King Yao chimes in with his plan to buy Patriots futures and then bet against them in individual games, planning to arbitrage the two markets for a guaranteed profit.

I found a similar strategy useful during the World Series, although my reasoning was that the futures odds were off, not the individual game odds. As it turned out, betting the Red Sox to win the series and the Rockies in each game would have yielded a tidy 5% profit for a week's work.

Given that the Pats are reportedly 1-8 favorites to win the Super Bowl at The Mirage, it looks like King will need to use a betting exchange to find a good price on them to win it all. If only Vegas let you bet the "no" on those ridiculous lines...

## Monday, December 31, 2007

### Updated NFL Probabilities

Team | Conf | SB |

NE | 65.4 | 54.4 |

Ind | 22.2 | 15.9 |

SD | 5.7 | 3.7 |

Pit | 2.4 | 1.5 |

Jax | 3.7 | 2.5 |

Ten | 0.6 | 0.2 |

Dal | 57.8 | 13.4 |

GB | 24.3 | 4.9 |

Sea | 7.7 | 1.5 |

TB | 4.3 | 0.7 |

NYG | 3.6 | 0.7 |

Was | 2.3 | 0.4 |

I think if there's one general lesson about playoff futures betting, it's that you don't want to bother betting on a 6 seed to win the Super Bowl; the Redskins are going off around 50-1 when they should be 250-1. By betting the Skins game-by-game, you'll get a much better price than 50-1.

Actually, maybe another lesson is not to bet an NFC team to win the Super Bowl this year; only the Cowboys have a payoff that's close to fair odds.

(edited to fix rounding errors)

## Monday, December 24, 2007

### What the Patriots Can Teach Us About Futures Odds

A coin has landed on heads 15 times in a row. What are the chances of it landing heads on the 16th flip?

Many of you will pick one of three answers:

- The coin is "hot", so the chances are greater than 50%.

- The coin is fair, so the chances are exactly 50%.

- The coin is "due", so the chances are less than 50%.

These answers are all using incorrect logic. The correct answer considers the possibility of a loaded coin. Loaded coins are rare enough that when we start flipping, we don't think about them. But when 15 consecutive heads are flipped, Bayesian probability tells us that the chances of a loaded coin have gone way up. Thus, the probability of a heads on the 16th flip is significantly greater than 50%.

Now think about analyzing the probability of a team going 16-0 before the season starts. If you're a good handicapper, you can estimate the moneyline for each game and multiply the team's winning probabilities together. But this wouldn't give you an accurate estimate.

If a team is 15-0, chances are very good that the team is much better than you believed at the start of the season. Certainly this is the case for the 2007 Patriots; their season wins over/under was set at 11.5. Thus, your preseason estimate for the 16th game is likely to underestimate their chances of winning. The same is true for other intermediate games. So if you really want to handicap the chances of an undefeated team, or a similar proposition, you must account for the probabilities of teams performing much better or worse than you expected.

This principle has other applications as well. Many preseason baseball simulations have 80-projected-wins teams almost never making the playoffs (except in the NL Central, of course). But 80 is just a mean estimate; there's a significant chance the team actually has 88-win talent. A team that has a fixed talent level of 80 wins will make the playoffs very rarely, but if their actual talent follows a normal distribution from 70 to 90 wins, they have a legitimate shot. (Remember, a 90-win team can still overperform and win 100 games.)

And that, kids, is how the Colorado Rockies made it to the World Series. Colorado probably won't repeat, but I'd bet that at least one ".500 team" will play in October next year.

Many of you will pick one of three answers:

- The coin is "hot", so the chances are greater than 50%.

- The coin is fair, so the chances are exactly 50%.

- The coin is "due", so the chances are less than 50%.

These answers are all using incorrect logic. The correct answer considers the possibility of a loaded coin. Loaded coins are rare enough that when we start flipping, we don't think about them. But when 15 consecutive heads are flipped, Bayesian probability tells us that the chances of a loaded coin have gone way up. Thus, the probability of a heads on the 16th flip is significantly greater than 50%.

Now think about analyzing the probability of a team going 16-0 before the season starts. If you're a good handicapper, you can estimate the moneyline for each game and multiply the team's winning probabilities together. But this wouldn't give you an accurate estimate.

If a team is 15-0, chances are very good that the team is much better than you believed at the start of the season. Certainly this is the case for the 2007 Patriots; their season wins over/under was set at 11.5. Thus, your preseason estimate for the 16th game is likely to underestimate their chances of winning. The same is true for other intermediate games. So if you really want to handicap the chances of an undefeated team, or a similar proposition, you must account for the probabilities of teams performing much better or worse than you expected.

This principle has other applications as well. Many preseason baseball simulations have 80-projected-wins teams almost never making the playoffs (except in the NL Central, of course). But 80 is just a mean estimate; there's a significant chance the team actually has 88-win talent. A team that has a fixed talent level of 80 wins will make the playoffs very rarely, but if their actual talent follows a normal distribution from 70 to 90 wins, they have a legitimate shot. (Remember, a 90-win team can still overperform and win 100 games.)

And that, kids, is how the Colorado Rockies made it to the World Series. Colorado probably won't repeat, but I'd bet that at least one ".500 team" will play in October next year.

## Sunday, December 23, 2007

### Why You Can't Always Trust CoolStandings

Check out their current NFL odds.

There's nothing fundamentally wrong with their algorithm; it just isn't considering motivation. The Redskins and Titans each play a superior team in Week 17, but their opponents, the Cowboys and Colts, will be resting their starters for the playoffs while Washington and Tennessee play their hearts out to get their respective 6 seeds.

Tennessee opened as a 4-point favorite against Indy, and would probably be about a 7-point dog if Indy was trying. That's a huge swing, enough to make them substantial favorites instead of severe underdogs. Washington would ordinarily be an underdog to Dallas, but facing an unmotivated Cowboys team at home, the Redskins will probably open as solid faves.

Here are my updated odds estimates:

Edit: If you're wondering how the Giants' chances managed to get worse despite their clinching a playoff spot, bear in mind that they were almost certain to get in the playoffs anyway, plus I tweaked the numbers some.

That Titans number is not a typo. To win the AFC, they have to win at Indy, at San Diego (or Pittsburgh), at New England, and probably at Indy again. That's one brutal path.

There's nothing fundamentally wrong with their algorithm; it just isn't considering motivation. The Redskins and Titans each play a superior team in Week 17, but their opponents, the Cowboys and Colts, will be resting their starters for the playoffs while Washington and Tennessee play their hearts out to get their respective 6 seeds.

Tennessee opened as a 4-point favorite against Indy, and would probably be about a 7-point dog if Indy was trying. That's a huge swing, enough to make them substantial favorites instead of severe underdogs. Washington would ordinarily be an underdog to Dallas, but facing an unmotivated Cowboys team at home, the Redskins will probably open as solid faves.

Here are my updated odds estimates:

Team | Conf | SB |

NE | 67.8 | 54.6 |

Ind | 21.2 | 15.1 |

Pit | 4.1 | 2.6 |

SD | 4.3 | 2.6 |

Jax | 2.3 | 1.4 |

Ten | 0.4 | 0.1 |

Dal | 56.6 | 15.0 |

GB | 25.2 | 5.4 |

Sea | 6.6 | 1.2 |

TB | 4.5 | 0.7 |

NYG | 3.7 | 0.7 |

Was | 2.4 | 0.4 |

Edit: If you're wondering how the Giants' chances managed to get worse despite their clinching a playoff spot, bear in mind that they were almost certain to get in the playoffs anyway, plus I tweaked the numbers some.

