CRIS Salami Line

[mathdotcom]

Away +3 -105
Home -3 -115

Away ML +135
Home ML -155

In 2009, the probability of the home team winning by 1, 2, or 3 runs was 0.29.

These lines do not add up.

[Pancho sanza]

Away +3 -105
Home -3 -115

Away ML +135
Home ML -155

In 2009, the probability of the home team winning by 1, 2, or 3 runs was 0.29.

These lines do not add up.

.29 sounds low for winning by 1,2 or 3 runs.

Think its closer to 34 %

[sharpcat]

If anything the line suggests that the probability of the home team 1,2,3 is more in the 10% range

[mathdotcom]

If anything the line suggests that the probability of the home team 1,2,3 is more in the 10% range

That's the point of the thread

Pancho, you are correct. I think I forgot to add the Prob(Margin=3) in that figure. 35% it is.

[sharpcat]

That's the point of the thread

Pancho, you are correct. I think I forgot to add the Prob(Margin=3) in that figure. 35% it is.

5dimes has the spread at 3.5 -110

[mathdotcom]

So does SBG.

We are hammering AWAY +3.5!

[ForgetWallStreet]

So does SBG.

We are hammering AWAY +3.5!

Might as well take the -104 Pinny is currently dealing +3.5 at if you're dead set on doing this...

[mathdotcom]

Thanks FWS

You might have the best username on SBR.

[djiddish98]

Wouldn't this be away / home matchup dependent?

However, a quick eyeball of the lines seems to indicate not too many large chalk home faves.

I would think a possible approach might be taking the sum of the differences in team totals?

[tomcowley]

Wait, are you trying to apply single-game push %s to the salami spread-ML conversion?

[mathdotcom]

Wait, are you trying to apply single-game push %s to the salami spread-ML conversion?

When I say the home team wins by 1, 2, or 3, I am referring to the sum of all home team runs on a given day.

[tomcowley]

Don't have numbers in front of me, but there's simply no way home wins the salami by 1-3 34% of the time. And that's a crappy metric anyway for obvious reasons.

[mathdotcom]

Don't have numbers in front of me, but there's simply no way home wins the salami by 1-3 34% of the time. And that's a crappy metric anyway for obvious reasons.

1] Maybe you should look before you speak.
2] I am dying to hear this obvious reason.

[djiddish98]

When I say the home team wins by 1, 2, or 3, I am referring to the sum of all home team runs on a given day.

Are you controlling for number of games?

[TomG]

Each day's Salami is unique, composed of multiple games each with its own unique run distribution. Some days have lots of games with an expected run total around 7 or below. Some days have more games lined at 10 or higher. Some days have 15 games being played. Some days only have 9.

For Salami totals, you need to determine the push percentages for each game's run total and combine them. For the home/away ML and spread, you'll need each games distribution or Team Totals to create the Salami spreads and MLs.

[mathdotcom]

Are you controlling for number of games?

No I'm ignoring that as most days have a full slate of baseball. Maybe I would if it were monday.

99% of games are played on days where the sum of the market totals is over 100 (which should indicate at least 10 games being played on that day).

Any model can be criticized, but I think this stat is pretty telling.

[mathdotcom]

Each day's Salami is unique, composed of multiple games each with its own unique run distribution. Some days have lots of games with an expected run total around 7 or below. Some days have more games lined at 10 or higher. Some days have 15 games being played. Some days only have 9.

For Salami totals, you need to determine the push percentages for each game's run total and combine them. For the home/away ML and spread, you'll need each games distribution or Team Totals to create the Salami spreads and MLs.

Thanks for your reply Tom.

I will need to think about this more, but it seems to me that using Team Totals is only important if you're concerned with variance. I only care about expected value. In that case shouldn't the moneyline already incorporate the information regarding the team totals? Suppose there are just two games:

Case 1:

Home Team A's Team Total: 6
Away Team B's Team Total: 3

Home Team C's Team Total: 6
Away Team D's Team Total: 3

Case 2:

Team A's Team Total: 10
Team B's Team Total: 0

Team C's Team Total: 10
Team D's Team Total: 14

In either case you expect the home salami to win by 6 runs, but there should be higher variance in case 2. I have no way to show this, but wouldn't the average home moneyline be quite close in either case?

In any event, I feel like the 34% figure quoted above is fairly representative of most days' slate of games. There's going to be a whole bunch of -110 to -150 favorites and a couple of -200 favorites. If we had a very unusual slate where every game has a -200 favorite maybe I would be more cautious. The 34% figure would have to be way off to justify the CRIS spread-to-ML conversion, though. Or maybe my 2009 sample is not a good one.

[djiddish98]

How did today's sum of the totals compare to the average from your sample?

I have no familiarity with the salami, but like TomG said, I would probably be looking at team totals difference as well as sum of the totals.

tomC is a smart guy - If it was me, I would question the unconditional use of 34% based on his opinion alone.

