Benter & public odds

[Sapio]

Originally Posted by flatstats

The way I interpreted it is that the ratings produced a basic oddsline, he then integrated it with the live market to produce a more realistic oddsline. The intention is to smooth his prices to that of the general public. If his prices are way out then the live market would tend to bring it back to a more realistic line.

Initial Oddsline
Lucky Joe 6/4
Blue Sky 2/1
Old Banana 5/1
Diamond Girl 10/1

Live Market
Blue Sky Evens
Lucky Joe 3/1
Old Banana 4/1
Diamond Girl 10/1

Benter would take that live market information and use it to adjust up or down his own forecast. From that he would produce a new oddsline

New Oddsline
Lucky Joe 7/4
Blue Sky 7/4
Old Banana 9/2
Diamond Girl 10/1

That would be the price list he would then use to find overlays.

Is that how he did it?

If yes, then the key to his method is indeed the integrating of his initial forecast with the live market. That's the piece I don't know how to reproduce.

Reading his paper, I don't bvelieve it is a matter of pulling his fundamental model in the direction of the tote odds. It is merely combining two expert opinions to arrive at a more accurate model.

The interesting part to me is the question of multiple models (lest's say 3 or 4) maybe better than 2. Possibly a model based soley on speed another on pace, etc. combined with the tote odds may allow for a better understanding and possibly more explanation of the variance (R2). Just thinking.

Thomas Sapio

Thomas Sapio

[TravisVOX]

Originally Posted by Sapio

Reading his paper, I don't bvelieve it is a matter of pulling his fundamental model in the direction of the tote odds. It is merely combining two expert opinions to arrive at a more accurate model.

The public is, generally speaking, a good handicapper. Combining the two models allows for unknown, not-present in the data, insider information present in the public odds to be included in the overall model.

That said, the combining of the two does pull the fundamental model toward the public odds in theory as the former is going to be more accurate in the long run. Otherwise, then the person who developed the fundamental model would be an extremely wealthy person.

[lansdale]

Originally Posted by dnlgfnk

Yes, Lansdale. Thank you for posting the article.

I had come across it before, but can't recall where.

Interesting that in table 8, his largest advantage in the example race is to bet #8, an 8-1 (9%) risk whose "true odds" are roughly 9-2 (14%). Assuming this race is representative of the system, betting $1 to win produces a 26% advantage. The "Contingencies" article stated an "upwards of 24% return" yearly.

Either this race was exceptional, in that he rarely benefited from simply betting the biggest advantage to win, or seldom encountered 8-1's who should be 9-2's, or he broke even playing the exotics, although "the greater the exotic, the greater the return". Sometimes some of this seems a little spurious.

Hi dnlfnk,

No prob posting this - I thought since you were the OP and your question involved Benter you would be interested in seeing it. Another reason is that Benter's name is frequently invoked here, but many seem not to have read the key article, in which he discusses his method in its original form

I'm not sure what about this example from this piece seems 'spurious'. BTW, you made a mistake on the odds of the #8 horse which were 9.2-1 (as listed in the right hand column under 'div.' - dividend, according to Benter's sometimes confusing terminology). And the odds implied by his model's estimate are 5.7-1 not 9/2. The percentages in the 'c' and 'p' columns are adjusted for 17% takeout.

Re the 'upwards of 24%' return for Benter, that also includes exotic betting, which I believe was the source of the bulk of the profits. However, if you look at the four overlays his model produced in this race, their mean is .24.

Cheers,

lansdale

[lansdale]

Originally Posted by sjk

Lansdale,

Thanks for posting the article. I was thinking about some of the same things as Benter in 1993.

SK

Hi sjk,

No prob posting this and I'm not surprised, based on your successful work with model building that you were thinking along similar lines.

One question that I'd like to ask about, which I had passed over in my previous reading, is his mention of an increased 'spread' of the actual results of the sample of races he cites in Table 5. I'm curious as to whether you this was simply a local phenomenon or whether it could be extrapolated as a generic feature of horseracing.

I seem to notice a similar trend in U.S. odds in the late 2000s, which I thought of as the 'hourglassing' of the odds distribution, but since this was such a tiny sample and thus anecdotal, I ignored it.