That Titans number is not a typo. To win the AFC, they have to win at Indy, at San Diego (or Pittsburgh), at New England, and probably at Indy again. That's one brutal path.

## Wednesday, December 19, 2007

### Tom Brady Redux

Tom Brady now needs five touchdown passes in the final two weeks to break Peyton Manning's record of 49. Will he get there?

The bettors at World Sports Exchange certainly think so; they've made Brady more than a 2-1 favorite to get to 50. But the betting market for obscure props like this one is rarely efficient; the ratio of 'fan money' to sharp bets is unusually high. So we can't trust the market for the answer to this one.

The big unanswered question, of course, is how much action Brady will see in Week 17 if the Patriots are still undefeated at that point. The Giants are heavily favored to clinch a playoff spot this weekend, so they likely won't be trying their hardest to stop the Pats' juggernaut. Will that convince Bill Belichick to coast to a seventeenth win by letting his backups play the second half? Will the Pats play it safe either way and not risk an injury to Brady, the one player they truly can't afford to lose?

I'll operate under these assumptions:

- If the Pats lose to the Dolphins (roughly a 6% chance), Brady sits almost all of Week 17.

- If the Pats are 15-0 and the Giants have clinched a playoff berth (66%), Brady plays with this frequency:

1 quarter: 20%

1st half: 10%

3 quarters: 15%

full game: 55%

- If the Pats are 15-0 and the Giants are still playing to get in (28%), Brady plays with this frequency:

1 quarter: 15%

1st half: 10%

3 quarters: 5%

full game: 70%

As for Brady's true skill level of throwing touchdowns, I'm going to set it at 2.5 per game, or 40 per season. I think this is fair. Yes, he's well over that pace this season, but his previous career high was 28, and only three other QBs in history have thrown 40 over a full season. Regression to the mean is a powerful force.

I'll spare you the boring calculations, but the Poisson distribution tells us that with this set of assumptions, Brady breaks the record 44.2% of the time, a far cry from 2/3.

If Brady is assumed to play all eight quarters of his remaining games, he breaks the record with 56.0% frequency.

Using a true rate of 50 TD/season and the above playing time distribution, Brady breaks the record 62.0% of the time.

If you assume eight quarters of play and a true rate of 50 TD/season, that number increases to 74.7%, but I think that's unreasonable on both counts.

The bettors at World Sports Exchange certainly think so; they've made Brady more than a 2-1 favorite to get to 50. But the betting market for obscure props like this one is rarely efficient; the ratio of 'fan money' to sharp bets is unusually high. So we can't trust the market for the answer to this one.

The big unanswered question, of course, is how much action Brady will see in Week 17 if the Patriots are still undefeated at that point. The Giants are heavily favored to clinch a playoff spot this weekend, so they likely won't be trying their hardest to stop the Pats' juggernaut. Will that convince Bill Belichick to coast to a seventeenth win by letting his backups play the second half? Will the Pats play it safe either way and not risk an injury to Brady, the one player they truly can't afford to lose?

I'll operate under these assumptions:

- If the Pats lose to the Dolphins (roughly a 6% chance), Brady sits almost all of Week 17.

- If the Pats are 15-0 and the Giants have clinched a playoff berth (66%), Brady plays with this frequency:

1 quarter: 20%

1st half: 10%

3 quarters: 15%

full game: 55%

- If the Pats are 15-0 and the Giants are still playing to get in (28%), Brady plays with this frequency:

1 quarter: 15%

1st half: 10%

3 quarters: 5%

full game: 70%

As for Brady's true skill level of throwing touchdowns, I'm going to set it at 2.5 per game, or 40 per season. I think this is fair. Yes, he's well over that pace this season, but his previous career high was 28, and only three other QBs in history have thrown 40 over a full season. Regression to the mean is a powerful force.

I'll spare you the boring calculations, but the Poisson distribution tells us that with this set of assumptions, Brady breaks the record 44.2% of the time, a far cry from 2/3.

If Brady is assumed to play all eight quarters of his remaining games, he breaks the record with 56.0% frequency.

Using a true rate of 50 TD/season and the above playing time distribution, Brady breaks the record 62.0% of the time.

If you assume eight quarters of play and a true rate of 50 TD/season, that number increases to 74.7%, but I think that's unreasonable on both counts.

## Sunday, December 16, 2007

### Updated NFL Probabilities

Standard disclaimers apply.

Team | Conf | SB |

NE | 67.4 | 54.1 |

Ind | 21.7 | 15.0 |

Pit | 4.2 | 2.7 |

SD | 3.8 | 2.2 |

Jax | 2.1 | 1.2 |

Dal | 56.3 | 15.3 |

GB | 26.1 | 5.7 |

Sea | 6.7 | 1.2 |

TB | 4.0 | 0.7 |

NYG | 4.4 | 0.8 |

## Friday, December 14, 2007

### What's On Tap For 2008

- I'm moving off Blogger and onto "real" hosting. If you have the Blogger address bookmarked, please adjust it to www.baseballplayoffodds.com, which currently redirects to this page.

- Right now, I'm working with someone on developing a Monte Carlo simulation like the ones you see on BP and Coolstandings, only better. I can't promise anything about the functionality yet, but the inputs will definitely be more accurate, since I can better account for injuries, trades, and updated player/team forecasts.

- For the playoffs and late in the regular season, the Monte Carlo simulation can give way to a mathematical analysis based on estimated odds for each individual game. Among other things, this should eliminate the problem of variance in quality of starting pitchers. (If your team is starting Johan Santana and Jose Lima in its two remaining games, they should be assigned winning chances of 65% and 35%, not 50% for each game.)

If nothing else, it should be interesting to look at.

- Right now, I'm working with someone on developing a Monte Carlo simulation like the ones you see on BP and Coolstandings, only better. I can't promise anything about the functionality yet, but the inputs will definitely be more accurate, since I can better account for injuries, trades, and updated player/team forecasts.

- For the playoffs and late in the regular season, the Monte Carlo simulation can give way to a mathematical analysis based on estimated odds for each individual game. Among other things, this should eliminate the problem of variance in quality of starting pitchers. (If your team is starting Johan Santana and Jose Lima in its two remaining games, they should be assigned winning chances of 65% and 35%, not 50% for each game.)

If nothing else, it should be interesting to look at.

## Wednesday, December 12, 2007

### Updated Projections

My predicted 2008 standings generated some criticism, fair and otherwise, but no one mentioned one error I'm going to correct here: I had the average AL team winning 80 games and the average NL team 82.

Each team plays a maximum of 18 interleague games, so these numbers shouldn't stray far from 81, but clearly the AL is the much stronger league at this point, so I re-ran the numbers with the AL averaging 81.8 wins and the NL 80.3, plus some number tweaking and roster updates through the signing of Fukudome:

Interesting how the 2008 White Sox project stronger than the 2007 squad even though they're coming off a season with 18 fewer wins. Some possible theories on why:

- Bounce-back seasons by Mark Buehrle and Javier Vazquez

- Ditching Scott Podsednik and Darin Erstad (and adding Carlos Quentin)

- Inaccurate inputs by me

Rumor has it that Fukudome is considering wearing a jersey that reads "Kosuke" much like Ichiro. I wonder how much that will hurt merchandise sales?

