Where is the figure of merit of the software ?

[cosmic]

Without a published figure of merit your software is difficult to assess.
What you seem to be doing is this:

Compute probabilities for the coming football matches, then convert those into odds - since odds = 1/p.
When these odds are bigger than those offered by the bookmakers then it's good, we bet.
When they are lower it's not good.

But is this correct ?
In order to be correct your probabilities must be more accurate than those of the bookies, or at least a little more accurate.

So you should really state a figure of merit in your page !

What is the figure of merit ?
Suppose for a given match the bookie prices are home = a, draw = b, away = c.
Then the probabilities as seen by the bookie are:

home P(1) = (1/a) / (1/a + 1/b + 1/c)
draw P(X) = (1/b) / (1/a + 1/b + 1/c)
away P(2) = (1/c) / (1/a + 1/b + 1/c)

To evaluate the strength of the bookie as a prognosticator do this:

If the match ends in a draw say add the quantity -ln(P(X)) and continue doing so for about say a couple of seasons.

Take the mean of that sum I = - Σ ln(Pi) / no of matches.
The figure of merit is

Q = exp(I)

To do this go to an odds monitoring site and copy-paste the history and then with a Python script you compute Q. One such site is oddsportal.com but there are more.

For the premiership I imagine you will find Q of bookies = 37.0% approximately.

Now do the same with your predictions.
Must hold:

Q(software) >= Q(book)

Otherwise, if you don't, we just don't know the quality of the software.

You may think this is complicated for the average "man in the street" but there is no other figure of merit and the man in the street - me just has to understand !

To demonstrate what kind of erroneous situation may result from software with poor figure of merit, let me make use of a fable.

I go to the house of my friend Jim and I say to him "hey Jim let's go to the casino on the mountain to play the roulette, the probability of finding a number is 1/33 and they pay 35 to 1 - we win !".
We do this and we come down from the mountain losers !
Why ? Because 1/33 was wrong - it's 1/37.

So it's something to look into.

[Alex]

Such test for Odds Wizard odds does already exist for a couple of decades. It can be run by Tools > Performance analysis > Entropy of successful probs.
One can read about it in Odds Wizard Guide > Tools > Performance analysis. It is exactly the same what you have suggested in your post:

Sum of expressions –(Di/N)*ln(pi), and their total sum, where Di = 1 if result of i-th game is consistent with the outcome which probability pi was computed for. Otherwise Di = 0

The above value is called entropy of successful probs. It is available not only within the software but also on the performance pages at https://www.newhavensoft.net/fair.htm.

We performed backtesting against 188bet.com odds for a couple of seasons (https://www.newhavensoft.net/forum/viewtopic.php?f=2&t=566#p1797) with ROI about 105% for the major leagues listed there. But we do not have enough resources to provide continuous comparison ourselves. It is rather a task of professional odds comparison websites like oddsportal.

At the same time, at the bottom of our homepage we urge other odds software developers to join a permanent contest to measure performance. In particular by using the above entropy as one of possible criteria.

[cosmic]

Such test for Odds Wizard odds does already exist for a couple of decades. It can be run by Tools > Performance analysis > Entropy of successful probs.
One can read about it in Odds Wizard Guide > Tools > Performance analysis. It is exactly the same what you have suggested in your post:

Sum of expressions –(Di/N)*ln(pi), and their total sum, where Di = 1 if result of i-th game is consistent with the outcome which probability pi was computed for. Otherwise Di = 0

The above value is called entropy of successful probs. It is available not only within the software but also on the performance pages at https://www.newhavensoft.net/fair.htm.

We performed backtesting against 188bet.com odds for a couple of seasons (https://www.newhavensoft.net/forum/viewtopic.php?f=2&t=566#p1797) with ROI about 105% for the major leagues listed there. But we do not have enough resources to provide continuous comparison ourselves. It is rather a task of professional odds comparison websites like oddsportal.

At the same time, at the bottom of our homepage we urge other odds software developers to join a permanent contest to measure performance. In particular by using the above entropy as one of possible criteria.

I used to like oddsportal but for strange reasons they decided to self-ban themselves from Greece.
But it's easy to compute entropy from their tables.
The corresponding figure from our side is more difficult because it takes time to work out all of the matches.
But I 'd like to see the figures published.

When you say ROI 105% is that net gain of 5% ?
I prefer the Q value as indicator.

Anyway what I think is happening is the bookies seldom make mistakes that can be trapped by someone's clever software.
After all they employ scientists themselves.
The Greek company OPAP back in the old old days when it was a pools company used to publish some percentage probabilities in case some matches were rained off so they could make a draw.
For this purpose they were employing one or two well known dancing hall singers and we all thought it was funny. The figures were also funny.
But nowadays they have connections with universities such as Nottingham, Cardiff, Catagna, Cambridge maybe.
They have to do this in order to do their job, but even if it was the old pools we were after it would n't be such a straightforward task to defeat the collective intelligence of the crowd. The collective intelligence has a good Q value.
Add to all this the taxation without representation we have and all that, things are getting difficult.

I believe it's possible to find the bookies in error only in specific circumstances.
Such as a) early in the season, b) with matches between teams of different countries and in general when something happens and the teams standard ratings become irrelevant (and that something is known to us of course).
Can you isolate such behaviours ?

[Alex]

When you say ROI 105% is that net gain of 5% ?

Yes, the net gain is 5%.

About Cambridge, etc. I can't imagine that those universities could be engaged in the odds research for decades, like we do. Sportsbooks aware of the OW strength, and they really afraid it of. For instance, all major sportsbooks rejected our affiliate applications during the last 10 years while earlier we did act as active affiliate for all of them.

About Q value of the crowd. Indeed, crowd can be smart in the fine tuning of the boomaker's odds by placing bets on the certain outcomes. OW offers Antibet filter 'Upward market trends' that reflects reducing chances for the certain event (outcome) to happen.

I believe it's possible to find the bookies in error only in specific circumstances.
Such as a) early in the season, b) with matches between teams of different countries and in general when something happens and the teams standard ratings become irrelevant (and that something is known to us of course).
Can you isolate such behaviours ?

There can be dozens of specific circumstances. Anyway, we continue research. And again, factors that can't be accounted by OW as for now, are covered by antibet filters.