I think I've refunded everyone who paid for future weeks in advance.

Sunday put an exclamation point on the decision to give it a rest.  Hopefully Neteller withdrawals will actually go smoothly; that would ease the pain a lot.

To all: Thanks for the support.

Week: 11-32-1, -30.87 units (Ouch)

YTD: 358-378, +136.89 units (Better)

Yesterday: 3-6, -4.45 units

I notice a 2+2 thread has popped up discussing whether my system is losing steam as the year goes on.  Obviously, it's hard to separate variance from the truth, but I'll try.

So far we're running at an ROI of about -7% this month, versus 15.5% from April-June.  I hope all of you realize that the July number is a mirage; this system is not more than three times worse than making picks blindly.  Of course, you should also understand that the 15.5% was not going to keep up either.  If we finish the year with our current YTD return of 10.6%, I think we'll all be happy.
That said, my estimated ROI for the month is down to 11.9% from the consistent 13.1-13.3% figures in each of the last three months.  I don't believe this is a coincidence.  Pitchers like Fausto Carmona and Horacio Ramirez, to name just a couple, have now shown their true colors.  Teams like the Brewers are no longer sneaking up on the league, and no one still thinks the White Sox are any good.  There will be pitchers and teams that surprise in the second half for better or worse, but the market will gradually get more efficient.  I suspect this happens every year.

Overall, we're wagering slightly fewer units this month than in the past, but it's not really that big a difference.  You can confirm this on your own if you like; make sure to correct for the All-Star Break off days.  This is a further indicator that the system is becoming slightly less profitable, but it's not a huge difference.

A few of you have noticed that we don't have as many 4+ unit plays now as before.  This is partially because the switch to Kelly fractions has reduced the recommended bet size on some big underdogs, and largely because the biggest inefficiencies are the quickest to correct themselves.  Furthermore, pitchers like Kuo and DeSalvo are no longer plying their trade.

A losing streak is never easy.  Back in my poker playing days, I would probably take an extended break at this point, so I'll understand if a few of you don't renew your subscriptions for next week.  But make sure it's because you find the swings emotionally difficult, not because you think you're going to be making -EV bets from here on out.

A lot of you are asking relevant questions all over the place, where I or the other readers may not see them.  I think it may be a good idea to keep them in one place, so if there's anything you'd like to ask me, post it in the comments for this entry.
Keep in mind that I won't answer any specific questions about how I calculate my own lines, but almost everything else is fair game.

If you can no longer see the picks posts, it means you missed this week's payment.  Get it in to me whenever and you'll be added back.  I think we're past the bugs I had last week, but feel free to contact me if you believe you've been removed in error.

Yesterday: 1-1, -1.00 units.  Tough loss on SD.

All based off my personal record, which varies slightly from the posted picks due to fractional units and the occasional last-minute play:

Units Risked: 1386
Units Won: +164
Expectation: +180

ROI: 11.8%
Expected ROI: 13.0%

Since I don't have a BBV forum, I'll just include this here:

July Units Risked: 258
July Results: -9.9 units
Expectation: +32.0 units

July ROI: -3.7%
Expected ROI: 12.1%

Oh well.  I have no regrets, except that most of you probably increased your unit size as the year went along, which wasn't the best plan in hindsight.

If you're planning on re-upping your subscription for next week, there's no time like the present to get your weekly payment in so I don't get overwhelmed tomorrow night.

You may have heard that it is never correct to hedge a pending bet when the hedge itself is a -EV play.  This is usually good advice, but not always.

The most common situation where a bettor wants to hedge is when he has hit every leg of his parlay with one game to go.  Hedging here makes no sense: you should have simply left this game off your parlay and taken the lower payoff for one less game.  People often don't realize until it's too late that their $5 parlay can leave them with over $1000 riding on the last game.  Technically, it may be better for your bankroll to hedge this last game than let it ride, but you never should have been in this situation in the first place.  If you can't handle this swing and will want to hedge the last game, either don't bet parlays or bet smaller ones.

That said, there are a few situations where hedging can be correct.  The common link is that you have already made a bet with a relatively large payoff, and it's better for your long-term bankroll growth to reduce your risk somewhat.  In other words, you want to hedge when doing so will increase the geometric mean of your possible outcomes, bringing you closer to the optimal strategy for bankroll growth.  (For more on this concept, I recommend the excellent book Fortune's Formula.)  A few of these situations aren't common, but there is one that occurs quite frequently, which we'll get to later.

Let's say that you're offered a $10 freeplay bonus, and it can only be used to parlay every NFL game on the board in a given week.  Unlike the previous example, here you don't have the choice to parlay fewer games, so a hedge can make sense.  If you've gone 15-for-15 so far, you should certainly hedge the Monday Night game unless you are already quite wealthy.  In fact, you should probably hedge before the Sunday Night game.  You're giving up 4.5% of your EV, but that's not a big deal when tens of thousands are at stake.  (Remember, this is only when you aren't able to simply parlay less teams and collect the smaller payoff without paying extra juice.)

David Sklansky outlined a couple of other examples in one of his books.  Let's say you want to bet the Brewers to win the NL Central at 9-1.  You can't find anyone offering these odds, but you do see 35-1 on the Brewers to win the NL Pennant.  If they make it to the playoffs, you estimate you can take an average line of -350 on them to NOT win the NL.