Each team plays a maximum of 18 interleague games, so these numbers shouldn't stray far from 81, but clearly the AL is the much stronger league at this point, so I re-ran the numbers with the AL averaging 81.8 wins and the NL 80.3, plus some number tweaking and roster updates through the signing of Fukudome:

NYY | 92 | Cle | 88 | LAA | 84 |

Bos | 91 | Det | 86 | Oak | 79 |

Tam | 84 | Min | 84 | Sea | 77 |

Tor | 84 | ChW | 76 | Tex | 72 |

Bal | 73 | KC | 72 | ||

NYM | 90 | ChC | 85 | SD | 87 |

Phi | 87 | Mil | 83 | LAD | 84 |

Atl | 83 | Cin | 82 | Ari | 79 |

Fla | 74 | StL | 75 | Col | 79 |

Was | 74 | Hou | 76 | SF | 74 |

Pit | 74 |

Interesting how the 2008 White Sox project stronger than the 2007 squad even though they're coming off a season with 18 fewer wins. Some possible theories on why:

- Bounce-back seasons by Mark Buehrle and Javier Vazquez

- Ditching Scott Podsednik and Darin Erstad (and adding Carlos Quentin)

- Inaccurate inputs by me

Rumor has it that Fukudome is considering wearing a jersey that reads "Kosuke" much like Ichiro. I wonder how much that will hurt merchandise sales?

## Sunday, December 9, 2007

### Conference/Super Bowl Odds

These are based on my estimated moneylines for playoff games, so they reflect any built-in market bias, plus my estimates may be inaccurate. Translation: Experimental, use at your own risk.

Note that the odds will not sum to 100% because I ignored teams with small chances to advance.

Note that the odds will not sum to 100% because I ignored teams with small chances to advance.

Team | Conf | SB |

NE | 69.0 | 55.0 |

Ind | 18.8 | 12.8 |

Pit | 6.9 | 4.5 |

SD | 2.4 | 1.4 |

Jax | 1.9 | 1.1 |

Dal | 58.9 | 16.3 |

GB | 24.0 | 5.1 |

Sea | 6.8 | 1.2 |

TB | 4.6 | 0.7 |

NYG | 4.1 | 0.7 |

## Thursday, December 6, 2007

### Extremely Preliminary Projections

Here's a teaser of my projected 2008 MLB standings. Keep in mind: these are very raw, as there's still plenty of transactions left between now and Opening Day, plus the numbers need fine-tuning from better projection systems, which aren't out yet:

I'm sure a lot of you are surprised at the high win totals for the Rays, Twins, Reds, and Padres, and the low totals for the Tigers and Angels. Here's a brief rundown on each:

Rays: Should get a huge boost from improved team defense this year, plus they have lots of good young players on the rise. They've also upgraded their pitching through several trades and the signing of Troy Percival.

Twins: Projection still includes Johan Santana and Joe Nathan. They still have a dominant pitching staff, and Mauer and Morneau give them some life on offense.

Reds: Loaded with young talent. Jay Bruce, Joey Votto, Homer Bailey, and Johnny Cueto are all top-shelf prospects who should make an impact in 2008.

Padres: Their hitters are better than you think--thanks, PETCO Park--and those pitchers are still devastating.

Tigers: I covered their 2008 prospects here. The trade with the Marlins doesn't help them as much as you may think, because Cabrera can't play defense and Willis is really no better than Miller going forward. I do think they'll win more than 83 games, but less than 90.

Angels: They only really have one solidly-above-average position player. Again, I think this number is a little low, but only by a couple of wins, not ten.

What's really impressive, at least to me, is that no team is projected to finish more than ten games away from .500. Of course, variance during the actual 2008 season will stretch these numbers out, so we'll probably see a team win or lose 100 games. Still, this is food for thought if you still believe baseball needs a salary cap to keep things competitive.

NYY | 91 | Cle | 86 | LAA | 82 |

Bos | 89 | Min | 83 | Oak | 77 |

Tam | 83 | Det | 83 | Sea | 77 |

Tor | 82 | ChW | 73 | Tex | 71 |

Bal | 73 | KC | 72 | ||

NYM | 91 | ChC | 85 | SD | 89 |

Phi | 89 | Mil | 84 | LAD | 85 |

Atl | 85 | Cin | 83 | Ari | 81 |

Fla | 76 | StL | 79 | Col | 80 |

Was | 75 | Hou | 79 | SF | 76 |

Pit | 75 |

I'm sure a lot of you are surprised at the high win totals for the Rays, Twins, Reds, and Padres, and the low totals for the Tigers and Angels. Here's a brief rundown on each:

Rays: Should get a huge boost from improved team defense this year, plus they have lots of good young players on the rise. They've also upgraded their pitching through several trades and the signing of Troy Percival.

Twins: Projection still includes Johan Santana and Joe Nathan. They still have a dominant pitching staff, and Mauer and Morneau give them some life on offense.

Reds: Loaded with young talent. Jay Bruce, Joey Votto, Homer Bailey, and Johnny Cueto are all top-shelf prospects who should make an impact in 2008.

Padres: Their hitters are better than you think--thanks, PETCO Park--and those pitchers are still devastating.

Tigers: I covered their 2008 prospects here. The trade with the Marlins doesn't help them as much as you may think, because Cabrera can't play defense and Willis is really no better than Miller going forward. I do think they'll win more than 83 games, but less than 90.

Angels: They only really have one solidly-above-average position player. Again, I think this number is a little low, but only by a couple of wins, not ten.

What's really impressive, at least to me, is that no team is projected to finish more than ten games away from .500. Of course, variance during the actual 2008 season will stretch these numbers out, so we'll probably see a team win or lose 100 games. Still, this is food for thought if you still believe baseball needs a salary cap to keep things competitive.

## Tuesday, November 20, 2007

### Patriots 16-0

The Pats certainly look dominant, but can they really go undefeated? Mercury Morris is pulling for them. ESPN anchors respond to this question with their typical yes/no approach, but I like to think I'm a little more sophisticated than that.

The chance at 16-0 is particularly appealing because you can bet both sides of the prop ('Yes' and 'No') for good prices; the Yes is as good as 1-1 (Intertops), the No as good as +230 (VIP).

I'm no NFL handicapper, but NFL game lines are usually pretty accurate. The lines for some future Patriots games are already out, so we can use them to roughly estimate their chances of winning each game:

Week 12: vs. Eagles: 95.0%

Week 13: at Ravens: 91.0%

Week 14: vs. Steelers: 90.0%

Week 15: vs. Jets: 96.0%

Week 16: vs. Dolphins: 96.0%

Week 17: at Giants: 88.0%

The Giants line is interesting; the Patriots are 11-point favorites, but that number is probably influenced by the possibility that New England rests their starters in Week 17. If they lose before Week 17, they'll probably do this, but a run at immortality might convince them to go for broke. In lieu of this possibility, I adjusted the Pats' winning percentage up from 83.0 to 88.0.

Remembering that these numbers are not tested for accuracy, the final verdict: The Pats go undefeated approximately 63.1% of the time, and you should bet both sides of the prop if you have accounts at both Intertops and VIP.

The chance at 16-0 is particularly appealing because you can bet both sides of the prop ('Yes' and 'No') for good prices; the Yes is as good as 1-1 (Intertops), the No as good as +230 (VIP).

