will to win surely must weigh over in our favor as Norrköping’s only motivation was to ruin our day. I didn’t know it but we were down to about 20% now. My optimistic psychosis didn’t loosen its grip though and to me it was now a 50/50 shot.

Half time

When half time came I climbed up to the top of the stand to find my friends. Not much was said but I could feel they weren’t as positive as I was. But it was still just two goals so I tried to spread some hope. Thankfully, no one had given up yet.

50’ – 2-1

When play resumed Djurgården continued to dominate, applying that slow, patient and grinding control that had resulted in so many late winners during the season. In the 50th minute it finally paid off when Jesper Karlström met a cleared corner with his right foot, guiding the ball into the back of the net. The stadium exploded with Djurgården supporters everywhere but the home stand. We were back to about a 40% chance for the title now but it felt like we were all the way back to where we had started at 70%. Surely, the goal would come?

65’ – 2-2

Djurgården had been piling on the pressure since the goal and 10 minutes later Emir Kujovic got the ball on the left side of the box and whipped in a hurried half shot, half cross. The ball didn’t need to travel far from Mohamed Buya Turay’s foot for me to see what was going to happen. Standing high up in the away stand I was in a perfect line with Turay and the keeper, and suddenly reality kicked in. My optimistic psychosis was completely gone and not even seeing the goal, I immediately sat down and started crying tears of joy, and of relief. Soon my close friend, always on the lookout for jinxes to clamp down on, pulled me up and scolded me before giving me a hug: “Not yet you idiot, there’s still much left!”. In reality we’d jumped up to nearly a 80% chance but my mindset had reversed a full 180 degrees and I now felt we were back at a 50/50 shot, at best.

75’ – Tick, tock…

Time was moving extremely slowly now and I was starting to get way too nervous. A 73rd minute red card for Norrköping did help to calm me down but despite time actually working for us now I was still pessimistically feeling a 50/50 shot. Back in the real world, we were approaching 90%.

90’ – So close

Stoppage time was announced and seeing the number 5 come up didn’t help to calm my nerves. Elliot Käck’s 93rd minute tackle giving Norrköping one last real chance with a free kick out on the wing nearly gave me a heart attack but the players managed to keep the home team at bay while my friend loudly cursed anyone who dared celebrate too early.

96’ – The Final Whistle

At 95:06 the referee finally blew the whistle and the pitch invasion started in wild celebration. We remained in the stand for a minute, hugging everyone we could find, before slowly climbing down and onto the pitch. It was a surreal feeling, like it all happened in slow motion, with people and manic euphoria all around us. In the centre circle we met more friends, some of them having travelled to Norrköping without any tickets yet somehow managing to enter the stadium through the away stand just as the final whistle blew. We stood there hugging, singing and celebrating as the players came out and the trophy was finally lifted. After 14 years of waiting and nearly 10 years of agony since the dramatic play-off match in 2009, we’d made it.

Epilogue

It took me a while to realise what had actually happened. I had dreamed of it my entire life but it still felt so unreal. It was only a couple of weeks after the match it finally set in that we had won and I could start to enjoy it for real. 

With the Corona virus delaying the start of the 2020 season and Allsvenskan kicking off without any crowds tomorrow I am ever more thankful for the win, as it would without a doubt feel even more strange without it. I don’t know how long it will take until me and my friends can discuss players, transfers, managers, referees and everything else over a couple of beers before seeing Djurgården play again, but I do know that fulfilling a lifelong dream last November certainly will make the wait so much easier.

A brief technical explanation

Historic in-play odds are hard to find but signing up for a free trial at Statistic Sports I found something I could work with. Using 3-way next goal odds I was able to derive goal expectancies (using a method I will keep undisclosed) for each team in the three relevant matches. There were only updated odds available about every minute or so and I wanted to calculate percentages for every second so I just had to assume that odds remained unchanged between updates. In reality this isn’t the case as odds can change many times per minute but it was good enough for me. Using the goal expectancies and the manually inputted goals scored I used a very simple Poisson approach to populate a correct score matrix for each second of each match.

