4th and 13

Date: Tue, Feb 5, 2008

In the first drive of the 3rd Quarter, with about 7 minutes left, the Patriots had the ball at the Giants 31 yard line, 4th down and 13 to go. They decided to go for the first down. Was that the right decision?

I believe Belicheck knows more about this stuff than almost anyone, including me. But it is still fun to analyze it instead of just saying "well, Belicheck always make the right decision." So, let's analyze it. Let's assume there was nothing wrong with Gostkowski. Throughout the post, I'll make a ton of other assumptions also. Changing any of the assumptions may change the evaluation. I don't pretend to think that all of my assumptions are spot on, I may be wrong on some of them. I do think it is useful to detail the process so any adjustments of assumptions can easily be made to give a better answer.

First, how likely was it for Gostkowski to make a 48-yard FG? I estimate 65%. It is tough to get detailed information on FG length, unless one wanted to pour through every boxscore, so this is how I got the estimate:

All NFL kickers this year in 50 yard or longer attempts were 47 for 99 for a 47.5% success rate. This stat was easy to get from NFL.com.

All NFL kickers this year in the 40 to 49 yard range were 201 for 266 for a 75.6% success rate.

I assumed 48 yards was tougher than the 40-49 yard range, but easier than 50+. I also assumed it is easier to kick a long FG in the dome on turf than in an average NFL game. So I picked 65%. Maybe I am off by 5% ... maybe it should be 60% or 70%...but I'll use 65% in this post.

If they miss the FG, the Giants will get the ball on their own 38. They get the ball at the spot it is kicked, which is about 7 yards behind the line of scrimmage. How much is the additional 7 yards worth? I estimate it is worth .7 points. This is just a guess. Let's also assume a blocked punt won't happen.

So we can now look at the EV in terms of points for going for the FG:

Make the FG: 65% x 3 = +1.95 points
Miss the FG: 35% x -.7 = -.25 points

Total in trying for the FG: +1.70 points

Now let's see what the value is if NE tries for the first down.
First, I will assume they have a 25% chance of completing the first down. This is just a guess.

I'll assume if they don't convert, it is worth 0 points.
I'll assume if they make the 4th down, it'll lead to a 65% chance of a TD, 25% chance of a FG and 10% chance of no score. However, if they don't score but do make the first down, it is likely that NYG get the ball deeper in their own field, I'll assume a value of +1 point for the Patriots if they make the 4th down but don't eventually score. They could intercept it and run it back, but on average, I'd estimate they get the ball at a worse position than their own 31.

The numbers:
Make 4th: 25%
Miss 4th: 75%

If Make 4th:
TD: 65%
FG: 25%
No Score: 10%

If the Patriots do score, to make it simpler, I'll assume the ensuing kickoff gives the Giants the ball at their own 31, which is where the ball is before the 4th down attempt.

TD: 65% x 7 = 4.55 points
FG: 25% x 3 = 0.75 points
No score: 10% x 1 = 0.10 points

That adds up to 5.4 points if they get the first down. If they have a 25% chance of converting the 4th down attempt, then:

Going for it: 25% x 5.4 = +1.35 points

So using these assumptions, I have the value of attempting a FG at 1.7 points, which is greater than the value of going for the first down at 1.35 points. But what if my assumptions are wrong? Let's just change one number....instead of assuming the Pats had a 25% chance of getting a first down, let's assume it is 32%. With that small adjustment, it makes going for it worth +1.73 points, slightly more than going for the FG.

Overall, I think Belicheck made a mistake. Of course, he could still be right, I doubt he'll correct my mistake if he thinks I made one. Some other thoughts:

• I don't think the assumption of converting the first down at 25% is too low. Maybe it was for the Patriots in the regular season, but given the way the Pats offense and the Giants defense were playing, 25% seems right. 32% seems way too high.
• Even if going for the FG or the first down had equal value, it is better to go for the FG in this position. That's because NE had the lead - 7 to 3, and 3 points makes a difference as a TD from the Giants only ties the game and does not give them the lead. The team that is ahead is willing to reduce variance. Teams that are ahead should be willing to give up a little EV (in terms of total points) if it means reducing variance. Reducing variance brings up the idea of punting.
• So what is the EV if the Patriots punted? Let's say on average they get the Giants the ball at their own 10 - only gaining 21 net yards on the punt. How much is that worth? Well, if 7 yards is worth 0.7 points as we used in the missed FG example above, then 21 net yards equals 3 x 0.7 or 2.1 points. Maybe punting was the best option.

