Draws And Ties, Averages Are Lies

Baz commented, passing on some thoughts on the Draw from Winabobatoo's Mike Lindley. I hope no one takes offence at my reproducing the comment in full:

Hi Cassini, I recall you believe fewer goals equals more draws, I'm not saying you're wrong, but here's an extract from Mike Lindley of the Winabobatoo weekly magazine, he's changed his mind. Copy and past from Mag.

"Is there a reason why some seasons produce higher/lower draws? Some years ago, I had a theory that if fewer goals were scored, the chance of a draw occurring would increase. In games that have two goals or fewer scored, the possible scorelines are 2-0; 0-2, 1-1, 1-0, 0-1 and 0-0. Out of the six possible combinations, two outcomes (33%) are draws. When up to three goals are scored in a game, the possible outcomes are 3-0, 2-1, 2-0, 1-0, 0-3, 1-2, 0-2, 0-1, 1-1 and 0-0. Out of the 10 possible combinations, there are only two combinations that result in a draw (20%). Do fewer goals mean more draws? The next table shows the average goals per game in each of the last 11 seasons:

The 2010-11 season saw the highest average goals per game but there were 26.88% draws, losing just -4.47%. The two rows at the bottom (the two lowest average goals seasons) do have smaller losses from backing the draw which does tie in with my theory, but 2006-07 was the 9th lowest for goals and draw bets lost -17.19% in that season. That blows my theory completely out of the water!

I can say that I've spent more hours than I care to remember over the last 17 years trying to fathom out the draw, and I always come back to the same conclusion: it's a semi-random result that we have no control over. We never know when it's going to be a pain, and we never know when it's going to go quiet. What we do know is that the evidence clearly shows that it eats up more than its fair share of the bookmakers' over-round. This means betting with the draw is the better long-term option than betting without the draw - Mike Lindley"

Mike's numbers above show that roughly 26.4% of matches result in a draw. 

Although I have no idea what leagues are included, it makes little difference - the last three completed seasons for the leagues I follow have 26.01% of matches ending as draws, but I do question whether the 'average' is useful when analysing the Draw. More on that later.

Yes, fewer goals will tend to result in more draws. 

An easy way to understand why, is to compare the relatively low scoring sport of football with higher scoring sports.

Ice hockey (NHL) averages around 5.35 goals per game and in the 2014-date period has had 1,116 draws (ties) from 4,601 games, i.e 24.25%, which is a lower Draw rate than football, but not that much lower. In fact the 24.25% is exactly the same as the lowest completed season from Mike's list above.  

Now we turn to baseball which in the three seasons 2014-16 averaged 8 runs a game and which saw 641 draws (ties) from 7,387 games, a Draw percentage of 8.7%.

English Premiership Rugby 2010-16, 792 matches averaging 43.19 points a game, and just 22 Draws, 2.78%.

American Football 2014-date, 782 matches averaging 45.6 points a game, 46 draws (ties), which is a Draw percentage of 5.9%.

For anyone wondering why American Football has a higher Draw percentage than Rugby, despite a similar points per game total, I believe this is due to greater parity in American sports. 

NBA basketball 2014-date, 3,226 matches averaging 203.5 points a game, resulting in 174 Draws (ties), a Draw percentage of 5.4%.

And finally a quantum leap to Test Match Cricket, 1877-date, 2,247 matches, with one tie - December 1960 Australia (505 + 232) v West Indies (453 + 284) - 0.04%.

I could go on, but it should be clear by now that the higher scoring an event, the less likely it is that a draw, or a tie will result. 

Mike's mistake is in comparing goals per game averages that are very close to each other, and expecting to see a difference in the number of resulting draws from a small sample.

My example above shows that even the jump in scoring from football (2.61) to ice hockey (5.35) only results in a small percentage decrease in Draws. The percentage drops more dramatically as the points per game climbs into double and triple digits, but to all intents and purposes, the difference between 2.29 and 2.76 in Mike's sample is negligible.

The image below from the interesting Eighty Five Points shows how a more significant decline in goals between 1960 and 1980 resulted in a noticeably higher number of draws:

The author notes "The uptick in draws in the 60's coincides with a drop in goals/game (it's a small effect though)". 

Another way of confirming that fewer goals means more draws is to look at the Under / Over 2.5 results. Some of you may remember that years ago I suggested backing the Unders as a less volatile alternative to backing the Draw, which can result in long losing runs even with value on your side. 

In the four completed EPL season for which we have Pinnacle's Closing (i.e. most accurate) prices, 2012-16, 727 matches went Under, 783 went Over. 70.47% of the draws were also Unders, i.e. were 0:0 or 1:1.

37.4% of Unders games ended as Draws. When three or more goals are scored, only 14.38% of matches ended in Draws.

I mentioned at the beginning that I don't feel using averages is helpful in this debate. The average (mean) Draw price on the four season sample is 4.11, and blindly backing the Draw at higher than this price isn't a sensible strategy and would have cost you 88.84 points. 

The Draw price is higher sometimes than others, for a reason. 

Given that backing every Draw would have 'only' lost you 43.01 points, and it doesn't take a genius to work out that there was value backing the Draw up to a certain point. I've previously referred to this basic system as the Draw-4 (it's catchier than the Draw-4.11, and the 4.0 / Implied Probability 0.25 is close enough) but if you're going to be backing the Draw, you're generally not helping yourself by looking at games like Manchester City v Cardiff City at 12.38.

The above table shows the average Draw odds (Avg D) from Pinnacle, with numbers for the Under / Over totals as well as highlighting the futility of backing Draws with a sub ~25% probability.

In conclusion, in my opinion Mike is expecting too much from small differences in goals per game, and in using sweeping averages.

The two images to the left are from one of my spreadsheets sorted by Goals Per Game. 

On top we'd expect the Draw percentages to be higher, while the below image showing the lowest, should see the Draw percentages lower.

Overall it looks reasonable - the lowest goals per game did result in a lot of 29% and higher draws but there are some anomalous 25% seasons in there.

Conversely, while there's a lot of red in the second image, there are some rogue greenies in there. The correlation is never going to be perfect or perhaps even close to it, but the fewer the goals, the higher the probability of a Draw.

Mike concluded that the Draw is "a semi-random result that we have no control over. We never know when it's going to be a pain, and we never know when it's going to go quiet". 

Aren't ALL bets "semi-random"? Football is "semi-random" because it is low scoring and luck often plays a big part. The best team doesn't always win. Would we have it any other way? 

As for not having 'control over' it, I'm not really sure what that means. We have control over what bets we place and how much we stake, but of course we can’t control results. 

Every time you place a bet, you risk taking a loss, but you can help yourself hugely by researching trends and identifying areas where value is more likely to be found, and just as importantly eliminating bets where value is unlikely to exist.

Yes, there's the occasional Draw at 10.0 that's a winner (e.g. Manchester City v Sunderland in 2013-14) and backing long-shot Draws in the second half of the season in this sample would have been profitable, but bet before Xmas and you'd have had just the one winner at longer than 5.5 - from 65 bets. Ouch.