Birth of a "Hedge"

[u21c3f6]

I am going to try to explain one of the ways I approach finding profitable wagers. One of those ways is to find situations that can be exploited through the use of a “hedge”. To clarify, I differentiate between what is called an arb and what I refer to as a hedge. An arb to me is wagering on both sides of an event essentially during the same time-frame such as before the game starts. A hedge to me is wagering on one side and then “hedging”, if possible, with the other side during a different time-frame or after an event. One example of a hedge to me is when I make a wager before the game and then hedge that wager by wagering on the opposite side during live action wagering. Another example of a hedge to me (and the one I am going to describe in more detail) is making a wager in the futures market for a tournament during one round and then “hedging”, if possible, with the other or different side in a subsequent round of the tournament. I understand that some may object to the use of the word “hedge” as I described above. For purposes of this discussion, when I use the word “hedge”, please understand that I am referring to my definition as posted above.

I am going to ask for participation in this thread by asking questions along the way. It is not about whether your or my answers are “right” or “wrong”, it is about possibly passing along a different way to approach finding profitable wagers than you currently use. My questions are not intended to be insulting, they are intended to attempt to “teach a man (woman) to fish”. Hopefully there will be those that benefit from this discussion regardless of whether one learns something to do or something not to do.

Here goes:

The futures market for the XYZ Tournament in the semi-final round is as follows:

Team A W/L +148 -152
Team B W/L +272 -278
Team C W/L +495 -505
Team D W/L +495 -505

Team A plays Team B and Team C plays Team D to get to the final round. What do you think the no-vig line should be for the contest between Team A and Team B and between Team C and Team D?

Joe.

[sycoogtit]

I have no freaking clue but I look forward to reading this as it progresses.

[Bsims]

I'll bite. Team A -150 Team B +150
Team C +100 Team D +100

[u21c3f6]

I'll bite. Team A -150 Team B +150
Team C +100 Team D +100

That is correct. In fact, if the lines deviated too far from 150 and 100 respectively, one could set-up a hedge to exploit that deviation. That particular hedge is not my focus for this discussion.

Now let’s assume that the lines for the Team AB and Team CD contests are in line and are as follows:

Team A: -152
Team B: +148

Team C: -102
Team D: -102

Now a “new” term: CP (Calculated Profit): Your calculated W% * Amt to be won – your calculated L% * Amt to be lost.

For example: If you calculate that your wager has a 60% chance of winning (which could be from your own independent data and not necessarily based on the “closing” line), then if you made that wager at -160 you would have: .6*100 - .4*160 or 60 - 64 or -4 or –CP. If you made that wager at -140 you would have: .6*100 - .4*140 or 60 – 56 or +4 or +CP.

Now, since there isn’t any independent data available at the moment, let’s calculate the W%’s from the given lines. Please note that I am going to round numbers as necessary for ease of calculation (which will be more than adequate for this discussion).

From the first post above, the futures lines give the “approx” W%’s for the tournament as follows:

Team A: 40%
Team B: 26.66%
Team C: 16.67%
Team D: 16.67%

For the head-to-head contests, the W%’s to get to the finals is as follows:

Team A: 60%
Team B: 40%
Team C: 50%
Team D: 50%

Based on the W%’s above, I calculate that any single wager made on any of the lines from the futures or head-to head markets above will result in a –CP wager. At this point I am seriously asking for confirmation that we agree on the above.

This request is based on a previous thread where apparently most apply EV differently than I do and why I “created” CP. If someone has a different interpretation of the above, let’s discuss.

Joe.

[Bsims]

I have no disagreement with your logic. I'm not sure everyone has the same measure when they are looking for +EV (or what they mean by that). Your CP approach is one that will identify these situations. I've always used expected return. In your example, the expected return on the -160 wager with 60% chance of winning is $0.975 per dollar wagered (bad bet). At -140 and 60% it computes to $1.029 return per dollar, a decent bet.

Obviously, all of our endeavors are to find wagers with expected return >$1.00. The computations are fairly straight forward, once the probability of winning is determined. Doing that is our lifelong pursuit. There are many ways of doing that including inferring it from the lines as you have done in your example. Simulations, regression, line movements, are other approaches that can be used.

Your discussion of arbs and hedges are good ways of exploiting the lines. These can be used to lower risk of variance but tend to result in lower expected returns (one or two percent). Using the probability you determined to take a side does offer greater return opportunity at greater risk. But again, your success will be a function of how good an estimate of that actual probability is.