Now, I wonder if there was some truth to this, and whether this means that horses in the 5-1 to 8-1 range now offer the most likely source of overlays. I know that Trifecta Mike has made a few observations to this effect.

Grateful for any feedback, as always.

Best,

lansdale

[lansdale]

Originally Posted by Robert Fischer

Hey, thanks for posting that.

As above.

[Sapio]

Originally Posted by lansdale

Hi sjk,

No prob posting this and I'm not surprised, based on your successful work with model building that you were thinking along similar lines.

One question that I'd like to ask about, which I had passed over in my previous reading, is his mention of an increased 'spread' of the actual results of the sample of races he cites in Table 5. I'm curious as to whether you this was simply a local phenomenon or whether it could be extrapolated as a generic feature of horseracing.

I seem to notice a similar trend in U.S. odds in the late 2000s, which I thought of as the 'hourglassing' of the odds distribution, but since this was such a tiny sample and thus anecdotal, I ignored it.

Now, I wonder if there was some truth to this, and whether this means that horses in the 5-1 to 8-1 range now offer the most likely source of overlays. I know that Trifecta Mike has made a few observations to this effect.

Grateful for any feedback, as always.

Best,

lansdale

lansdale,

Interesting observation. Who is Trifecta Mike? You make reference to him, but I don't see any posting by him.

Thomas Sapio

[lansdale]

Originally Posted by Sapio

lansdale,

Interesting observation. Who is Trifecta Mike? You make reference to him, but I don't see any posting by him.

Thomas Sapio

Hi Thomas,

Trifecta Mike was a prize-winning math professor on the faculty of a New York area college who used to post here often. He made a number of very interesting posts explaining his Bayesian approach to handicapping, but its novelty along with a fairly blunt delivery, seems to have created a disconnect and led to his unfortunate departure. Since you seem to be well-versed in math, I think you might benefit from a search on his posts.

Cheers,

lansdale

[sjk]

Lansdale,

I have seen a shift over the years in the bets that I have made (the model is the same; it is the public odds that are different). A preponderance of my bets are now in the higher odds range. Many bets revolve around a horse that I make 8-1 or 10-1 and which is going off at a big price. I take this as evidence that the pools have become more efficient in all but the higher odds ranges.

Looking at table 5 and Benter's comments it looks like his line is underestimating probabilities in each odds range; I might have renormalized if presented with data like that. His method of combining the lines is more complicated than a simple linear combination which is what I effectively do as he seems to have two independent parameters.

SK

[Sapio]

Originally Posted by lansdale

Hi Thomas,

Trifecta Mike was a prize-winning math professor on the faculty of a New York area college who used to post here often. He made a number of very interesting posts explaining his Bayesian approach to handicapping, but its novelty along with a fairly blunt delivery, seems to have created a disconnect and led to his unfortunate departure. Since you seem to be well-versed in math, I think you might benefit from a search on his posts.

Cheers,

lansdale

lansdale,

Even though my understanding of Bayesian Statistics is limited, what I have read so far is extremely interesting.

Thanks for the info.

Thomas Sapio

[Cratos]

Originally Posted by Sapio

lansdale,

Interesting observation. Who is Trifecta Mike? You make reference to him, but I don't see any posting by him.

Thomas Sapio

Both Magister Ludi and TrifectaMike were very good posters who added strong insight to the use and application of Bayesian statistics to further the handicapping methodology on this forum to an advanced statistical level; read their posts I believe you will enjoy them.

[lansdale]

Originally Posted by sjk

Lansdale,

I have seen a shift over the years in the bets that I have made (the model is the same; it is the public odds that are different). A preponderance of my bets are now in the higher odds range. Many bets revolve around a horse that I make 8-1 or 10-1 and which is going off at a big price. I take this as evidence that the pools have become more efficient in all but the higher odds ranges.

Looking at table 5 and Benter's comments it looks like his line is underestimating probabilities in each odds range; I might have renormalized if presented with data like that. His method of combining the lines is more complicated than a simple linear combination which is what I effectively do as he seems to have two independent parameters.

SK

Hi sjk,

Thanks for these insights, and I do remember you mentioning the increased efficiency of lower odds horses. Combined with TM's comments and what I hear from others, it makes me wonder to what extent EMH now obtains for lower (below 4-1?) odds animals and whether anyone would be making a profit betting in that region sans rebate. Even though your playable odds range has moved higher, your model displays impressive durability. As you've said, you've been in the black using basically the same model for what, about 15 years now? Not many could make that claim.

