Betting on football
July 2009 (index)
A look at patterns in betting odds for English Premiership football (soccer) over the past few years.
The data is all taken from betexplorer.com, a site that has archive results and betting odds for many sports, countries, and seasons. We'll only look at English football here. For each match we extract the following: date; names of home and away teams; goals scored by home and away teams; and pre-match odds of home-win, draw, away-win.
First a summary of the results for the last season to check they are being read correctly:
380 games
184 home wins (48%)
95 away wins (25%)
101 draws (26%)
587 home goals (1.54 per game)
405 away goals (1.07 per game)
Next we can take a look at some simple betting strategies. What happens if we bet 1 unit on all three possible results for all matches? Overall we bet 3x380=1,140 units and in the 2008-09 season we would have got back 1,012.78 for a loss of 11.2%.
Strategy Winnings Bets Net Net(%)
------------------------------------------------------------
All 2008 1012.78 1140.00 -127.22 -11.2%
Home or away
But not all bets are created equal. Looking at strategies of betting on home-win, away-win, or draw:
Strategy Winnings Bets Net Net(%)
------------------------------------------------------------
Home 2008 356.74 380.00 -23.26 -6.1%
Draw 2008 343.36 380.00 -36.64 -9.6%
Away 2008 312.68 380.00 -67.32 -17.7%
None of these are winning strategies, but there seems to be a bias towards the home team. We can see if this holds in other years.
Strategy Winnings Bets Net Net(%)
------------------------------------------------------------
All 2004 993.55 1140.00 -146.45 -12.8%
All 2005 965.08 1140.00 -174.92 -15.3%
All 2006 1002.55 1140.00 -137.45 -12.1%
All 2007 968.05 1140.00 -171.95 -15.1%
All 2008 1012.78 1140.00 -127.22 -11.2%
All TOTAL 4942.01 5700.00 -757.99 -13.3%
Home 2004 351.73 380.00 -28.27 -7.4%
Home 2005 393.09 380.00 +13.09 +3.4%
Home 2006 382.25 380.00 +2.25 +0.6%
Home 2007 342.48 380.00 -37.52 -9.9%
Home 2008 356.74 380.00 -23.26 -6.1%
Home TOTAL 1826.29 1900.00 -73.71 -3.9%
It seems that "Home" is consistently a less bad bet than the others.
Favourite or underdog
We can do a similar analysis on whether it's generally to bet on the favourite, the underdog or the "middledog" (neither the favourite or the underdog of the three results).
Strategy Winnings Bets Net Net(%)
------------------------------------------------------------
Favourite 2004 352.44 380.00 -27.56 -7.3%
Favourite 2005 385.35 380.00 +5.35 +1.4%
Favourite 2006 348.66 380.00 -31.34 -8.2%
Favourite 2007 381.87 380.00 +1.87 +0.5%
Favourite 2008 372.69 382.00 -9.31 -2.4%
Favourite TOTAL 1841.01 1902.00 -60.99 -3.2%
Middledog 2004 372.18 378.00 -5.82 -1.5%
Middledog 2005 307.09 380.00 -72.91 -19.2%
Middledog 2006 324.61 378.00 -53.39 -14.1%
Middledog 2007 320.03 380.00 -59.97 -15.8%
Middledog 2008 327.06 378.00 -50.94 -13.5%
Middledog TOTAL 1650.97 1894.00 -243.03 -12.8%
Underdog 2004 268.93 382.00 -113.07 -29.6%
Underdog 2005 272.64 380.00 -107.36 -28.3%
Underdog 2006 329.28 382.00 -52.72 -13.8%
Underdog 2007 266.15 380.00 -113.85 -30.0%
Underdog 2008 313.03 380.00 -66.97 -17.6%
Underdog TOTAL 1450.03 1904.00 -453.97 -23.8%
(Our implementation means that that if two of the three odds are equal then they're both favourites or both underdogs, hence we have slightly fewer middledog bets than others.)