[u21c3f6]

Bsims, I agree with everything that you have written. I would only add to your statement: "Obviously, all of our endeavors are to find wagers with expected return >$1.00." While this seems obvious, I think there is some misunderstanding as to what this really means based on reading some postings of others but I don't want to clutter this thread.

I am also not going to ask as many questions as I planned going forward and just post some of the calculations. However, if I post anything that someone does not agree with and/or understand, please post so I can clarify.

To continue, At the end of the semi-final round there are 4 possibilities for the final round. They are: AC, AD, BC and BD.

The probabilty for each of the matchings above to become the final pair are as follows:

AC: 30% (.6*.5)
AD: 30% (.6*.5)
BC: 20% (.4*.5)
BD: 20% (.4*.5)

Assuming a 120 final game sample (just a number for easy calculation), the number of games for each pair would be:

AC: 36 (120*.3)
AD: 36 (120*.3)
BC: 24 (120*.2)
BD: 24 (120*.2)

Now, based on the futures market, the following are the "expected" number of tournament wins per team:

A: 48 (.4*120)
B: 32 (.2666*120)
C: 20 (.1667*120)
D: 20 (.1667*120)

Since C & D are of equal "strength", we can assume that A & B's wins will be split equally between the C & D final games as follows:

AC: A will win 24 (48/2), C will win 12 (36-24)
AD: A will win 24 (48/2), D will win 12 (36-24)
BC: B will win 16 (32/2), C will win 8 (24-16)
BD: B will win 16 (32/2), D will win 8 (24-16)

Now the question: Does anyone see a problem with the distribution of final wins based on the semi-final lines?

Joe.

[u21c3f6]

This thread is now a continuation of a discussion started in the thread: spreads as stocks.

My question in the previous post still stands: Does anyone see a problem with the distribution of final wins based on the semi-final lines? (Hint: I definitely see a problem).

Joe.

[Megaman]

Interesting thread, thanks!

The final win distribution shows that C and D got an equal probability of winning the final against both A and B. The probabilities from the semi-finals indicates that A are a better team than B so A should be more likely to win over C and D than B.

[rookie]

According to the above calculations, A and B will have same probability of winning the final (though A is more likely to make the final). But, A is better than B and has higher probability of winning against C / D.

EDIT: Did not see the above post.

[byronbb]

You state you hedge out in live-play "if you can". Aren't you always throwing away money by doing this since you only hedge when your side is winning and never when your side is losing? Or are in-play lines often so overly swingy that they can present a very +EV situation that over-comes the downsides? Also when you hedge in-play do you totally close out your position or do you do it gradually?

[suicidekings]

You state you hedge out in live-play "if you can". Aren't you always throwing away money by doing this since you only hedge when your side is winning and never when your side is losing? Or are in-play lines often so overly swingy that they can present a very +EV situation that over-comes the downsides? Also when you hedge in-play do you totally close out your position or do you do it gradually?

Think about playing a big ML dog in the NBA (+1200) x1 only to see the dog keep the game close or possibly lead at the half. The fave ML is going to decline to the point where you can wager the other side and guarantee a profit. You could hold on to your big dog ticket, but then you're depending on what is likely an inferior team to hold off the better team for the entire 48 minutes. A small profit at no risk is better than a larger profit at a much higher risk, IMO.

[sharpcat]

Think about playing a big ML dog in the NBA (+1200) x1 only to see the dog keep the game close or possibly lead at the half. The fave ML is going to decline to the point where you can wager the other side and guarantee a profit. You could hold on to your big dog ticket, but then you're depending on what is likely an inferior team to hold off the better team for the entire 48 minutes. A small profit at no risk is better than a larger profit at a much higher risk, IMO.

problem is that you are not taking into consideration all of the times you make a play that you can not hedge at half time therefore running the risk that your straight up losses are not going to be covered by the small amount you are making when you actually can make your hedge bet.

[Megaman]

Team A W/L +148 -152
Team B W/L +272 -278
Team C W/L +495 -505
Team D W/L +495 -505

I don't understand how you can get the no vig probability of A playing B from these numbers alone. I need the probability of team A winning against C/D and team B winning against C/D as well. Team A got 40% chance of winning the tournament and team B got a 26.7% chance. To get the 60/40 chance of A playing B you seem to do 40/(40+26.7).
This assumes that the chance of winning the final is the same for both team A and team B which is exactly the result that you see in the distribution of final wins.