I'm no NFL handicapper, but NFL game lines are usually pretty accurate. The lines for some future Patriots games are already out, so we can use them to roughly estimate their chances of winning each game:

Week 12: vs. Eagles: 95.0%

Week 13: at Ravens: 91.0%

Week 14: vs. Steelers: 90.0%

Week 15: vs. Jets: 96.0%

Week 16: vs. Dolphins: 96.0%

Week 17: at Giants: 88.0%

The Giants line is interesting; the Patriots are 11-point favorites, but that number is probably influenced by the possibility that New England rests their starters in Week 17. If they lose before Week 17, they'll probably do this, but a run at immortality might convince them to go for broke. In lieu of this possibility, I adjusted the Pats' winning percentage up from 83.0 to 88.0.

Remembering that these numbers are not tested for accuracy, the final verdict: The Pats go undefeated approximately 63.1% of the time, and you should bet both sides of the prop if you have accounts at both Intertops and VIP.

## Thursday, November 8, 2007

### Adrian Peterson

Adrian Peterson is on pace to set all kinds of records this year, but will he? Sportsbook.com is offering odds that Peterson will break Eric Dickerson's rookie rushing record of 1808 yards. The line is Yes -250/No +190, meaning that the bookies think he has somewhere between a 65.5% and 71.4% chance to do it.

To break the record, Peterson needs 773 yards in his final eight games. It's easy to say that he's on pace for another 1036, so he should break the mark with room to spare. I, on the other hand, think this is another case where we're not giving fair consideration to regression to the mean.

773 yards in eight games is a full-season pace of 1546 yards. How many running backs were projected to top 1546 yards before the season started? Just one, according to KUBIAK: Frank Gore, who's not exactly lighting the world on fire right now.

Furthermore, Gore isn't splitting time. Peterson has Chester Taylor taking ten carries a game from him. Though AP took the rock 30 times Sunday, that looks like an aberration; he should get about 20 carries per game the rest of the way, IF he stays healthy.

With 160 carries, Peterson needs to average over 4.83 yards per carry to break the record. I'll gladly take the Under on that. Feel free to search for a running back who averaged 4.9 yards or better as a starter in his rookie year; you'll be busy for awhile. Furthermore, given Peterson's dominant stats and the Vikings' total lack of passing game, it's very likely defenses will key in on Purple Jesus the rest of the way.

Getting +190, I have to strongly recommend the Under here, which should probably hit 50% of the time or so.

To break the record, Peterson needs 773 yards in his final eight games. It's easy to say that he's on pace for another 1036, so he should break the mark with room to spare. I, on the other hand, think this is another case where we're not giving fair consideration to regression to the mean.

773 yards in eight games is a full-season pace of 1546 yards. How many running backs were projected to top 1546 yards before the season started? Just one, according to KUBIAK: Frank Gore, who's not exactly lighting the world on fire right now.

Furthermore, Gore isn't splitting time. Peterson has Chester Taylor taking ten carries a game from him. Though AP took the rock 30 times Sunday, that looks like an aberration; he should get about 20 carries per game the rest of the way, IF he stays healthy.

With 160 carries, Peterson needs to average over 4.83 yards per carry to break the record. I'll gladly take the Under on that. Feel free to search for a running back who averaged 4.9 yards or better as a starter in his rookie year; you'll be busy for awhile. Furthermore, given Peterson's dominant stats and the Vikings' total lack of passing game, it's very likely defenses will key in on Purple Jesus the rest of the way.

Getting +190, I have to strongly recommend the Under here, which should probably hit 50% of the time or so.

## Sunday, November 4, 2007

### Tom Brady

(Yes, it's not baseball, but we have to branch out in the offseason before this blog gets condemned.)

What are the odds Tom Brady breaks Peyton Manning's record by throwing for 50 touchdowns this year?

To do so, Brady needs 17 or more TDs in the Patriots' seven remaining games. Of course, it seems unlikely that Brady will play full games in Weeks 16 and 17, but stranger things have happened (like running up the score in a 38-0 game.)

The possible outcomes can be approximated by a Poisson distribution. If we assume Brady's true level of performance right now is 40 TD/year, and that he plays the equivalent of six full games from here on out, his expected number of touchdowns for the rest of the year is 15. The Poisson distribution tells us that 33.6% of the time, he will throw for 17 or more scores.

If you question those assumptions (and who wouldn't) here's the full chart:

What are the odds Tom Brady breaks Peyton Manning's record by throwing for 50 touchdowns this year?

To do so, Brady needs 17 or more TDs in the Patriots' seven remaining games. Of course, it seems unlikely that Brady will play full games in Weeks 16 and 17, but stranger things have happened (like running up the score in a 38-0 game.)

The possible outcomes can be approximated by a Poisson distribution. If we assume Brady's true level of performance right now is 40 TD/year, and that he plays the equivalent of six full games from here on out, his expected number of touchdowns for the rest of the year is 15. The Poisson distribution tells us that 33.6% of the time, he will throw for 17 or more scores.

If you question those assumptions (and who wouldn't) here's the full chart:

True Rate | Record % |

12 | 10.1% |

13 | 16.5% |

14 | 24.4% |

15 | 33.6% |

16 | 43.4% |

17 | 53.2% |

18 | 62.5% |

19 | 70.8% |

20 | 77.9% |

21 | 83.7% |

22 | 88.3% |

## Sunday, October 28, 2007

### Futures vs. Game Odds

4 G | 5 G | 6 G | 7 G | |

Rockies | .023 | |||

Red Sox | .545 | .242 | .141 | .049 |

The 2007 World Series makes for a good case study in how betting markets perceive futures bets vs. individual game bets. In general, you're going to see more efficient lines for single games than futures, because single games attract more action, which tends to move the line to a more accurate spot. In contrast, many futures bettors are the stereotypical "squares" betting on the hometown nine to win it all, leading sportsbooks to shade the lines against popular teams like the Yankees and Cubs.

This year's World Series was particularly interesting because it pitted an obviously superior Boston squad against an underdog that had as much "momentum*" as any team ever. This type of situation is likely to lead to squares betting on the winning streak to continue. In other words, we'd expect the Red Sox to be a lesser favorite for the Series than they would be against a team that was just as talented as the Rockies but didn't begin the Series on a big winning streak.

Indeed, the Series line closed at a market price of roughly Rockies +210/Red Sox -210. For those of you not familiar with money lines, that means the Rockies are expected to win the World Series 100 / (210 + 100) = 32.3% of the time.

The individual game lines, which should be a more accurate portrayal of each team's odds to win, closed at roughly:

Game 1: Rockies +205 (32.8%)

Game 2: Rockies +190 (34.5%)

Game 3: Rockies +130 (43.5%)

Game 4: Rockies +130 (43.5%)

The numbers in parentheses indicate the expected chances for the Rockies to win each game based on the closing money line. Since Games 5-7 feature the same pitching matchups as Games 1-3, we can estimate the money lines by extrapolation, with slight changes for the DH and home-field advantage:

Game 5: Rockies +125 (44.4%)

Game 6: Rockies +190 (34.5%)

Game 7: Rockies +210 (32.3%)

Given these individual game percentages, we can calculate the chances of the Rockies winning the Series--using the same method I did to come up with my pre-WS estimate. It comes to...

24.9%.

The Rockies, based on the bookie's own lines, should have been 3-1 dogs. Instead they were going off at almost 2-1.

