What is a point worth?

[Carni]

Hi guys

Anyone done any analysis on how much the odds should change to give a team an extra point?

So if Collingwood +20.5 is 1.96 but I find Collingwood +21.5 elsewhere for 1.91, which is better value?

Interested in trying some middle betting where the lines are different, but not sure what a good rule of thumb is.

[admin]

Hi Carni, which bet is deemed better value could come down to your level of risk aversion. Some will prefer higher odds, while others prefer the higher chance of winning.

To make thing simple, let's presume you are risk neutral, so you're analysing your options purely based on expected payout, which equals payout * probability of winning. For those with a finance/economics background, we are assuming risk neutral behaviour so that we can ignore utility theory.

PLEASE BE WARNED THAT THE FOLLOWING WAS OFF THE TOP OF MY HEAD!

To begin, the first thing to do is come up with an estimate for how much more likely the +21.5 bet is to win than the +20.5 bet.

Looking at the AFL, the value of a one-point difference will depend on the values concerned. For example, one more point between +20.5 and +21.5 will have a bigger impact on your chance of winning than +120.5 vs. +121.5.

Using historical AFL data you can create a histogram using Excel. Over the last 1481 fixtures the frequencies of winning margins in this range are:

15 points: 21 (1.42%)
16 points: 21 (1.42%)
17 points: 19 (1.28%)
18 points: 23 (1.55%)
19 points: 27 (1.82%)
20 points: 25 (1.69%)
21 points: 18 (1.22%)
22 points: 23 (1.55%)
23 points: 19 (1.28%)

So historically 1.22% of games between 19-Jun-2009 and 14-Aug-2016 resulted in a win by exactly 21 points. Based on all data, a +21.5 bet implies a 1.22% higher chance of winning than a +20.5 bet. Note that 1.22% is the absolute difference in probability (x - y), not the relative difference in probability (x - y)/y.


However, if you only look at fixtures where the pre-game margin is between +19.5 and +22.5, the data is more limited (65 observations), but the frequencies of winning margins in this range are:

15 points: 4 (6.15%)
16 points: 0 (0%)
17 points: 1 (1.54%)
18 points: 1 (1.54%)
19 points: 1 (1.54%)
20 points: 1 (1.54%)
21 points: 1 (1.54%)
22 points: 0 (0%)
23 points: 1 (1.54%)

Based on this specific set of fixtures, a +21.5 margin implies a 1.54% higher chance of winning than a +20.5 line bet.

So which should you use? One is based on a larger sample size, while the other concerns fixtures of a very similar nature to the one in question. Also note that I've chosen the +19.5-22.5 range arbitrarily. You could also experiment with 18.5-23.5, 17.5-24.5, etc.

Coming up with the best answer is for another day, but for the sake of discussion, let's take the average of 1.22% and 1.54% and pretend that we estimate the +21.5 line bet at 1.91 odds has a 1.38% better chance of winning than a +20.5 line bet at 1.96 odds. So which should you choose?

It actually comes down to the absolute probabilities. If you believe that the +21.5 bet has a 54% chance of winning, then the +20.5 odds bet has the same expected payout (odds * probability), so you would be indifferent. If you believe the +21.5 bet has less than a 54% chance of winning then you would prefer +21.5 at 1.91. If, however you believe the +21.5 bet has a higher than 54% chance of winning, then you will prefer +20.5 at 1.96.

In the table below the 1.96 bet probability is equal to the probability of the 1.91 bet, minus 0.0138. The expected payout equals (probability) * (odds).

1.91 Probability 1.96 Probability 1.91 Expected Payout 1.96 Expected Payout Difference 50.00% 48.62% 0.9550 0.9530 0.20% 50.50% 49.12% 0.9646 0.9628 0.18% 51.00% 49.62% 0.9741 0.9726 0.15% 51.50% 50.12% 0.9837 0.9824 0.13% 52.00% 50.62% 0.9932 0.9922 0.10% 52.50% 51.12% 1.0028 1.0020 0.08% 53.00% 51.62% 1.0123 1.0118 0.05% 53.50% 52.12% 1.0219 1.0216 0.03% 54.00% 52.62% 1.0314 1.0314 0.00% 54.50% 53.12% 1.0410 1.0412 -0.02% 55.00% 53.62% 1.0505 1.0510 -0.05% 55.50% 54.12% 1.0601 1.0608 -0.07% 56.00% 54.62% 1.0696 1.0706 -0.10% 56.50% 55.12% 1.0792 1.0804 -0.12% 57.00% 55.62% 1.0887 1.0902 -0.15% 57.50% 56.12% 1.0983 1.1000 -0.17% 58.00% 56.62% 1.1078 1.1098 -0.20% 58.50% 57.12% 1.1174 1.1196 -0.22% 59.00% 57.62% 1.1269 1.1294 -0.25%

If x is the probability of the +21.5 bet winning, then the exact crossover point is when:
1.91 * x = 1.96 * (x - 0.0138)

Solving for x gives:
x = 0.0138 / (1 - 1.91/1.96)
x = 54.096%

Hope that makes sense! It was all off the top of my head so I apologise for any errors.

[Carni]

This is awesome thanks! Going to take me a while to work through it all, but thanks very much!

[Carni]

*** post edited to remove earlier data errors ***

Ok I think I did something clever, and figured out a point is worth 6 cents.

I downloaded all the AFL data from this website (810 games with closing line odds). Then I calculated the % games won by the home team, after the closing line is taken into account. This is 51.48% (417 of 810 games) .

Then I altered the line by adding a point to each individual line. So this new field is "closing line +1". So a +14.5 line becomes a +15.5, and a -22.5 becomes -21.5.

Then I recalculated the % games won by the home team, after the closing line +1 is taken into account. This comes out to 52.96%. So there is a 1.48% difference between the two. This is a small sample size, so I also calculated the difference if I subtracted 1 from the closing line. This is new field "closing line -1". So a +14.5 line becomes a +13.5, and a -22.5 becomes -23.5. Now only 403 games win, or 49.8%.

So we have

Beat with closing line -1 49.8%
Beat with closing line 51.48%
Beat with closing line +1 52.96%

There's a 26 game difference between the -1 and +1 lines. Fair odds for -1 line is 2.0099. Fair odds for +1 line is 1.8881. There is 2 points difference between the two. There is a 12cent difference and so for 1 point, we should be neutral going forward as to whether we receive 6 cents for a lower by 1 line.

So, the value of a point is 6 cents. Note that this only applies when we are talking about the line that splits games 50/50. If you were trying to add (say) 8 points, this relationship would break down.

Make sense?

[admin]

Hi Carni, good stuff! That's a great approach because you get to use the entire sample for the calculations.

[Carni]

Thanks!

Any views on how I could modify it to do NRL? Obviously with NRL I can't just do the same, because points have different values based on whether it's (for example) +3.5 or +4.5, because lower scoring games and tries being with 4....

[nomore4s]

Because the scoring system is different instead of working out per point you may have to work out per 2 points (penalty goals/conversions) or per 4 points.
But you would probably be better off working it out per common margin.

IE: Do research into common margins in league games
2,4,6,8,10,12 - Find out which are more common then place a value on the difference between the margins and the frequency of those margins.

I hope I'm making sense.

[admin]

You might find this article interesting:
http://www.aussportsbetting.com/2013...margin-survey/

It's a bit out of date now, but it looks at winning margin frequencies for the NRL.

[Carni]

That's exactly the sort of thing I was looking for - that's great thanks!