[u21c3f6]

You state you hedge out in live-play "if you can". Aren't you always throwing away money by doing this since you only hedge when your side is winning and never when your side is losing? Or are in-play lines often so overly swingy that they can present a very +EV situation that over-comes the downsides? Also when you hedge in-play do you totally close out your position or do you do it gradually?

Let me clarify. I always hedge regardless if I have a guaranteed gain or loss. I only wrote "if possible" because there have been very rare occasions where I was unable to close out a hedge. Remember that the initail wagers could be made well before the game starts. In one case there was a medical emergency and I was not able to place my hedge wagers during the live game and therefore those wagers became let-it-ride wagers. The rare times my wagers become let-it-rides, some lose and some win for a negligible impact on bankroll.

The +EV is created by wagering on situations where I "know" that I will be able to hedge at a profit in total more than the amount that I have to hedge at a loss. In addition to a series of these hedges being profitable on their own, I get the additional chance of windfall profits if any of the "middles" I set-up in this process hit. In fact, I hit more of these "middles" in games where I have hedged for what was going to be a guaranteed loss but hitting the middle turned a guaranteed small loss into a substantial gain.

Joe.

[u21c3f6]

... Also when you hedge in-play do you totally close out your position or do you do it gradually?

I usually close out the hedge in total at one time. There are occasions (for some reason) that I may gradually close out a position but they are almost always closed out in their entirety and they are almost always totally balanced meaning that regardless of which side wins I would win or lose an equal amount. This is not Kelly optimal but it fits my conservative personality and it gives up very little in gain.

Joe.

[u21c3f6]

Interesting thread, thanks!

The final win distribution shows that C and D got an equal probability of winning the final against both A and B. The probabilities from the semi-finals indicates that A are a better team than B so A should be more likely to win over C and D than B.

Megaman and rookie, you are correct. There seems to be an anomaly converting the semi-final odds to the final game %'s. A certainly should win the final at a higher % than B.

I don't understand how you can get the no vig probability of A playing B from these numbers alone.

This is how the %'s work. If they didn't, then there would be riskless hedges available and that process should in fact get those prices back in line. If you now look at these markets with an eye to the relationships between the individual games and the Conference, Championship etc markets, you will see this relationship. This example is a real case that I wagered on. I changed the odds slightly for ease of calculation but the change has no effect on the concept or eventual outcome. I will reveal what it is later. I want to leave it generic for now because I want to focus on the concept and not bias it with biases that people may have about the ability of one specific team over another specific team.

Joe.

[u21c3f6]

New question: Given the semi-final lines:

Team A W/L +148 -152
Team B W/L +272 -278
Team C W/L +495 -505
Team D W/L +495 -505

Assuming that the odds won't change regardless if C or D is in the final, what do you think the no-vig line would be if the final was:

A against C or D
B against C or D

Joe.

[dentry]

Interesting thread, updating my knowledge

[byronbb]

How sharp are futures markets typically? Can you take the winners market for a golf tournament and derive "fair" matchup odds?

[u21c3f6]

Can you take the winners market for a golf tournament and derive "fair" matchup odds?

It would seem logical to me that the player with the lower odds to win the tournament should also be the lower odds in a matchup. But this does not tell you if the wager is +EV and I don't know how you can reasonably approach this as a hedge (though I never tried for golf). You have to keep track of wins and losses to determine EV.

I will also make mention about EV in my next post. I don't usually know which side if any is +EV but it doesn't matter to me because I am creating a +EV wager through the use of a hedge.

Joe.

[u21c3f6]

How sharp are futures markets typically?

Frankly, I don't know the answer to this question because I don't look at it that way. However, the answer doesn't matter because I am looking to hedge based on the correlation between different markets.

I will try to make this clearer by expanding on my response to the question posed by Megaman, "I don't understand how you can get the no vig probability of A playing B from these numbers alone."

Based on the final round no-vig odds of A: +150 and B: +275, the contest between A and B should have odds at or very near 150. Why? Because if the odds differed significantly from 150, that should lead to profitable hedges which should get the odds back in line. For example, let's assume for a moment that the finals odds are as above but the contest between A and B is at 200. Based on the finals odds, B should only be +150 against A. Now this does not mean that a wager on B alone at +200 is +EV. Maybe A at +150 for the finals is the +EV wager or maybe it's both or maybe it's neither. The only way to know which wager is possibly +EV is to record the wins and losses over a series of similar wagers to see if the wins and losses conform to one or both of the offered odds.