Conclusion:

There are a ton of assumptions in this post. Change any of them drastically enough, and the answer may change. Overall, I really do think going for the first down is a mistake in this spot. Punting may not be better than trying for a FG, but I think those are the two options, not going for the first down. If anyone reading this thinks any of the assumptions should be changed, or if there is an error in my thought process, feel free to email me at kingyao@gmail.com I'm hoping for an email from a guy with BB initials, and I don't mean Barry Bonds.

Giants winning is good for future Super Bowls

Date: Tue, Feb 5, 2008

The Giants winning is a good thing for opportunities in the money line in future Super Bowls. The money line of -400 is too cheap relative to a point spread line of -12, although Jeff Fogle (a guy I respect tremendously) disagrees - see this thread on LVA Sports for a discussion on that issue.

Anyway, if you agree with me that the money line of -400 is too cheap and grabbing that along with +12 on the Giants was a good combination (in appropriate amounts of course), then the Giants winning the game wasn't good (but it wouldn't have been any worse in that combo than the Patriots covering the -12 points if you bet the correct amounts). But to keep things optimistic, it is a good thing for future Super Bowls. The public won big on the money line, the sports books got scared. This means the money line will be that much better of a bet in the future. Gotta look on the bright side.

More on Brady passing TD props

Date: Sat, Feb 2, 2008

Some people have asked me where I estimated Brady's average passing TDs in the Super Bowl. When I posted some of my bets earlier in the week, I was using around 2.65. That made Under 2.5 +170 look like a good bet.

But since then, a few things has happened. First, the total has gone up. That means slightly more points for the Patriots. Second, the team total for the Patriots is 34 at most books. That means Brady should be expected to pass for slightly more TDs. Lastly, there has been rumors from some seemingly credible sources that the Patriots will be passing much more often early in the game. I don't know if that's true or not, but I wouldn't discount it. So, let's assume for a second that Brady's estimated average TD should be 3.0. That's a big move from 2.65. What does that do to the Under 2.5 wager? Using the Poisson Distribution, Under 2.5 would be worth +136. +170 is still a good bet given that scenario. Of course, Under 3 is probably a better bet, but it is all price relative. Under 3 -119 is equal to Under 2.5 +136.

So did I lose value on this bet? Probably. But I also gained value on other bets that was pro-Brady. Bets such as:

1Q Brady TD Pass Yes +140 +124
4Q Brady TD Pass Yes -120 -130
Brady TD Pass before INT -280 -364
NE's first TD is pass -210 -212
First TD is Passing TD -170 -187


The first number is the price I bet at, the second is the value when I also thought Under 2.5 TD passes by Brady was worth +170. Those values should all increase now.

If Brady is going to throw for 4 or more TDs (remember, I don't have just Under 2.5, I also have Under 3 and Under 3.5...if he throws for exactly 3, I'm ok), then the other 5 related bets will have a better chance of winning than the prices I paid for them.

To sum it up, I thought I had edge in all of these bets. Even if I am wrong on one of them, many of the bets hedge each other. It is one thing to try to identify a positive-EV bet, and another to try to identify multiple positive-EV bets that hedge each other.

Yes, I could have waited and probably gotten a better price on the Brady Under 2.5 bet..maybe the Under 3 bet also (but probably I wouldn't have gotten a better price on the Under 3.5). But if I waited, I would probably also have missed value on the other bets, as some of those have moved to. I know the 1Q and 4Q bets are no longer available, and the Brady -1.5 vs Manning is mostly +160 in the books I see.

If I wanted to take on more risk, I would have taken the other props and left myself naked on the Brady Under 2.5 to bet now. There are two reasons I didn't do that:

1. I'm not in Vegas anymore, I left Friday. Not being a Vegas resident has some disadvantages, one is not having the ability to bet into possible softer lines as the game approaches.

2. My entire portfolio shows that I am rooting for NE to win the game. If they win by a blowout, I do well. So in essence, even with the Under 2.5 TD passes on Brady, I'm still rooting for him to do really well. Well, at least financially I'm rooting for him.