I leave it to the reader to interpret this result, but it sure looks like the bookies knew they would get plenty of money on Colorado without offering a big price, and then laughed all the way to the bank.

* - The quote marks indicate that I do not agree with the media definition of the word "momentum" in sports. In physics, momentum does not magically switch from one direction to another, back and forth.

## Friday, October 26, 2007

### GG Rockies

4 G | 5 G | 6 G | 7 G | |

Rockies | .035 | .060 | ||

Red Sox | .277 | .267 | .233 | .127 |

This seems more productive than simply giving the chances of winning the series. Yes, the Red Sox sweep three times as often as the Rockies win the Series.

Thanks for playing, Colorado. This Cinderella story is more Brothers Grimm than Disney.

## Thursday, October 25, 2007

### More Validation!

Diamond Mind's take

Here were my estimates for the Series results prior to Game 1:

Pretty close match.

For the record, I had the Rockies at 45.8% to win the Series if they had taken Game 1, which is probably the biggest discrepancy I have with the Diamond Mind numbers.

Edit: Hat Tip, along with MGL/Tango numbers that also closely resemble mine: The Book blog

Here were my estimates for the Series results prior to Game 1:

4 G | 5 G | 6 G | 7 G | |

Rockies | .027 | .075 | .085 | .091 |

Red Sox | .118 | .181 | .230 | .193 |

Pretty close match.

For the record, I had the Rockies at 45.8% to win the Series if they had taken Game 1, which is probably the biggest discrepancy I have with the Diamond Mind numbers.

Edit: Hat Tip, along with MGL/Tango numbers that also closely resemble mine: The Book blog

### Validation!

Just noticed this article from Clay Davenport, where he goes into detail about different ways to handicap the World Series.

Two things to take from it:

1. His 73.6% Red Sox estimate (from before Game 1) squares up pretty well with mine.

2. The gap in percentages across different methods shows just how dangerous it can be to blindly follow a postseason odds report that doesn't use the proper inputs.

Kudos to Clay for putting forth the effort.

Two things to take from it:

1. His 73.6% Red Sox estimate (from before Game 1) squares up pretty well with mine.

2. The gap in percentages across different methods shows just how dangerous it can be to blindly follow a postseason odds report that doesn't use the proper inputs.

Kudos to Clay for putting forth the effort.

### 10/25 Update

Team | WS% |

Boston | 82.2 |

Colorado | 17.8 |

Take this with a grain of salt, because I think Ubaldo Jimenez should be a substantially bigger underdog tomorrow than +170.

## Tuesday, October 23, 2007

### Number Tweaking

Aaron Cook is in as the Game 4 starter, and Tim Wakefield is out. How does this affect the odds?

Assuming Jon Lester starts Game 4 and Cook is on a tight pitch count:

On the plus side for Colorado, Game 4 is their best chance to actually be favored in any individual game in the Series. I have the line estimated at Colorado -103.

There are all kinds of other possibilities if Terry Francona is willing to throw Josh Beckett in games 1, 4, and 7, but I see no evidence that this will happen.

Assuming Jon Lester starts Game 4 and Cook is on a tight pitch count:

Team | WS% |

Boston | 72.2 |

Colorado | 27.8 |

On the plus side for Colorado, Game 4 is their best chance to actually be favored in any individual game in the Series. I have the line estimated at Colorado -103.

There are all kinds of other possibilities if Terry Francona is willing to throw Josh Beckett in games 1, 4, and 7, but I see no evidence that this will happen.

## Sunday, October 21, 2007

### World Series Update

Team | WS% |

Boston | 73.1 |

Colorado | 26.9 |

I guess I just flat-out disagree with the oddsmakers here. If you're thinking of betting the Rockies, I urge you to bet individual game lines, which should be far more favorable than the opening Series line.

### Efficient Market? Yeah, Right

Before Game 6, the consensus of the exchange markets was that the Red Sox were roughly 33.5% to win the AL and 24% to win the World Series. These numbers squared pretty well with mine, and pegged Boston as over 70% to win the World Series should they get there.

Now? Those numbers are around 62% and 39%. After winning a 12-2 blowout, Boston's chances of beating the Rockies go down to 63%? Huh? And the Indians, who were dogs in every game of the ALCS, are at 38% and 25%--indicating they would be bigger favorites in the World Series than the Red Sox?

The market may be full of savvy bettors, but from where I stand, it still looks like they can't do math. And I still say the Red Sox series line gets bet to at least -230 before the first pitch of Game 1. I'm not so sure on the Indians.

Now? Those numbers are around 62% and 39%. After winning a 12-2 blowout, Boston's chances of beating the Rockies go down to 63%? Huh? And the Indians, who were dogs in every game of the ALCS, are at 38% and 25%--indicating they would be bigger favorites in the World Series than the Red Sox?

The market may be full of savvy bettors, but from where I stand, it still looks like they can't do math. And I still say the Red Sox series line gets bet to at least -230 before the first pitch of Game 1. I'm not so sure on the Indians.

## Saturday, October 20, 2007

## Friday, October 19, 2007

### Big Comebacks or Faulty Algorithms?

It seems like every year, we see an MLB team make an epic comeback or collapse in the playoff race. In 2007, the Mets shot themselves in the foot, resulting in their postseason chances going from 99.8% to 0% in 18 days (and 96% to 0% in the final 5 days); the Phillies were roughly 200-1 dogs on September 13. Additionally, Arizona won the NL West as a 70-1 dog on July 21.

Last year, the Twins were at one point a 500-1 shot to win the AL Central. In 2005, the Astros made it as a 240-1 dog, and the Indians blew a 96.5% chance in the final week.

How do we account for all these longshots hitting in a span of only three years? There are three possibilities:

A) We've witnessed several anomalies

B) The BP Postseason Odds aren't perfect

C) A little of column A, a little of column B

Well, B is certainly true--I'll bet even Clay Davenport would agree with this--but I think we're looking at C. Even if we have a perfect playoff odds model, it's not going to project the Mets to dump seven games in a row to the Phillies, plus some more to the Nationals and Marlins. It won't expect the Diamondbacks to have a 17-game stretch starting July 19 where they go 13-4 with a -2 run differential.

These were examples of what Football Outsiders would call Non-Predictive Events: certainly the Phillies and D-Backs played well to reach the playoffs, but if they had to do it again, they'd probably come up short.

For now, though, I'd like to focus on B. There are several things standing between between the BP Odds and a perfect model, but how many of them can be practically implemented?

- Tiebreakers

I think this is doable. Coolstandings already includes tiebreakers in their simulations. In the first half of the season, it's usually difficult to forecast how the tiebreakers are going to pan out, but by August you can usually tell.

If the report doesn't break ties, it could at least display the probability of a tie so that readers can make manual adjustments.

- Differences in Starting Pitcher Quality

This is certainly impractical for use in April, but it could be added for late September, or certainly for the playoffs themselves. Facing Brandon Webb instead of Livan Hernandez is a pretty big deal, and the September 27 (or mid-October) odds report should account for that.

- Shifting Team Composition

This is tricky. Certainly you want to adjust the odds report when Chris Carpenter goes down for the season or Mark Teixeira is traded, but where do you draw the line between significant and insignificant changes? I'm sure if Clay gambled on his reports, he would account for these things, but he can't be expected to account for every little injury or trade.