[TomG]

You need to take into consideration both the ML and Total for each game. Mix those situations around and see what happens...

Game 1
ML -105 / -105
Total o6.5 -105

Game 2
ML +300 / -330
Total o10.5 -105

Now you have one game that is expected to be a pretty low scoring, balanced affair but another that is a potential high scoring blowout. Are you properly accounting for the likely range of outcomes from each game?

[mathdotcom]

I realize that the distribution matters, but I am assuming that the distribution from my 2009 sample reasonably matches the distribution of today's games. 34% does seem high, but in order for that spread to be justified, it must mean that the true distribution of the home salami victory margin of today's games is wildly different than the average distribution of the 2009 sample. I don't buy that.

This is done all of the time, like calculating the value of a half point off of an MLB total of 7.5. I'm sure it depends on the team totals, but a rule of thumb is that it's still worth about 31 cents.

There are a couple of other practical considerations as well. I don't have previous data on team totals, nor do I think the team totals market is particularly efficient. So it's a question of somewhat dirty analysis or none at all. I can only imagine how dirty some peoples handicapping models are.

[mathdotcom]

How did today's sum of the totals compare to the average from your sample?

I have no familiarity with the salami, but like TomG said, I would probably be looking at team totals difference as well as sum of the totals.

tomC is a smart guy - If it was me, I would question the unconditional use of 34% based on his opinion alone.

I appreciate Tom's input, but I am defending my post in the hopes of either being more convinced I am right, or being proven wrong. Either outcome is good for me.

[mathdotcom]

I believe today's totals summed up to 138.5 and the average sum of market totals in 2009 was about 119.

By the way, in 2009 when the sum of market totals was 138.5 (happened 30 times), 14/30 of those times the home salami won by either 1, 2 or 3 runs. But this doesn't really mean much so I'm not sure why you're asking. At the most it shows that the margin of victory is often this small.

[djiddish98]

If there are more total runs expected, I would imagine then each individual spread run is worth less in comparison to your average sample, like I think you were alluding to in your half point calc example.

What was the std dev for today's sum total?

Also, like you said, we can't say much about that 14/30, because we don't know what the MLs were (in comparison to today).

[djiddish98]

Also, might be interesting to run a regression on the salami margin of victory using just [sum of the totals] and [number of games] as variables and see if they are significant?

I'm starting to get to the edge of my stats knowledge though.

[mathdotcom]

Also, might be interesting to run a regression on the salami margin of victory using just [sum of the totals] and [number of games] as variables and see if they are significant?

I'm starting to get to the edge of my stats knowledge though.

That's the idea. At the moment it was just salami margin of victory on sum of totals, average (fair) ML, and average (fair) over probability [this last variable is a small tweak to account for the fact that not all totals are -110/-110]. You could throw in number of games but I imagine it would only have a very small effect.

In any event, this thread was about taking the CRIS ML as being correct and converting it to a spread, not necessarily generating the salami lines themselves.

[andywend]

mathdotcom,

With a full slate of 15 games, there is no way the home teams will beat the away teams by exactly 1, 2 or 3 runs 34% of the time.

You indicated you backtested this for 2009 but I would be very surprised if that number held up over say 10 seasons.

I would estimate the chances at closer to 15% then 34%.

In any event, if you really believe that the 34% is close to accurate, you would want to crush the Home Teams ML and take the +3 1/2 on the Away teams as you'd be getting close to 7-1 on the middle.

The fact that the books are offering the 7-1 leads me to believe that even my 15% estimate might be too high but the books do occassionally make mistakes in their pricing. The problem I see is that several different books would have to be making the same mistake and that is real unlikely.

[tomcowley]

I appreciate Tom's input, but I am defending my post in the hopes of either being more convinced I am right, or being proven wrong. Either outcome is good for me.

Using that number is just absurd. Anybody who knows anything about anything can hackjob home 1-3 to ballpark 10-15% (in at least two different ways) and tell you that 30%+ must be completely ridiculous. I mean, if you look at that figure and can't instantly tell that it's horribly wrong, I don't know what to tell you. WTF do you think the 1-game push percentage for home 1-3 is? How can a 15-game salami be almost the same? McFly?

[RickySteve]

Awful thread for so many reasons.

[mathdotcom]

mathdotcom,

With a full slate of 15 games, there is no way the home teams will beat the away teams by exactly 1, 2 or 3 runs 34% of the time.

You indicated you backtested this for 2009 but I would be very surprised if that number held up over say 10 seasons.

I would estimate the chances at closer to 15% then 34%.

In any event, if you really believe that the 34% is close to accurate, you would want to crush the Home Teams ML and take the +3 1/2 on the Away teams as you'd be getting close to 7-1 on the middle.