Re Benter, I take your point on his underestimation, but it would seem to apply mostly to horses below 5-1. Above that level, his model seems relatively accurate, in fact, more accurate than the public model, but much less accurate than the public model below the 5-1 range, based on Tables 1 & 2. What strikes me as especially strange, is that even the Combined model of Table 5, some version of which was the basis of his successful betting, still features more error in the sub-5-1 odds group than the Public model of Table 1! If you can bear with my math ignorance, isn't there a way to combine the relatively accurate high-odds estimate of Benter with the original, more accurate low-odds estimate of the public, to create a better line than he achieved in Table 5? Or would renormalization address that?

Re this point, if we look at the sample race from Table 8, it looks as though all the overlays are in the high-odds range. I wonder if what happened with Benter's model, was that it produced a slight aggregate loss with lower odds horses, and all of his profits came from higher odds horses and exotics?

Best,

lansdale

[lansdale]

Originally Posted by Sapio

lansdale,

Even though my understanding of Bayesian Statistics is limited, what I have read so far is extremely interesting.

Thanks for the info.

Thomas Sapio

Hi Thomas,

Glad you liked TM's posts. So did I, and I would second the comments of Cratos. Don't forget you can always try PMing TM, if you want to follow up - you never know.

Cheers,

lansdale

[sjk]

Lansdale,

I have been in the black for 14 of the last 15 years with basically the same program. Thanks for noticing.

It is not necessary for an odds line to be more accurate than the public odds for it to bring profits. If it is different enough from the public odds it can point to overlays even if not quite as good.

It is striking how many long priced horses and how few short priced ones are in Benter's tables. Bigger fields and a much different looking odds board than what we see in the US.

It is pretty rare that I find a short priced horse to bet to win although many exactas include them. I was reading a post the other day where the writer stated that his key to success was betting the right even money horses. That would not work for me.


Best Regards,
SK

[lansdale]

Originally Posted by sjk

Lansdale,

I have been in the black for 14 of the last 15 years with basically the same program. Thanks for noticing.

It is not necessary for an odds line to be more accurate than the public odds for it to bring profits. If it is different enough from the public odds it can point to overlays even if not quite as good.

It is striking how many long priced horses and how few short priced ones are in Benter's tables. Bigger fields and a much different looking odds board than what we see in the US.

It is pretty rare that I find a short priced horse to bet to win although many exactas include them. I was reading a post the other day where the writer stated that his key to success was betting the right even money horses. That would not work for me.


Best Regards,
SK

sjk,

Important to note the stability of your model, since it tends to belie the notion, frequently expressed on this site, that any model or betting strategy requires constant tweaking due to the 'dynamic' nature of the game. Both deeper insights and more contrarian perspectives can produce 'undervalued assets' that remain undervalued for years. As you have said, there can be many ways to beat this game.

As you say, the robust fields of the Hong Kong circuit offered a great opportunity to Benter and the other computer teams playing it in the '90s, offering high-odds choices U.S. bettors can only dream about.

Re low-odds betting, one would truly need to have a very large rebate to profit from even-money plays, but apparently, some do.

Thanks again for your input.

Best,

lansdale

[Magister Ludi]

Originally Posted by sjk

Lansdale,

I have seen a shift over the years in the bets that I have made (the model is the same; it is the public odds that are different). A preponderance of my bets are now in the higher odds range. Many bets revolve around a horse that I make 8-1 or 10-1 and which is going off at a big price. I take this as evidence that the pools have become more efficient in all but the higher odds ranges.1

Looking at table 5 and Benter's comments it looks like his line is underestimating probabilities in each odds range; I might have renormalized if presented with data like that. His method of combining the lines is more complicated than a simple linear combination which is what I effectively do as he seems to have two independent parameters.2

SK

1I agree. A track-dependent objective measure of odds entropy can reveal significant midrange odds overlays.

2 I don't know how Mr. Benter aggregated probability forecasts. A nonlinearly recalibrated beta-transformed linear opinion pool is probably the present day state-of-the-art.