Again a pretty clear pattern, similar to home/draw/away. This time it seems that betting on the favourite is the least bad option.
Take
All six of the simple bets we've looked at so far give a negative return overall. To understand this it's instructive to look at odds for a few games.
The odds are shown as "decimal odds": the number of units you get back if you win per one unit bet. Decimal odds are always at least 1 (you'd never bet if you couldn't get your stake back), and they're nicer to deal with than the traditional 100-30, 7-2 or 1-2.
Supposed we're forced to bet on a match against our will with a gun against our heads (an albeit implausible scenario). Is there a strategy we can take to avoid a big loss? For a concrete example we'll suppose the match has odds of (1.93,3.38,3.78) for (home-win,draw,away-win) respectively (taken from Wigan-Portsmouth on the last day of the 2008-09 season.)
If we bet amounts 1/1.93, 1/3.38, 1/3.78 then we're guaranteed to get back exactly 1 no matter what the result of the match. But unfortunately the total amount we'd have to bet is 1/1.93 + 1/3.38 + 1/3.78 = 1.079.
So we can bet 1.079 and get a guaranteed 1.000 back; or (scaling the bet) bet 1.000 and get a guaranteed 0.927 back for a loss of 7.3%. This is the "take". If it were nil or positive then bookmakers wouldn't make any money and would go out of business.
If we bet in any way other than the ratio 1/1.93 : 1/3.38 : 1/3.78 then there will always be at least one possible result that gives a bigger percentage loss.
What about other sets of odds? Looking at all 380 matches during the 2008-09 season shows a median of 7.4% for the take. This seems fairly stable across recent seasons.
We can think of the odds as implying a probability distribution, once we've allowed for the take. In our example odds of (1.93,3.38,3.78) imply probabilities of (0.927/1.93,0.927/3.38,0.927/3.78), or (48%,27%,25%). We'll call betting in these proportions (0.48 on a home win, 0.27 on a draw, 0.25 on an away win) the "implied probs" strategy. Betting this way gives a loss of around 7-8%.
Strategy Winnings Bets Net Net(%)
------------------------------------------------------------
Implied probs 2004 344.84 380.00 -35.16 -9.3%
Implied probs 2005 347.00 380.00 -33.00 -8.7%
Implied probs 2006 347.69 380.00 -32.31 -8.5%
Implied probs 2007 351.57 380.00 -28.43 -7.5%
Implied probs 2008 355.10 380.00 -24.90 -6.6%
Implied probs TOTAL 1746.21 1900.00 -153.79 -8.1%
Arbitrage
However there are some odd results. Nine matches have a negative take (a "give"?), with odds of:
(3.83,5.37,5.75)
(4.08,5.10,4.64)
(4.23,5.02,3.81)
(2.44,3.50,6.69)
(3.18,3.29,3.08)
(1.42,5.82,13.92)
(2.46,3.20,4.13)
(1.45,5.03,10.74)
(2.86,3.15,3.09)
(2.79,3.25,2.99)
(3.04,3.24,2.55)
The first three of these (and the fifth) make the guaranteed profit aprticularly clear: since the decimal odds are all 3 or higher, just bet equal stakes on each possible outcome and you're guaranteed a profit.
I'd be surprised if any single bookmaker offered a set of these odds as they'd leave themselves open to a guaranteed loss. (Although an enterprising but not very numerate chap running a book at my school sports day when we were both teenagers did make such a mistake. However he was shrewd enough to refuse multiple bets so I couldn't take advantage of it.)
The home/draw/away odds we're using come from a range of bookmakers, picking the best odds in each case. So any single bookmaker might be happy with all the odds he's offering.