Here is how these new odds could be hedged. This example is not exacly the way I would do it because I would set each side to be equal, this example is to keep the calculations simple. Now, one could wager 100 to win 200 on B in the AB contest and at the same time wager 200 to win 300 on A in the finals. If B wins, you win 200 on B and lose 200 on A. No gain, no loss. The more likely result will be that A will win the AB contest. If A wins you are now essentially left with a wager of 300 to win 200 (-150) on A in the finals. The question now becomes what do you think the odds on C or D will be in the finals when it is down to AC or AD? Certainly it will be at least +200 if B was +200 against A and the finals odds had B at lower odds than C or D. The finals odds seemed to imply that the minimum odds for C or D playing A would be +240 (I will use this for the example even though the actual answer would be higher!). At +240 you can close out this hedge by wagering 147 to win 353 which would leave you with a profit of 53 regardless of who won the game. Only if for some reason C or D was less than +150 in the finals would you lose any money and the chance of that happening based on the odds is actually very remote. The point is that because the two markets (the finals and the head-to-head contest) are highly correlated, the odds will also be highly correlated.

Was that clearer? Anyone going to give a shot at the probable odds for an A vs C or D and a B vs C or D contest?

Joe.

[suicidekings]

problem is that you are not taking into consideration all of the times you make a play that you can not hedge at half time therefore running the risk that your straight up losses are not going to be covered by the small amount you are making when you actually can make your hedge bet.

It's obviously not a blanket rule. Two +1000 MLs are not necessarily equally valuable. Hedging just at half time is harder. You need to have live betting to make the most out of opportunities.

[DoubleEM]

The odds that A will win the championship = odds A defeats B * (odds C defeats D * odds A defeats C + odds D defeats C * odds A defeats D) -> .4 = .6 * (.5 * x + .5 * x) -> x = .6666667

Based on that method, odds are:

A vs C -200/+200
A vs D -200/+200
B vs C -200/+200
B vs D -200/+200

[djiddish98]

I'm trying to wrap my head around this, so this may be off.

It seems the issue is with the fact that the odds for C and D are set regardless of the outcome on A vs. B. Hence, A and B have the same line against C / D even though one team is stronger than the other.

[u21c3f6]

The odds that A will win the championship = odds A defeats B * (odds C defeats D * odds A defeats C + odds D defeats C * odds A defeats D) -> .4 = .6 * (.5 * x + .5 * x) -> x = .6666667

Based on that method, odds are:

A vs C -200/+200
A vs D -200/+200
B vs C -200/+200
B vs D -200/+200

This is what the odds imply but surely this can't be correct (and the reason why there is an excellent hedging opportunity). Team A would almost certainly be a larger favorite if they make it to the finals as that comparison based on the semi-final lines also implies .4/.1667 or -240/+240 for an AC or AD contest.

Joe.

[djiddish98]

Again, here's another brain fart.

It seems like the best bet is to bet A on the ML in the head-to-head (Edit: against B) and C&D on winning the tourney. Winnings from A = risk on C&D.

If A wins, you are made whole on your C/D bet, with a small chance for some nice profit if C or D does win the tourney.

If B wins, you need to hedge against B winning the entire tourney,since that's the exposure.

So you'd risk to win on B what you risked on C&D, and the longs odds on C & D should make up for the amount needed to risk on B.


Does that sound right? Edit: No - you'll lose too much if you lose the A bet.

[djiddish98]

If I am right (still not sure) - does this happen often? I would figure the more likely scenario in a tournament is for A vs. D and C vs. B - although I'm sure you could have probably found these prices during the final four, with (5) butler vs. (5) mich st. and (1) duke vs. (2) WVA.

[u21c3f6]

I'm trying to wrap my head around this, so this may be off.

It seems the issue is with the fact that the odds for C and D are set regardless of the outcome on A vs. B. Hence, A and B have the same line against C / D even though one team is stronger than the other.

See my previous post. The issue is that in reality, the final lines will be quite different than what the semi-final lines are implying, and again, this is what creates the opportunity for a hedge.

Now this is where (most of) the "math" ends and "experience" takes over for me.

The above odds with some minor inconsequential changes for ease of calculation comes from the 2010 NCAA Basketball semi-finals. When I saw those odds, I honestly said to myself: "free money".

Here was my reasoning based on the odds and my experience. The odds were clearly saying that Butler (C) or MI (D) had only a small chance to win the finals. Since the actual odds on C and D were close, I considered them as one entity. The key for me was, what would the odds be if the finals became A/CD or B/CD? At a minimum A should be -240 but in reality A will be a bigger favorite because its odds in the semi-final round were being adversly affected by B (and vice-versa). My experience told me that in fact a conservative estimate for A in the finals would be from -275 to -300 and my conservative estimate for B was -200 to -225. We will never know for sure what the BC odds would have been but we do know that eventually you could get odds on the AC final in the low 300's. I think the odds went higher than I expected due to A's double digit win over B.