The fact that the books are offering the 7-1 leads me to believe that even my 15% estimate might be too high but the books do occassionally make mistakes in their pricing. The problem I see is that several different books would have to be making the same mistake and that is real unlikely.

I just found a brutal mistake in my code which I should have caught. No wonder people were wondering if I was using the single game home margin - that's what I was getting when I thought I had the total home margin.

The home salami wins with the following probabilities in 2009:

Prob(Margin=1) = 0.01325
Prob(Margin=2) = 0.01863
Prob(Margin=3) = 0.0099

Now it seems the CRIS line is a little bit off but the other way.
Fair odds on the ML = +145/-145
Fair odds on the spread given the above margins = ~ +123/-123

At least Away +3 hit last night

[mathdotcom]

Using that number is just absurd. Anybody who knows anything about anything can hackjob home 1-3 to ballpark 10-15% (in at least two different ways) and tell you that 30%+ must be completely ridiculous. I mean, if you look at that figure and can't instantly tell that it's horribly wrong, I don't know what to tell you. WTF do you think the 1-game push percentage for home 1-3 is? How can a 15-game salami be almost the same? McFly?

Settle down cowley. Sounds like you lost a lot yesterday.

[mathdotcom]

Awful thread for so many reasons.

Thanks Ricky, you never cease to amaze how with that many posts you never have anything constructive to say.

[tomcowley]

The home salami wins with the following probabilities in 2009:

Prob(Margin=1) = 0.01325
Prob(Margin=2) = 0.01863
Prob(Margin=3) = 0.0099

This is impossible. Not just wrong, actually impossible.

[mathdotcom]

thanks for your help cowley

have a wonderful day

[Ganchrow]

Obviously a complete and thorough modeling of Salami lines would include as input data substantially more than just home MOVs. Nevertheless, as a first order approximation such an analysis could prove interesting.

From 1990-2009 the distribution of MLB home team MOVs (≠ 0) follows:

The population distribution parameters are:

μ ≈ 0.12943
σ ≈ 4.3908
γ₁ ≈ -0.05355
γ₂ ≈ 0.63773

The slight negative skew is to be expected given the outsize prevalence of 1-run home team victories with a distribution otherwise fairly balanced about the mean. The small skew along with a reasonable kurtosis suggests that even with the gap at MOV = 0 we might be able to impute a fair characterization of the distribution of daily summed home MOVs that comprise the Salami via the central limit theorem.

The CLT gives us an asymptotic distribution over n games ~ N(nμ, nσ²), with convergence more rapid close to the peak.

So for a 15-game Salami the CLT would predict a mean and and standard deviation of 1.94139 and 17.00553 runs respectively. The following table compares the predicted frequencies (using a continuity correction) with actual 15-game Salami results over the in-sample time period:

This yields a chi-square goodness-of-fit statistic of 7.62722, which with 12 degrees of freedom implies a p-value of 18.6458%.

This is obviously a fair bit short of the generally accepted p-value for statistical significance of 5%, but by visual inspection it's clear that an outsize proportion of the test statistic is due to the considerably lower than expected occurrence of a 3-run home Salami MOV.

Indeed, the data point accounts for more than two-thirds of the total Χ² statistic and were we to remove it completely we'd see the p-value drop to the a level of 0.3949% which would be well within the generally accepted level of statistical significance.

Unfortunately for our simple theory, however, it does not appear that the low rate of occurrence of 3-run home Salami MOVs is a statistical aberration, but more likely the result of outcome clumping due to the absence of 0-run MOVs (and possibly to a lesser extent the prevalence of 1-run home MOVs). We see a similar dynamic at play at the 3-run level for 13-game Salamis although not for 14-game Salamis, which tend to fit predictions quite reliably.

To get a better picture of this, a full combinatorial analysis of single-game home MOVs could prove fruitful.

Anyway, now that we have some in-sample results, the next step would be to determine how these predictions fared out-of-sample, say for the 2010 season-to-date.

Such measurements, however, provide no vindication for this CLT-driven theory. With 50 15-games days on the books so far for the current season, we see that 29 of them ended in a home Salami MOV of > 5 runs. Taken in isolation this would occur less than 1.5% of the time were the predicted frequency of 41.712% accurate (although because we're cherry picking the most extreme value from a 14-category multinomial distribution, the real likelihood isn't nearly that bad).

While these overall results are less than encouraging, remember that they were derived purely using home MOV data without any regard to individual head-to-head match ups. Of course, we did expect such an analysis to provide less than stellar results and at least in that respect there should be no disappointment.

I think the most interesting take-away from this would be the low observed frequency of the 3-run home Salami MOV (and, it turns out, for subsequent multiples of 3). As previously mentioned, combinatorial analysis would likely shed more light on this particular observation, and in general, taken in conjunction with some simple match up considerations should bring the enterprising bettor reasonably close to fair value.

[mathdotcom]

Thanks for your input Ganch. You take back of the envelope to a new level