Betting following this arbitrage strategy (bet the implied odds strategy if the take is negative, otherwise don't bet) gives the following:
Strategy Winnings Bets Net Net(%)
------------------------------------------------------------
Arbitrage 1998 0.00 0.00 +0.00
Arbitrage 1999 1.00 0.68 +0.32 +47.0%
Arbitrage 2000 0.00 0.00 +0.00
Arbitrage 2001 0.00 0.00 +0.00
Arbitrage 2002 0.00 0.00 +0.00
Arbitrage 2003 0.00 0.00 +0.00
Arbitrage 2004 0.00 0.00 +0.00
Arbitrage 2005 0.00 0.00 +0.00
Arbitrage 2006 0.00 0.00 +0.00
Arbitrage 2007 7.00 6.68 +0.32 +4.8%
Arbitrage 2008 9.00 7.65 +1.35 +17.7%
Arbitrage TOTAL 17.00 15.00 +2.00 +13.3%
The past few years are highly unusual in offering such opportunities. It's hard to know whether this is a change in the betting market or just bad data.
Other strategies
We saw that a home win offered better returns than a draw or away win; and betting on the favourite gave better returns than the underdog or middledog. Can we combine the two and bet only on the home team when it's a favourite? This is close to break-even but not good enough to beat the take.
Strategy Winnings Bets Net Net(%)
------------------------------------------------------------
Home favourite 2004 270.14 287.00 -16.86 -5.9%
Home favourite 2005 293.01 286.00 +7.01 +2.5%
Home favourite 2006 280.50 288.00 -7.50 -2.6%
Home favourite 2007 272.32 271.00 +1.32 +0.5%
Home favourite 2008 266.65 281.00 -14.35 -5.1%
Home favourite TOTAL 1382.62 1413.00 -30.38 -2.2%
Note that using this strategy we bet on nearly 75% of matches: the home team is usually the favourite.
Conversely, betting on the away team only if they're the underdog is pretty disastrous:
Strategy Winnings Bets Net Net(%)
------------------------------------------------------------
Away underdog 2004 99.71 199.00 -99.29 -49.9%
Away underdog 2005 120.48 200.00 -79.52 -39.8%
Away underdog 2006 143.96 207.00 -63.04 -30.5%
Away underdog 2007 101.98 212.00 -110.02 -51.9%
Away underdog 2008 152.09 206.00 -53.91 -26.2%
Away underdog TOTAL 618.22 1024.00 -405.78 -39.6%
We can refine the "home favourite" approach. The strategy "bet on the home team if its implied probability of winning is over 50%" gives:
Strategy Winnings Bets Net Net(%)
------------------------------------------------------------
Home if 50+% 2004 110.68 122.00 -11.32 -9.3%
Home if 50+% 2005 139.50 129.00 +10.50 +8.1%
Home if 50+% 2006 119.80 126.00 -6.20 -4.9%
Home if 50+% 2007 157.98 143.00 +14.98 +10.5%
Home if 50+% 2008 126.90 132.00 -5.10 -3.9%
Home if 50+% TOTAL 654.86 652.00 +2.86 +0.4%
Changing "50%" to different values:
Strategy Winnings Bets Net Net(%)
------------------------------------------------------------
Home if 30+% TOTAL 1510.66 1563.00 -52.34 -3.3%
Home if 40+% TOTAL 1152.79 1164.00 -11.21 -1.0%
Home if 50+% TOTAL 654.86 652.00 +2.86 +0.4%
Home if 60+% TOTAL 328.11 331.00 -2.89 -0.9%
Home if 70+% TOTAL 167.77 175.00 -7.23 -4.1%
Home if 80+% TOTAL 11.33 12.00 -0.67 -5.6%
Home if 90+% TOTAL 0.00 0.00 +0.00
Data mining and over-fitting
The danger here is that if we try a lot of strategies then some of them will be good just by chance for a particular season or period. It doesn't mean they'll work in other seasons.
To avoid this problem we should have a set of training data which we use to find a strategy, and then use independent test data to see if it really works.
Summary so far
There are some patterns in the data. Home teams and favourites do better than the probabilities implied by the odds would suggest. But this isn't enough to overcome the take.
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