Super Bowl Player Props article

Date: Sat, Feb 2, 2008

Here is my latest article for the Two Plus Two Internet Magazine:

Super Bowl Player Props

Please note that when I wrote it, the market lines were -12 and 53. Since then, the total has crept up to 54, so the expected averages of the teams should be .5 point higher each.

Does the distribution of Touchdowns scored fit the Poisson Distribution?

Date: Fri, Feb 1, 2008

For Super Bowl props, I have been using the poisson distribution to help describe the distribution of touchdowns. For more on applying the poisson distribution to sports betting, get Sharp Sports Betting by Stanford Wong...note he is also my publisher, but believe me, I wouldn't recommend his book unless I thought it was good.

Here is an example of how I used the poisson distribution. In Las Vegas, one of the sportsbooks had a contest prop with multiple possibilities. It was on the exact number fo TD passes that Tom Brady would throw in the Super Bowl. They also had the same prop (with different prices) for Eli Manning.

For both players, I found there to be positive-EV in betting that they would throw exactly zero TDs. I bet Brady to throw zero TDs at 25 to 1 and Manning to throw zero TD passes at 4 to 1. I used two methods to value these props. The first was a simulation method which simulated the results of drives for the game for each team. I ran the simulation 10,000 times. The second method was using the Poisson Distribution. Both methods needed an accurate expected number of TD passes for the two QBs as the main input. Assuming I was accurate on that mean (if I wasn't, all results would be off), I found both 25 to 1 on Brady and 4 to 1 on Manning to be positive-EV bets.

Today I started thinking: does the poisson distribution really describe Touchdowns in the NFL well? Or probably better phrased: is the distribution of touchdowns in NFL games similar to a poisson distribution? (remember, I am not a statistician, just a gambler who tries to use techniques to get better values....so I apologize if this is not the correct technical way to say it)

That's a tough question to answer. First I would need to know the true mean of TD passes for the QBs. But with such small sample sizes (just 16 regular season games in a year), and other factors (quality of opponent's defenses for example), it is really difficult to peg it down too closely. So instead, I decided to throw a big net on the NFL and look at all games and see if the distribution of the number of TDs matched the poisson distribution. I think it does. Here are the results:

I took all games from 1989 to the end of the regular season of 2007 (including all playoff games except this year's playoff games as I had not inputed them yet). I have the number of rushing TDs, passing TDs and defensive/special teams TDs in all games during that span. I lumped defensive TDs with special teams TDs in one category.

Here are the averages both both teams combined. I did not separate out to individual teams.

Rushing TD: 1.61
Passing TD: 2.59
Def/ST TD: 0.44

Next, I added up the number of games with exactly 0 rushing TDs, exactly 1 rushing TDs, exactly 2 rushing TDs, etc. etc. and repeated it for the other two ways to score TDs.

Next, I plugged in the mean for each way to score a TD and had the poisson distribution spit out the expected number for each exact number of TD.

These two methods (the actual exact number of TDs in real games and the expected exact number of TDs using the poisson distribution) were very similar. Here are the results. The first number is the exact number of TDs, the second is the percentage of games that actually had that exact number of TDs, the third is the poisson distribution's prediction of the expected percentage of games that had that exact number of TDs.

Rushing TDs
0 19.6% 20.1%
1 32.6% 32.2%
2 25.8% 25.9%
3 14.6% 13.9%
4 4.8% 5.6%
5 1.8% 1.8%
6 0.5% 0.5%
7 0.1% 0.1%

Passing TDs
0 7.9% 7.5%
1 20.3% 19.4%
2 24.0% 25.1%
3 20.4% 21.7%
4 14.7% 14.1%
5 7.7% 7.3%
6 3.2% 3.2%
7 1.2% 1.2%
8 0.3% 0.4%
9 0.2% 0.1%

Defensive and Special Teams TDs
0 64.8% 64.3%
1 27.6% 28.4%
2 6.3% 6.3%
3 1.2% 0.9%
4 0.1% 0.1%


As you can see, the percentage numbers match up very closely. As a first pass, my opinion is that the possion distribution describes the distribution of TDs quite well, but one needs to be correct with the expected mean numbers. For example, it would be incorrect to assume that Brady's distribution of TD passes is the same as Manning's. Brady has a much higher average. So the crucial step is still estimating the average number of TD passes they will throw.