The ELO report is designed to account for these changes, but it's not very effective in that regard. How long does it take for the Teixeira trade to show up in the ELO numbers? A month? If Tex doesn't hit in the first few weeks, you may never notice the difference.

- Accurate Regression Numbers

Now we're talking. There's a good discussion on THE BOOK blog, with the authors concluding that the current Davenport formula does not regress each team's stats far enough toward their preseason projections, especially early in the season.

Take another look at the list of longshot winners. The 2007 Diamondbacks, 2006 Twins, and 2005 Astros were all expected to be serious contenders, and all were much better teams than their early-season records would have you believe. Did the BP Odds read too much into their slow starts? MGL and DFL seem to think so in posts 15 and 21 from the thread linked above.

Could it be that the '06 Twins, despite being 12 games out in the division race, were actually 50-1 dogs rather than 500-1? Between their disappointing start and the first-half over-achievement of the Tigers and White Sox that year, I think it's entirely possible.

Tom Tango and others have done good work determining the proper amount of regression to use in projections. I think this is one area the Odds Report can easily improve upon.

---

I don't mean to deride the BP Odds Report, a useful tool that sparked my interest in betting sports futures. But as with all things baseball, when I see something that's working at 80% efficiency, I want to see that number move closer to 100.

Can I just build a better model myself? Maybe. I'd need some help with computer programming, if anyone's willing to volunteer, but it could be an interesting project to keep me busy in the offseason.

Last year, the Twins were at one point a 500-1 shot to win the AL Central. In 2005, the Astros made it as a 240-1 dog, and the Indians blew a 96.5% chance in the final week.

How do we account for all these longshots hitting in a span of only three years? There are three possibilities:

A) We've witnessed several anomalies

B) The BP Postseason Odds aren't perfect

C) A little of column A, a little of column B

Well, B is certainly true--I'll bet even Clay Davenport would agree with this--but I think we're looking at C. Even if we have a perfect playoff odds model, it's not going to project the Mets to dump seven games in a row to the Phillies, plus some more to the Nationals and Marlins. It won't expect the Diamondbacks to have a 17-game stretch starting July 19 where they go 13-4 with a -2 run differential.

These were examples of what Football Outsiders would call Non-Predictive Events: certainly the Phillies and D-Backs played well to reach the playoffs, but if they had to do it again, they'd probably come up short.

For now, though, I'd like to focus on B. There are several things standing between between the BP Odds and a perfect model, but how many of them can be practically implemented?

- Tiebreakers

I think this is doable. Coolstandings already includes tiebreakers in their simulations. In the first half of the season, it's usually difficult to forecast how the tiebreakers are going to pan out, but by August you can usually tell.

If the report doesn't break ties, it could at least display the probability of a tie so that readers can make manual adjustments.

- Differences in Starting Pitcher Quality

This is certainly impractical for use in April, but it could be added for late September, or certainly for the playoffs themselves. Facing Brandon Webb instead of Livan Hernandez is a pretty big deal, and the September 27 (or mid-October) odds report should account for that.

- Shifting Team Composition

This is tricky. Certainly you want to adjust the odds report when Chris Carpenter goes down for the season or Mark Teixeira is traded, but where do you draw the line between significant and insignificant changes? I'm sure if Clay gambled on his reports, he would account for these things, but he can't be expected to account for every little injury or trade.

The ELO report is designed to account for these changes, but it's not very effective in that regard. How long does it take for the Teixeira trade to show up in the ELO numbers? A month? If Tex doesn't hit in the first few weeks, you may never notice the difference.

- Accurate Regression Numbers

Now we're talking. There's a good discussion on THE BOOK blog, with the authors concluding that the current Davenport formula does not regress each team's stats far enough toward their preseason projections, especially early in the season.

Take another look at the list of longshot winners. The 2007 Diamondbacks, 2006 Twins, and 2005 Astros were all expected to be serious contenders, and all were much better teams than their early-season records would have you believe. Did the BP Odds read too much into their slow starts? MGL and DFL seem to think so in posts 15 and 21 from the thread linked above.

Could it be that the '06 Twins, despite being 12 games out in the division race, were actually 50-1 dogs rather than 500-1? Between their disappointing start and the first-half over-achievement of the Tigers and White Sox that year, I think it's entirely possible.

Tom Tango and others have done good work determining the proper amount of regression to use in projections. I think this is one area the Odds Report can easily improve upon.

---

I don't mean to deride the BP Odds Report, a useful tool that sparked my interest in betting sports futures. But as with all things baseball, when I see something that's working at 80% efficiency, I want to see that number move closer to 100.

Can I just build a better model myself? Maybe. I'd need some help with computer programming, if anyone's willing to volunteer, but it could be an interesting project to keep me busy in the offseason.

## Tuesday, October 16, 2007

### 10/17 Update

Team | LCS% | WS% |

Boston | 16.5 | 12.3 |

Cleveland | 83.5 | 54.7 |

Colorado | 100.0 | 33.0 |

As if Colorado's championship hopes hadn't risen enough lately, the Indians' three-game win streak is presenting the Rockies with a more favorable World Series matchup. Snow delays, anyone?

### Aaron Cook

Apparently I've missed this because no one in the mainstream has mentioned it, but the Rockies may be considering adding Aaron Cook to their World Series roster.

Will this help them out? Obviously it depends on whether he's ready to return. A healthy Cook would be a huge upgrade over Josh Fogg and a solid upgrade over Franklin Morales or Ubaldo Jimenez. Of course, if Cook does come back, it may be as a long reliever, or maybe he pushes Morales out of the rotation instead of Fogg. Maybe Clint Hurdle will feel the same way he did with the NLCS roster: that he doesn't want to shake up a winning formula.

Whatever the case, it appears unlikely Hurdle will play his cards optimally. Still, this is something to consider; Cook could give the Rockies a fighting chance in the World Series if he's all the way back.

Will this help them out? Obviously it depends on whether he's ready to return. A healthy Cook would be a huge upgrade over Josh Fogg and a solid upgrade over Franklin Morales or Ubaldo Jimenez. Of course, if Cook does come back, it may be as a long reliever, or maybe he pushes Morales out of the rotation instead of Fogg. Maybe Clint Hurdle will feel the same way he did with the NLCS roster: that he doesn't want to shake up a winning formula.

Whatever the case, it appears unlikely Hurdle will play his cards optimally. Still, this is something to consider; Cook could give the Rockies a fighting chance in the World Series if he's all the way back.

### 10/16 Update

Team | LCS% | WS% |

Boston | 37.8 | 28.1 |

Cleveland | 62.2 | 40.8 |

Colorado | 100.0 | 31.1 |

The Rockies pull ahead of Boston for the first time this season. Still, look at the contrast in their LCS percentages despite the similar WS numbers.

Again, it's possible I'm being too hard on Colorado here, but I still think the individual WS game lines will make these numbers seem reasonable when all is said and done. Here are some sample moneylines I actually used in the calculations for these percentages:

Cleveland (Westbrook) -107 @ Colorado (Fogg) +107

Cleveland (Sabathia) -105 @ Colorado (Francis) +105

Boston (Beckett) -118 @ Colorado (Francis) +118

Do these numbers look terribly unrealistic to anyone? The only problem is that these are among the MOST favorable matchups for the Rockies; they will be big underdogs in every road game. Colorado doesn't really have a great option at DH, and they face a top pitcher (or the solid Jake Westbrook) every time they play in Jacobs Field or Fenway Park.

