Tuesday 27 January 2015

To Hull And Back - The Statistical Probabilities Of The Title Run In


There's around a third of the EIHL season to go and we've got 5 teams not just in contention for the title but with their destiny in their own hands. 

Due to the fixture least meaning all of the top teams have to play each other at least once any team that wins out from here is guaranteed to be champions. It would be a surprise to see anyone go 15-0-0 or 17-0-0 from now until late March but they all know that nobody can catch them if they do.

The last close title race involving multiple teams was in 2010/11 when Sheffield just pipped Cardiff and Belfast. Just one point separated those three teams in the final standings and we are probably in for a similarly close finish this season. The Steelers came out on top largely because of their record against their rivals in the late-season matches. They won in OT in Cardiff and then against them at home the following night. The Steelers and Giants split their two remaining games, as did the Devils and Giants. Sheffield's 6 points gained compared to Cardiff's 5 and Belfast's 4 determined the final standings. If just one of those wins goes the other way the title changes hands.



There are still 22 games to be played between the top 5 teams and it would be logical to say whoever comes out on top in those games will be the champions but it's not quite that straight forward. Look at how many games against the top 5 each team has left:

Braehead 5
Cardiff 9
Belfast 9
Sheffield 10
Nottingham 11

Which means the teams have the following games remaining against opponents in the bottom half of the league:

Braehead 10
Cardiff 7
Sheffield 7
Belfast 6
Nottingham 6

Yes, there have been plenty of examples of 'surprise' results this season with the Gardiner teams in particular producing some scorelines that we just haven't seen in recent years. Despite that, the top 5 has a winning percentage of 81% against the bottom 5. Against each other the title contenders have the following winning percentages:

Nottingham 67%
Belfast 61%
Sheffield 53%
Cardiff 50%
Braehead 46%

(It adds up to more than a 50% average because a tie is worth half a win. Although it's called win percentage, it's really a points percentage.)

Based on this there can be little doubt that Braehead have the easiest run in. If they keep winning at the rate they have been they'll pick up 4 points from their 5 games against the other top teams and 17 from their games against the bottom half. Another 21 points would give them a total of 74.

Whether or not that proves to be enough will depend on how the teams they lose to get on. Let's say Braehead lose their remaining 2 games to Nottingham. That's a couple of big wins for the Panthers but to take advantage they'll need to not have any other slip ups. The chance of them winning all their other games are slim. They might win most of them but if they lost twice to Cardiff that would bring them right into contention, especially since Braehead have already lost games. But those wins for Cardiff are only useful if they can beat Sheffield and so on. It's starts to go round in circles. Someone needs to run away with this. If everyone beats everyone else it just plays into Braehead's hands.

It's possible to figure out just how likely it is that Braehead, or any of the other contenders, will win the league based on the games that are left.

The log5 formula (look it up online if you want a full explanation) calculates how likely a team is to win based on the win percentage of themselves and their opponents. When two teams with equal records take on each other they'll win half the games each. A team with a win percentage of 70% should beat a team with a 40% win rate nearly 8 times out of 10. Since we know the win percentages of all the teams we can plug in these number for all the remaining fixtures and see what happens. By accounting for home advantage you can refine and improve the outcome even further.

If I flipped a coin 10 times you'd expect 5 heads and 5 tails. Well, I've just done this and got 7 heads and 3 tails. That's a perfect example of randomness. Even though both outcomes are equally likely one happens more than another. If I'd flipped the coin 100 times I'd expect to be closer to 50% for each. If I did it 1000 times I'd expect it to be even closer to 50% each. The more you do something the smaller the effect a random outcome can have. 7 heads out of 10 is possible, 700 out of 1000 is considerably less likely.

This is called a Monte Carlo simulation. Doing something thousands or millions of time to find out the true likelihood of an event occurring. It's possible to do this for the remaining games of the EIHL season. Simulate the results of all the remaining games and see who wins the league. Then do it again and again and again. By doing this you can see who wins the league and how often.

Here's what the numbers say:

Braehead 70%

Cardiff 10%

Sheffield 9%

Nottingham 8%

Belfast 3%

(Every team in the league is still mathematically in title contention at this stage of the season but only the Hull Stingrays of the teams outside the current top 5 won the title in any of the simulations. It took a 19-0-0 run and even then only 1% of the time was it enough to be champions with that run to the end of the season. Their chance of winning the title is about 1 in 40000.)

The most common result was Braehead winning the league with 75 points. That would mean going them 11-4. That seems reasonable.

The tipping point for the other contenders is 76 points. When Cardiff, Sheffield, Nottingham or Belfast reached the 76 point mark they won the title on more than 50% of those occasions. It's possible they could win with fewer points or lose out with more but 76 is a good target to aim for. If any of Braehead's rivals can get to that mark they'll force the Clan to win 12 out 15 to stop them.

These simulations just back up the ideas from earlier. If the Clan keep up their current form it'll probably be enough for them. If they don't one of their rivals will have to go on a great run. Back in 2010/11 Belfast or Cardiff would have caught Sheffield if they could have won both of their head to heads. They split those two February meetings and that gave Sheffield the edge. Yes, other games get spoken about more from that season but what happened then is likely to be repeated this time round.

When a title race comes down to the wire and there is only a point (or less) in it then every match in the run in takes on huge significance. Winning the 'big' games isn't much use if you're losing others. Braehead aren't going to win them all from here in, so someone else is going to have to go pretty close to doing that in order to stop them.

Jonathan Fearnley is the Hull Stingrays webcast commentator, and also provides commentary for Steelers TV Live. Follow him on Twitter @JJFearnley

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