Some prop bets I made

Date: Wed, Jan 30, 2008

These prop bets were all made in Las Vegas. I don't know if any of them are still available at the same prices anymore. I've attached the price I got (first number) as well as my opinion of fair value (second number). Some of the bets were made at fair value, that's because I thought they hedged my exposure well, so I didn't mind making a zero-EV bet. The good thing about these combination of bets is that they all hedge another prop bet and usually with positive-EV.


Brady exactly 0 TD pass 25-1 +1800
Brady exactly 1 TD pass 10-1 +464
Brady Under 2.5 TD passes +170 -108
Brady Under 3 TD passes -135 -226
Brady Under 3.5 TD Passes -150 -335
Welker No TD -135 -150
Watson TD NO -165 -250
Stallworth score TD? No -260 -342
Gaffney no TD -200 -255

1Q Brady TD Pass Yes +140 +124
4Q Brady TD Pass Yes -120 -130
Brady TD Pass before INT -280 -364
Brady throws INT Yes +105 -110
NE's first TD is pass -210 -212
First TD is Passing TD -170 -187

Manning exactly 0 TD passes +400 +328
Manning Under 1.5 TD Passes +140 -154
Manning Under 1.5 TD Passes +140 -154

NYG's first TD is pass -150 -151
NYG Over 24.5 +215 +204
NYG Over 2.5 TD +150 +118
Brady -1.5 TD Passes vs Manning +200 +139
Manning +1 TD Pass +145 vs Brady +125
Manning +0.5 TD passes +225 Brady +200

Copycats in Super Bowl Props

Date: Mon, Jan 28, 2008

In my book, I wrote about a Las Vegas sportsbook that copied Super Bowl prop lines and made a mistake that cost them. I found another one a minute ago:

Kevin Faulk's longest rushing attempt will be over/under 3.5 yards.

I took the Over at -110.

The book mis-copied the line. The prop should have been: Kevin Faulk's FIRST rushing attempt. Faulk may not rush many times, so I may still lose, but this bet has great value. Now I just have to hope that they don't notice their mistake and cancel my wager...and if they allow it, they don't grade it incorrectly once the game ends. Books that mis-copy lines also tend to have a greater frequency of mis-grading winners/losers.

Some Super Bowl Props at the Hilton

Date: Mon, Jan 28, 2008

I was at the Hilton on Tuesday night to see their props open. Here's three that I bet that night:


Different number of Giants to score Under 3 +140
This doesn't seem like a great bet to most people, but I think there is nice value here. The bad thing about the under is that just one TD means two different Giants have scored. But the good thing about it is that it takes 3 TDs by the Giants for me to have a chance of losing...and even then, I may still push. It really is tough to put it into words because all the calculations is in the simulations. Sometimes things just can't be explained clearly in words, its all in the numbers.

Shortest TD is under 1.5 yards -140
I wrote about the shortest TD prop in my book, Weighing the Odds in Sports Betting. Although -140 is not cheap, it still has value. One reason I chose that prop to write about is that I was a bit comfortable that I might still find value in that prop in upcoming years. I can see a person who hasn't cranked out the math (or doesn't understand the math), thinking how likely is a 1-yard TD? Not very likely, I'm getting plus-money on the over, let's do it.

Patriots score before they punt -150
I think this has good value too, I think it is worth -180. That would be the case for most teams that are such a big favorite in a game with such a large total. But it is especially more so for the Patriots since they have the (correct) idea that punting is overrated. They often go for it on fourth down in unconventional spots. That means even if they get stopped, it is more likely that they were stopped on fourth down compared to other teams. Thus slightly more likely they score before they punt compared to other teams that are expected to score 33 points.

I'll write up a few more between now and the Super Bowl. On Wednesday, I'll be one of the many guests on Jon in Oakland's conference call. You can get more information on hist site:
http://www.sportsconferencecall.com/

Polls show how stupid the public can be

Date: Fri, Jan 18, 2008

Polls show how stupid the public can be. I don't mean political polls, I don't know much about politics. I mean the polls that are broadcast on the ESPN bottomline, I think they are called SportsNation or something like that. Apparently people log into ESPN.com and vote on who they think will win. In the upcoming championship games, the last time I saw it, 81% chose the Packers and 76% chose the Patriots. So the public thinks the Packers have a better chance to win than the Patriots? Or better put, more people think the Packers will win than think the Patriots will win. Given the line is Patriots -13.5 / -14 and Packers -7/-7.5, this shows the disparity between public opinion and where the money is. The money is usually right.