If the Brewers make it to the playoffs either as a Wild Card or the division champ, you can hedge the bet for the full amount, risking 28 units to win 8 and guaranteeing a 7 unit profit.  In effect, you're getting 7-1 on the Brewers to make the playoffs.  It's not quite 9-1, but you also collect when they win the Wild Card, so it's close enough.  Even if you suspect the -350 hedge is somewhat -EV on its own, this combination of bets is well worth making if you think Milwaukee will make the playoffs 25% of the time.  The hedge allows you to risk a larger portion of your bankroll on the NL Pennant bet than you would otherwise, since it will not be a disaster if the Brew Crew lose in the playoffs.  It is this ability to risk more of your bankroll, and thus increase your overall EV, that makes the hedge a valuable tool.

Another example: Suppose that you know a stupid but honest bookie who is dealing a +150/-160 moneyline on a game when everyone else has it at +120/-130.  You estimate the correct line at +110/-110.  Assuming that your bet won't get no-actioned, you clearly want to make a max bet with your bookie.  However, this maximum may be a large fraction of your bankroll, far above the recommended Kelly bet size.  In this case, your best play is to max out your bookie, but take the -130 for a partial hedge/arb.  This gives you the equivalent of a better line than +150 on your overall bet, and doesn't put your bankroll at too much risk.  (This is similar to another Sklansky example where you play a middle in football rather than just one side, because you can bet larger amounts that way with little risk.)

A similar situation comes up all the time in sports betting.  You bet a team heavily at +150 against an estimated correct line of +100, wagering the correct amount for long-term bankroll growth.  Close to game time, the line has moved to +120/-130.  Is it correct to hedge part of this bet by laying -130 on the other team?

Absolutely it is.  Assuming you sized your first bet correctly, it will always be better for your long-term bankroll growth to hedge a fraction of this bet.  If you don't believe me, calculate the geometric mean of your possible outcomes before and after hedging $1 of your bet.  It will improve after the hedge every time.

An example will help clarify.  You have only one bookie, but he lets you bet juice-free; each game's moneyline looks like +125/-125.  Furthermore, you have a perfect estimate of the correct line for each game.  With this information, you can calculate optimal bet sizes for every game.  The optimal bet size is something of an equilibrium for a given game; after you bet that amount at +150, you're essentially indifferent to wagering an additional $1 at +150 or hedging $1 back at -150.  However, if you are offered better odds than +150 or -150, this shifts the equilibrium point, and you would now place additional bets to restore equilibrium.  (If that doesn't make sense, try re-reading it.  Those who did well in high-school science classes will probably better grasp the equilibrium concept.)

What happens if the line on this game suddenly moves to +130/-130?  Now you have a strong incentive to hedge, even if the game is a coin flip.  Remember, you didn't want to add to your bet at +150.  If you don't want to subtract from it at -130, that essentially means you are inclined to bet more at +130, or you're at least indifferent to doing so.  Something's gotta give: Either you should have bet more at +150 or you should hedge a portion of your bet now.  Since we have established that you bet the correct amount to begin with, the hedge must be correct.

I'm guessing that plenty of you have encountered this situation following these picks.  Yesterday's Florida-St. Louis game was an example.  I advised a hedge at StL +107, even though I believed that they were slightly bigger dogs to win than this.  But for the purposes of long-term bankroll growth, it was best to hedge most of the bet on Fla +102.

In general, it will always be correct to hedge part of the bet when the line moves this much.  However, I've yet to find an easy function to calculate what hedge amount is best, so that's for another post.

If you can't see Tuesday's picks, get your payment in!  You'll be re-added to the friends list as soon as you do.

Edit: Please make sure you're logged in before assuming you've been removed from the friends list.  If you're not logged in, you won't see the pick posts.

Remember to submit next week's payments by Sunday night.  I prefer sooner to later, since it can be a hassle when you're flooded with payments from every direction.  Hopefully next week we won't have any teams jump out to 3-0 first inning leads; those are real killers.

Sportsbook.com appears to have paid me (in under a month!) for the Cardinals bet fiasco.  My account balance has been adjusted for the amount of the bet, though no one gave an explanation why.  Perhaps not coincidentally, they just told my friend that they processed his cashout from a month ago.

Yesterday's results: 2-3, -2.50 units

I've received some questions about how much we should re-size our bets in response to a move from the posted line.  If you don't like math, feel free to skip to the end.


For + moneylines: Edge = (SB Line + 100) / (Est. Line + 100) - 1

For - moneylines: Edge = (Est Line * (SB Line - 100)) / (SB Line * (Est Line - 100)) - 1

We'll use + moneylines from here on out to simplify.  If the sportsbook line moves from SB1 to SB2 against our estimated line EL, how does our edge change?

For + moneylines:

d(Edge) = ((SB2 + 100) / (EL + 100) - 1) - ((SB1 + 100) / (EL + 100) - 1)

d(Edge) = (SB2 - SB1) / (EL + 100)

So the difference in percent edge equals the difference in cents of the line move, divided by the estimated line plus 100.  You don't have the estimated line, but you can approximate it, and generally speaking, if you plug in the actual sportsbook line in its place, you will be close enough.

(IF YOU SKIPPED AHEAD, RESUME READING HERE.)

Since a difference of one credit is a 2.5% change in edge, here are some rough estimates of line moves that would decrease the recommended bet size by 1 full credit:

+116 to +110
+148 to +140
+180 to +170
+200 to +188

Another decent rule of thumb is to multiply the line move in cents by the sportsbook line, then divide by 600.  This is approximately the number of credits by which you should alter your bet.  Obviously you will bet less with a less favorable line and more with a more favorable line.

If the line becomes more attractive and you have NOT YET bet it at the posted odds, you can add one credit to your bet size.  If you have already placed a bet at the old odds, you should add less than a credit to your existing bet.

Of course, this assumes that no additional information has become available.  If it turns out that Albert Pujols is not starting tonight for the Cardinals, you can throw all this out the window; you need a substantial line move to bet St. Louis for the same amount.