## Sunday, October 14, 2007

### 10/15 Update

Team | LCS% | WS% |

Boston | 57.0 | 42.3 |

Cleveland | 43.0 | 28.1 |

Arizona | 5.2 | 1.7 |

Colorado | 94.8 | 27.9 |

Wait a minute, am I actually suggesting that not one but BOTH AL teams have a better chance of winning the World Series than the Rockies, who are up 3-0 in the NLCS?

Yup. 20 wins in 21 games is something special, but this team is still inferior to the Indians and a far cry from the Red Sox--Boston rates as nearly a 3-1 favorite should they get there.

Am I being unfair to Colorado? Possibly, but I'm using the same numbers I did for previous interleague games, which matched the estimated World Series line (AL -210 / NL +210) when the playoffs opened. Yes, the Rockies won 90 games, but they had healthy starting pitching for most of the season. Can you really imagine a World Champion team with Josh Fogg penciled in to start two Series games?

Colorado opened the night trading at 38 (sell) / 42 (buy) to win the World Series on WSEX. (For those unfamiliar with WSEX, this basically means they have between 38% and 42% chance to win, and if you disagree you can buy or sell Rockies futures.) That line has already been bet down to 35/39, but I think it will come down even more before the first pitch of the Fall Classic.

## Saturday, October 13, 2007

### 10/13 Update

Team | LCS% | WS% |

Boston | 73.2 | 54.5 |

Cleveland | 26.8 | 18.0 |

Arizona | 13.8 | 4.2 |

Colorado | 86.2 | 23.3 |

How's this for a prop bet at the start of the year: Rockies to be the square pick to win the World Series on October 13. Probably could have gotten 500-1 odds on that easy.

Edit: The picture only gets worse for the non-Boston teams if the Red Sox throw Beckett on short rest in Game 4, a possibility that became far more likely when he cruised to a 10-3 win yesterday and hit the showers early. Terry Francona probably left Beckett in for an unnecessary inning, but at least he didn't pull a Bob Brenly. (Remember Randy Johnson being left in to protect the D-Backs' 15-0 lead in Game 6, 2001?)

## Friday, October 12, 2007

## Monday, October 8, 2007

### 10/9 Update

Team | LCS% | WS% |

Boston | 59.7 | 43.8 |

Cleveland | 40.3 | 26.5 |

Arizona | 47.2 | 14.8 |

Colorado | 52.8 | 14.8 |

If those NL numbers look like they've changed yet again, it's because I played around with a few numbers, and Colorado benefits.

If Arizona and Cleveland each throw their ace in Games 1, 4, and 7 of the LCS, the numbers look like this:

Team | LCS% | WS% |

Boston | 58.1 | 43.0 |

Cleveland | 41.9 | 27.9 |

Arizona | 49.9 | 14.9 |

Colorado | 50.1 | 14.1 |

Interestingly, it looks like Arizona's chances at a championship aren't really helped by burning through Webb three times against Colorado, since he is then only available twice in the World Series. Of course, this is only a problem if the series goes the full seven games.

### 10/8 Update (II)

Chien-Ming Wang is now pitching Game 4 for the Yankees, leaving Andy Pettitte to Game 5.

Note to the Red Sox: Great job picking the extra day of rest in your division series! I'm sure you'd rather face the Yankees than a team led by Eric Wedge anyway.

Team | DivS% | LCS% | WS% |

Boston | 100.0 | 56.7 | 41.6 |

Cleveland | 71.1 | 29.3 | 19.3 |

New York | 28.9 | 14.0 | 10.3 |

Arizona | 100.0 | 48.6 | 14.8 |

Colorado | 100.0 | 51.4 | 14.0 |

Note to the Red Sox: Great job picking the extra day of rest in your division series! I'm sure you'd rather face the Yankees than a team led by Eric Wedge anyway.

## Sunday, October 7, 2007

### 10/8 Update

Team | DivS% | LCS% | WS% |

Boston | 100.0 | 56.8 | 41.6 |

Cleveland | 71.6 | 29.5 | 19.4 |

New York | 28.4 | 13.7 | 10.2 |

Arizona | 100.0 | 48.6 | 14.8 |

Colorado | 100.0 | 51.4 | 14.0 |

If Eric Wedge grows a brain and starts C.C. Sabathia in Game 4, this changes to:

Team | DivS% | LCS% | WS% |

Boston | 100.0 | 57.0 | 41.8 |

Cleveland | 74.1 | 30.5 | 20.1 |

New York | 25.9 | 12.5 | 9.3 |

Arizona | 100.0 | 48.6 | 14.9 |

Colorado | 100.0 | 51.4 | 14.0 |

Looks better, doesn't it? Maybe Wedge is a square and bet on the Yankees.

Edit: Why did the Ari/Col numbers change, you ask? I reduced the impact of a variable to account for Brandon Webb starting three games in the series, because I haven't seen any indications that it will happen.

### 10/7 Update

Team | DivS% | LCS% | WS% |

Boston | 91.1 | 52.5 | 38.5 |

Cleveland | 83.0 | 35.2 | 23.1 |

Los Angeles | 8.9 | 3.9 | 2.5 |

New York | 17.0 | 8.4 | 6.2 |

Arizona | 100.0 | 49.9 | 15.6 |

Colorado | 100.0 | 50.1 | 14.1 |

## Saturday, October 6, 2007

### A Quirk

You may have noticed that the current incarnation of the playoff odds indicates the Rockies have the edge over the D-Backs in the NLCS, but Arizona has a better shot to win the World Series once they get there. What gives?

It is very likely Arizona will set up their World Series rotation with Brandon Webb starting Games 1, 4, and 7. For them not to do so would be both colossally stupid and inconsistent with Bob Melvin's track record. (It's actually possible they will do this in the NLCS as well. Right now, I've set a low probability that Webb goes three games in the NLCS, but this may change based on developments, and take Arizona's NL% up with it.)

Meanwhile, I don't see the Rockies doing the same with Jeff Francis, and anyway, Francis is no Brandon Webb. Colorado has a more balanced rotation, which doesn't give them any additional help in a short series.

Really, this D-Backs team is reminiscent of the '01 incarnation, except they're missing the second stud SP and the big bopper in the middle of the lineup. Of course, those are some big shoes to fill, but if Webb can win three games, Arizona may have a puncher's chance.

It is very likely Arizona will set up their World Series rotation with Brandon Webb starting Games 1, 4, and 7. For them not to do so would be both colossally stupid and inconsistent with Bob Melvin's track record. (It's actually possible they will do this in the NLCS as well. Right now, I've set a low probability that Webb goes three games in the NLCS, but this may change based on developments, and take Arizona's NL% up with it.)

Meanwhile, I don't see the Rockies doing the same with Jeff Francis, and anyway, Francis is no Brandon Webb. Colorado has a more balanced rotation, which doesn't give them any additional help in a short series.

Really, this D-Backs team is reminiscent of the '01 incarnation, except they're missing the second stud SP and the big bopper in the middle of the lineup. Of course, those are some big shoes to fill, but if Webb can win three games, Arizona may have a puncher's chance.

### How This Works

This is essentially a three-step process for each team:

1. Determine the target number of wins to achieve the team's desired outcome.

For example, the goal might be to clinch a division or to win a playoff series. In the case of a division race, the target (magic number) can also be reached by virtue of the other team losing games.