Losing on line movement

Date: Tue, Jan 15, 2008

Right after Sunday's games, I made two bets:

NYG +7.5 -125 vs GB
NE -15 -110 vs SD (I also took NE -14 -110 later that night when the line moved).

Whether these bets win or lose, I know I've already lost because the line has moved where I can easily get a better price right now.

GB is -7 everywhere. That means I can easily get NYG +7.5 -120 by buying a half-point. I was thinking the line would go down to GB -6.5, thus showing NYG +7.5 -125 as a close-to-fair-market wager. So I've definitely lost 5 cents on value, and probably 10 cents depending on how well I shopped for the Giants.

I was surprised the NE line went down. I thought there was a change it would go up to 17. Clearly I'm wrong. So I've alreadly lost a good chunk of EV since the line is now NE -13.5.

These two bets were bad due to line movement. I've had other good bets in the past. I took NYG +7.5 -110 against DAL early last week - the line moved to DAL -7 -110 so I won a little to line movement in that game. I also took NE -11 -110 against JAX, and then bought back JAX at +14.5 -120, so I won on the early bet on NE last week too. That one turned out to be a nice half-middle as NE won by exactly 11 points - not that 11 is a key number, but it is always nice to get a middle or half-middle.

I think keeping records and tracking wins/losses is very important. Without records, it is easy for poker player or a sports bettor to think they are winning when they are in fact losing...or think they are winning more than they actually are. But keeping records for line movement issues takes a lot more work. I wish I had kept more detailed records on that issue the past few years. A good new year's resolution for me is to start carefully detailing line movement issues on bets I make early.

NFL Divisional Round: the ATS record of favorites

Date: Fri, Jan 11, 2008

In the sports betting forums, posters sometimes post false facts or incomplete facts. Over the past few days, I've seen several posters mention that the second-round of the NFL playoffs is dominated by the home team, even against-the-spread. It all depends how far back you want to go with the records, but the word "dominating" is definitely an overexaggeration.

Here are the records for NFL home teams in the second round:

last ten years: 1997-2006:
Straight-up record: 30-10 or 75%
Against-the-spread record: 19-19-2 or 50%

The average line in these games was home -6.8.

Those numbers look like the market is doing a good job of pricing this round of the playoffs. It is a very small sample size.

If you see anyone tout the favorites this week (DAL -7.5, NE -13.5, GB -7.5 and IND -9) and they throw out the "home teams in this round dominate ATS", you may want to be skeptical of their handicapping skills.

Article on NFL Team Total push rates

Date: Sun, Jan 6, 2008

My latest article for the Two Plus Two Internet Magazine is on NFL Team Total push rates. This may come useful during the playoffs for comparing lines at different sportsbooks since so many are now offering Team Totals as a betting option.

Betting strategy on the Patriots in the playoffs

Date: Mon, Dec 31, 2007

Talking to some non-gambling sports friends, I keep hearing the same thing: "no one can beat the Patriots in Foxborough". They are making the mistake of assuming that just because no team is expected to beat the Patriots, that it means it can't happen. I'm looking forward to seeing the Patriots being big favorites, and waiting until game time to bet against them. Non-gambling sports fans sometimes turn into gamblers during the playoffs and make the market a bit more inefficient with the new money coming in on the favorite. I think there's a good chance for that to happen.

So my strategy is to bet the Patriots in any futures (AFC or Super Bowl) at fair value. Of course, that would be based on my projected odds. Unfortunately finding them at fair value is now difficult, but fortunately for me, I did load up on them earlier in the year :)

The next part of the strategy is to hedge with a positive-EV hedge on the underdog in the point spread when the games come up. I hope to implement this strategy in every game the Pats play, as I think they'll be overvalued and/or overbet in each game.

Recapping Season Long Bets

Date: Mon, Dec 31, 2007

The NFL regular season is over. I'll quickly recap the two set of prop bets I posted before the season began.

In the Regular Season Win Totals, I listed 13 teams. 6 of them won, 7 lost.

In the Interception props, I listed 17 unders. 11 won and 6 lost.