Now, instead of having to simulate all three matches every second to get a set of final tables and win percentages, I instead calculated which unique combination of results would end up in a league title for Djurgården, Malmö and Hammarby respectively. With a correct score matrix of 0 to 10 goals this meant 121 possible results per match, and 1,771,561 unique combinations in total. This took way too long for my liking so after studying the table as it looked at the start of the last day I instead chose to work with goal differences as individual goals didn’t matter, only goal differences. With the same 0 to 10 matrix this left me with 11 goal differences per match and 1,331 in total, a much smaller number.

Having all possible goal difference combinations linked to their respective title winner I could now easily calculate win percentages for each second. Keeping everything on the same scale I started off at the official kick off time 13:00:00 and went from there, manually fitting it with the (real and game) time stamped odds to come up with the underlying data for the graph.

This blog post is one of the half-done follow-ups to the staking post I did back in 2017. I wrote most of it at the same time as the original post but busy with work and other projects I never got to finishing it until now. What prompted me to finally publish was an interesting discussion on Twitter on how to best track your bets. The discussion fit well with what I had intended to say with the post so here you go, my first (and last) blog post of 2019.

Ok, so we start out with the same situation as last time: a punter has set out to bet on 10,000 coin flips. The big difference here is that he doesn’t know if the coin is fair or not, i.e. if he has an edge or not. He can choose to quit at any time though, so if he suspect he’s getting the worst of it he can just call it quits and save his time (and money). Speaking of time, manually flipping 10,000 coins is some task and as our punter has other things to do on most days, he’ll limit his betting to 10 flips a day. This will make the total series of 10,000 flips take 1,000 days, or roughly 2.7 years.

And now to the main point of this exercise. The result of each coin flip is recorded by a trustworthy third party and made available to all parties only when time for settlement. The bets should be settled on a regular basis but exactly how often is up to the punter: every day, week, month or year?

Now remember that our punter doesn’t know what his edge is, or even if he has one. What time frame should he choose to settle his bets on? In the real world, there’s probably no correct answer as this is mostly down to individual factors like total net worth, appetite for risk, tolerance of variance etc etc.

But, we can try to gain some insights by simulation. Using the coin flipping code from last time (ignoring the bankruptcy part) and adding on a function to compare the different settlement intervals we can run a simulation of the punter’s 10,000 coin flips to see how the results would look if he were to settle the score by each day, week, month or year.

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import seaborn as sns

sns.set()

def coin_flips(n=10000,odds=1.97,bankroll=100,stake=1,bankrupt=False):
    '''
    Simulates 10000 coinflips for a single punter, betting at 1.97 odds,
    also calculates net winnings
    
    NEW: default bankroll and stake set at 100 and 1, respectively
    now also calculates if player went bankrupt or not
    '''
      
    # create a pandas dataframe for storing coin flip results 
    # and calculate net winnings
    df = pd.DataFrame()
    # insert n number of coinflips, 0=loss, 1=win
    df['result'] = np.random.randint(2,size=n)
    # calculate net winnings
    df['net'] = np.where(df['result']==1,stake*odds-stake,-stake)
    # calculate cumulative net winnings
    df['cum_net'] = df['net'].cumsum()
    
    # calculate total bankroll
    df['bankroll'] = df['cum_net'] + bankroll

    # if bankroll goes below the default stake, punter will stop betting
    # count times bankroll < stake
    df['bankrupt'] = np.where(df['bankroll']<stake,1,0)
    # count cumulative bankruptcies, with column shifted one step down
    df['bankruptcies'] = df['bankrupt'].cumsum().shift(1)
    # in case first flip is a loss, bankruptcies will be NaN, replace with 0
    df.fillna(0,inplace=True)
    # drop all flips after first bankruptcy
    if bankrupt:
        df = df[df['bankruptcies']==0]
    
    return df

def compare_scales(n=10000,odds=2.03,n_day=10,df=False):
    '''
    Puts coinflips on a timeline to
    10/flips per day, 30 days/month
    '''
    
    # if no df specified, create a new one
    if not df:
        # create df of a single punter's coinflips
        df = coin_flips(n,odds)
        