2. Estimate the winning chances for both teams in each relevant remaining game.

I'm a professional baseball handicapper. It's my job to get this step right, although I'm not always going to be 100% accurate.

"Relevant" game means we're dealing with all games involving the team itself, plus the teams chasing them in a division race, and their potential future opponents in the playoffs. For example, the current Red Sox probability to win the World Series is affected by every game played, because each game changes their likelihood of facing a given opponent later on. Their chances to win the AL are affected only by AL games.

It is this step which I hope will separate me from the pack of others who have developed playoff odds estimates. If Clay Davenport ever decides to start handicapping individual games, I'll be out of business in no time.

3. Use probability calculations to determine the chance of the team achieving its goal.

If a team needs to win three games in a row with winning probabilities of .474, .475, and .395, it has a (.474)(.475)(.395) = 8.9% chance to win all three. (This is the actual situation the L.A. Angels are in right now.)

Most calculations are going to be more complex than this, which is why I'm doing them for you.

1. Determine the target number of wins to achieve the team's desired outcome.

For example, the goal might be to clinch a division or to win a playoff series. In the case of a division race, the target (magic number) can also be reached by virtue of the other team losing games.

2. Estimate the winning chances for both teams in each relevant remaining game.

I'm a professional baseball handicapper. It's my job to get this step right, although I'm not always going to be 100% accurate.

"Relevant" game means we're dealing with all games involving the team itself, plus the teams chasing them in a division race, and their potential future opponents in the playoffs. For example, the current Red Sox probability to win the World Series is affected by every game played, because each game changes their likelihood of facing a given opponent later on. Their chances to win the AL are affected only by AL games.

It is this step which I hope will separate me from the pack of others who have developed playoff odds estimates. If Clay Davenport ever decides to start handicapping individual games, I'll be out of business in no time.

3. Use probability calculations to determine the chance of the team achieving its goal.

If a team needs to win three games in a row with winning probabilities of .474, .475, and .395, it has a (.474)(.475)(.395) = 8.9% chance to win all three. (This is the actual situation the L.A. Angels are in right now.)

Most calculations are going to be more complex than this, which is why I'm doing them for you.

### Why MLB Playoff Odds?

You may be familiar with some or all of the three sites that have produced postseason odds for MLB. Why are my numbers different, and more importantly, why are they better?

The three sites above use what is known as a Monte Carlo simulation. In effect, the Monte Carlo engine creates a million different possible futures. In each future timeline, every team has a fixed percentage chance to win each of its scheduled games. If the Yankees are a 60-40 favorite over the Indians at Yankee Stadium, they are assigned a 60% chance to win that game in each simulation.

This is a good method, but to use it optimally, we need accurate inputs. All of the above simulators assume that a .500 team is a .500 team on any given day. In our example, the Yankees will be assigned a 60% chance to beat the Indians regardless of whether the pitching matchup is Wang-Laffey or DeSalvo-Sabathia. If A-Rod and Jeter collide while going for a pop-up and knock each other out for tomorrow's game, the .600 figure remains unchanged.

Furthermore, of the three, only Coolstandings applies tiebreakers to determine a champion in deadlocked playoff races. There are many instances where one team has a tiebreaker advantage clinched well before the end of the season, but the simulator simply counts this as half a win. That's fine for rough estimates, but we can do better.

Now, over a long season, these things tend to even out. But late in the season, or during the playoffs, these factors have a great influence on the race and the probabilities of each team advancing.

I'm not familiar with running my own Monte Carlo simulations, although Clay Davenport or the Coolstandings guys are welcome to give me recommendations for learning. What I can work with is probability distributions. Say you handicap a team's chances to win each game of a 5-game series at respectively .629, .514, .723, .450, and .498. From there, it's a relatively simple process to determine their probability of winning the series (61.8%). If the team wins Game 1, this figure goes up (75.9%); if they lose, it declines (38.0%).

Similarly, in the last month of a playoff race, handicapping each individual game should give you substantially better accuracy than you'd get from a Monte Carlo simulation. If your team is playing the Yankees in the final week but Joe Torre is resting all his regulars for the playoffs, you shouldn't be rated as a tremendous underdog. If the schedule lines up so that the Padres can pitch Jake Peavy twice in their final five games, this is a big advantage for them.

My goal is to integrate these considerations. Since they're most useful in a simple and predictable format like the playoffs, there's no time like the present to debut them.

The three sites above use what is known as a Monte Carlo simulation. In effect, the Monte Carlo engine creates a million different possible futures. In each future timeline, every team has a fixed percentage chance to win each of its scheduled games. If the Yankees are a 60-40 favorite over the Indians at Yankee Stadium, they are assigned a 60% chance to win that game in each simulation.

This is a good method, but to use it optimally, we need accurate inputs. All of the above simulators assume that a .500 team is a .500 team on any given day. In our example, the Yankees will be assigned a 60% chance to beat the Indians regardless of whether the pitching matchup is Wang-Laffey or DeSalvo-Sabathia. If A-Rod and Jeter collide while going for a pop-up and knock each other out for tomorrow's game, the .600 figure remains unchanged.

Furthermore, of the three, only Coolstandings applies tiebreakers to determine a champion in deadlocked playoff races. There are many instances where one team has a tiebreaker advantage clinched well before the end of the season, but the simulator simply counts this as half a win. That's fine for rough estimates, but we can do better.

Now, over a long season, these things tend to even out. But late in the season, or during the playoffs, these factors have a great influence on the race and the probabilities of each team advancing.

I'm not familiar with running my own Monte Carlo simulations, although Clay Davenport or the Coolstandings guys are welcome to give me recommendations for learning. What I can work with is probability distributions. Say you handicap a team's chances to win each game of a 5-game series at respectively .629, .514, .723, .450, and .498. From there, it's a relatively simple process to determine their probability of winning the series (61.8%). If the team wins Game 1, this figure goes up (75.9%); if they lose, it declines (38.0%).

Similarly, in the last month of a playoff race, handicapping each individual game should give you substantially better accuracy than you'd get from a Monte Carlo simulation. If your team is playing the Yankees in the final week but Joe Torre is resting all his regulars for the playoffs, you shouldn't be rated as a tremendous underdog. If the schedule lines up so that the Padres can pitch Jake Peavy twice in their final five games, this is a big advantage for them.

My goal is to integrate these considerations. Since they're most useful in a simple and predictable format like the playoffs, there's no time like the present to debut them.

### October 6 Playoff Odds

Here are the playoff advancement percentages for the remaining MLB teams as of October 6. The chart should be self-explanatory:

Team | DivS% | LCS% | WS% |

Boston | 90.7 | 52.2 | 37.8 |

Cleveland | 83.0 | 35.2 | 22.8 |

Los Angeles | 9.3 | 4.1 | 2.6 |

New York | 17.0 | 8.4 | 6.1 |

Arizona | 83.1 | 40.2 | 12.6 |

Chicago | 16.9 | 9.4 | 3.2 |

Colorado | 85.3 | 41.7 | 11.7 |

Philadelphia | 14.7 | 8.6 | 3.1 |

### Inaugural Post

I'm not sure what will become of this blog. Chances are high it will die a quick death. If it doesn't, it could be something along the veins of Coolstandings and the BP Playoff Odds, but based on better inputs.

Welcome. When we hit it big, you can say you knew me before I was famous.

Welcome. When we hit it big, you can say you knew me before I was famous.

Subscribe to:
Posts (Atom)