Now, there are many ways to set-up a hedge. There is no one right way (other than to try to make sure that the set-up is +EV). If you believed my estimates for an A/CD and B/CD contest, how would you wager in the semi-final round?

I will post what I did (if there is any interest) in a later post as I don't wan't to taint the thought process of those that may be trying to figure out a hedge set-up.

Joe.

[DoubleEM]

This is what the odds imply but surely this can't be correct (and the reason why there is an excellent hedging opportunity). Team A would almost certainly be a larger favorite if they make it to the finals as that comparison based on the semi-final lines also implies .4/.1667 or -240/+240 for an AC or AD contest.

Joe.

I agree my numbers can't be correct. So, the finals no vig lines are:

A vs C or D -240/+240
B vs C or D -160/+160

So, have we come far enough for you to reveal what the events were, what the actual odds were, and what you bet, or do you have another test? :-)

[djiddish98]

I think I see now - I ran this through solver


Odds Risk Win Net
A Wins Tourney 1.48 4.23 6.26 0.50
B wins tourney 2.72 2.80 7.60 0.40
CD wins Title game 2.5 2.97 7.43 0.40

Invest 10 dollars with a risk free return of .40 cents, or a guaranteed 4% ROI (I set that as my minimum).

Like you said, there are a lot of ways to handle this - you could setup your bets so you'll win X if A wins, and 0 on B or C/D winning.

This also assumes +250 odds for C/D in the title game. It seems as long as C/D is >= +205 in the title game, you'll have some sort of profit.

[u21c3f6]

I think I see now - I ran this through solver


Odds Risk Win Net
A Wins Tourney 1.48 4.23 6.26 0.50
B wins tourney 2.72 2.80 7.60 0.40
CD wins Title game 2.5 2.97 7.43 0.40

Invest 10 dollars with a risk free return of .40 cents, or a guaranteed 4% ROI (I set that as my minimum).

Like you said, there are a lot of ways to handle this - you could setup your bets so you'll win X if A wins, and 0 on B or C/D winning.

This also assumes +250 odds for C/D in the title game. It seems as long as C/D is >= +205 in the title game, you'll have some sort of profit.

Thank you for your example djiddish98. Yes, hedging in the way that I am describing depends on your ability to estimate what the odds will be after an event. Frankly, with a little bit of math and after some experience, it is not all that difficult to do IMO. Once you learn how to estimate the odds, deciding how to use those estimates to your advantage (of which there are many) becomes the next task. Then using some math and money management, you can figure out how to size your wagers.

In the example above, once I determined my estimates for the A/CD and B/CD possible finals game, I decided to approach the hedge from the CD side because their odds were closer together %-wise. At the time I was making my wagers, the actual odds for C ranged from mid to high 400's and D ranged from low to mid 500's. Looking at the odds I could see that I could set-up my hedge by wagering on C and D to lose at an average of -190 (which was better than what I could have arranged on AB to win at the time). Since my minimum estimate for the other side of this hedge once we get to the finals is +200, as far as I was concerned, I was going to have a guaranteed profit (this is not always the case for other hedges such as the West Conf BB finals where I determined I had a +EV hedge but with a small risk of a medium size loss). Once I determined that I had a "guaranteed" profit, size was easy, all-in . Even if (and when) my estimates are wrong, they are not wrong by very much and I might wind up with a relatively small loss. Remember, this is a hedge, not all the money is actually at risk. Of course doing it this way meant that I had more potential profit if A went to the finals instead of B but I was OK with that because based on the odds, that was the more likely event and what eventually happened.

Knowing that you are going to hedge going in is very different than deciding to hedge later IMO because you can allocate a much larger % of your bankroll to hedging than you can to let-it-ride wagers since all the money is not really at risk in a hedge (unless you set it up very poorly).

Looking at the hedge supplied by djiddish98, prior to the actual final, you could have received at least +300 for the other side of this hedge for a profit of .84. As far as ROI, I look at it as you are only wagering $7.03 and not $10 because the money on the other side of the hedge is never really at risk and in fact not even all of the initial wagers is at risk unless you don't hedge.

So, have we come far enough for you to reveal what the events were, what the actual odds were, and what you bet, or do you have another test? :-)

I think I have revealed most everything. No more tests!

Joe.