    # calc number of days
    days = n / n_day
    # ...weeks
    weeks = n / (n_day*7)
    # ...months
    months = n / (n_day*30)
    # and years needed
    years = n / (n_day*365)
    
    # insert days
    df['days'] = np.repeat(np.arange(1,days+1),n_day)
    # ...weeks
    df['weeks'] = np.repeat(np.arange(1,weeks+2),n_day*7)[:n]
    # and months
    df['months'] = np.repeat(np.arange(1,months+2),n_day*30)[:n]
    # and years
    df['years'] = np.repeat(np.arange(1,years+2),n_day*365)[:n]
    
    # list of scales
    scales = ['days','weeks','months','years']
    
    # figure, subplots
    f, axes = plt.subplots(2,len(scales),gridspec_kw={'height_ratios':[len(scales),1]},
                           sharey='row', figsize=(12,6))
    # reorder axes
    day_axes = [axes[0][0],axes[1][0]]
    week_axes = [axes[0][1],axes[1][1]]
    month_axes = [axes[0][2],axes[1][2]]
    year_axes = [axes[0][3],axes[1][3]]

    axes = [day_axes, week_axes, month_axes, year_axes]
    
    # loop through views, groupby and calc cum net,
    # plot cum net and 'view' net
    for s, ax in zip(scales,axes):
        # groupby, recalc cumnet
        group = df.groupby(s).sum()
        group['cum_net'] = group['net'].cumsum()
        
        # plot total cumulative net as line
        group['cum_net'].plot(ax=ax[0])
        # and daily/weekly/monthly net as bar
        group['net'].plot(ax=ax[1],kind='bar',linewidth=0)
        
        # clean up lower plot x axis
        ax[1].set_xlabel('')
        ax[1].set_xticklabels('')
        ax[1].grid(False)

        # insert horizontal line at breakeven on both plots,
        # add label
        for i in ax:
            i.axhline(color='k',alpha=0.5)
            i.set_ylabel('Net profit')


    # fix the yearly y-tick labels to show whole years only
    ax[0].set_xticklabels(['1','','2','','3'])

    # 'fix' layout
    plt.tight_layout()
    # show plot
    plt.show()

Running the compare_scales() function returns a graph of the simulation results. With the default 2.03 odds (an 1.5% edge on a fair coin) it could look like this (though this particular results graph was chosen to prove my point):

So the above graph is the results of the same 10,000 coin flips settled on different time frames, or scales. We can see that our punter ended up a clear winner, making a stable profit every year. But what if he’d been settling his bets by the end of every day? Would he, not sure whether he really had an edge, resist the urge to quit and do something else with his time (and money) after being roughly breakeven sometime after 100 days? We can never know of course, but by settling the bets every day our punter exposed himself to a lot of randomness, opening up for a very bumpy mental ride as he had to face many losing days. We know he had an edge, but he didn’t, and having to pay up again and again he might just had called it quits then and there. The same goes for the huge downswing leading up to 400 days. Would he have weathered the storm?

My point here is that if he’d chosen a longer time frame to settle on, he wouldn’t even know about his losing days. Settling by the end of each week would see him exposed to a lot more winning than losing settlements, and even more so if he’d chosen months or years. This would of course increase the likeliness of our punter staying in the game to eventually profit from his edge. On the other hand, it could have prevented him from realizing he was losing badly, having to face a very expensive settlement he could have avoided by settling more often.

Keeping track of your results is of course crucial to betting success as you want to know how, when, where and why you win or lose to be able to improve your underlying process, but if you expose yourself to too much randomness you risk clouding your judgment and make changes to what could be a profitable betting process, or maybe even quit – not realizing you actually had an edge.

I’m not saying you shouldn’t track your bets at all, and I’m not saying you should only look at your betting results once a year – what I am saying is that you should try to avoid making decisions based on randomness. It’s an easy mistake to make and I see it all the time on Twitter, from people touting their daily betting ROI to discussions about the Expected Goals score of an individual football match. It’s human nature, but you should still try to avoid falling into the trap.

Even if you have an edge, the results of any football match or betting day, week or month will likely be due to a lot of randomness and are most often irrelevant. What matters are the decisions behind the results.