KenPom’s LOG5 predictions are here. If you don’t know what that means, to wit:

LOG5 = (a – a * b)/(a + b – 2 * a * b)

“a” and “b” here are winning percentages. KenPom uses his pythagorean winning percentages calculated by PPP and tempo rather than just points scored for and against, with an exponent of around 12.

(Numbers in each cell represent percentages sans the non-obligatory “%” symbol).

Mr. Pomeroy “likes” the Big Ten, Pinnacle doesn’t.

Top 5 Value:
Kansas
Indiana
Syracuse
Ohio State
SEC Field

It all started with this thought experiment. In a back room in a Las Vegas casino, you are handed a fair coin to flip. You will not be allowed to see the outcome, and the moment the coin lands you will fall into a deep sleep. If the coin lands heads up, the dealer will wake you 1 minute later; tails, in 1 hour. Upon waking, you will have no idea how long you have just slept.

The dealer smiles: would you like to bet on heads or tails? Knowing it’s a fair coin, you assume your odds are 50/50, so you choose tails. But the house has an advantage. The dealer knows you will almost certainly lose, because she is factoring in something you haven’t: that we live in a multiverse.

Oh god.

In any infinite multiverse, everything that can happen, will happen – an infinite number of times…How can we say that anything is more or less probable than anything else?

One procedure physicists are fond of is to draw a cut-off at some finite time, count up the number of events – say, heads and tails – that occur in the multiverse before the cut-off time, and use that as a representative sample.

It seems reasonable, but when tackling the casino experiment, something strange happens. Wherever the cut-off is drawn, it slices through some of the gamblers’ naps, making it appear as if those gamblers simply never woke up. The longer the nap, the more likely it is to be cut off, so if you do awaken, it’s more likely that you have taken a shorter nap – that is, that you flipped heads. So even though the odds seemed to be 50/50 when the coins were first flipped, heads becomes more probable than tails once you and the other gamblers wake up.

Somewhere deep down this is what J. L. Kelly, Jr. had in mind.  Accidental prescience?  I knew it.

Upon waking, you have new information: you know that time didn’t end. That now means it is more likely that you only slept for a minute than for an hour. After all, time could end at any minute, and an hour has an extra 59 of those to spare. Heads wins.

Ultimately, younger universes are more numerous than older universes, thus if I interpret each possible side as if its occurring primarily in younger universes, my probability increases at the rate proportional to y/u, where y is the number of younger universes, and u the number of older universes.  I’ve figured it out, guys.

New Scientist.  August 13, 2011

I created a coin toss simulator (at the bottom) to compare two different wagering methodologies.  But first I’m going to ramble.

Statistics, streaks, can be deceiving, and frequently this feature of statistics is abused.  Services and handicappers that sell picks often either just plain lie about their betting performance, or use statistics over a small subset of games that only act as data in a larger sample size.

You can take any record of picks over a certain time frame, and do a linear extrapolation into future expectation and growth, serving to highlight excellence in picking games.  I went 0-7 in college football two weeks ago, if I use that and do a linear extrapolation through the next 50 years I’ll be losing money at the speed of light expanding infinitely up into the outer regions of space.

Rarely does anybody have constant growth in bankroll, as the only thing absolute is that there will be variation and fluctuation in winners and losers.  But calculating expected growth is a practical application imposing upon a system of random performance.  If a bettor is betting 25% of her bankroll on every play, all it takes is one 0-4 sequence of wagers to lose everything.

Expected Value, to wit:

An example would be a standard -110 wager betting $100.

Expected growth is typically demonstrated in terms of bankroll growth and bankroll shrinkage.  Therefore X (Money wagered) would be expressed as percentage of bankroll.  For the above example, a bankroll of $10,000 at 1% per game equates to $100.  The formula for expected growth:

D = Decimal Odds

p = Win Probability

The Kelly Criterion accounts for such scenarios, and finds the most optimal distribution of bankroll to apply for each wager, given some designated edge.  Kelly is a formula to maximize expected growth, while minimizing risk.

Conversely, flat betting (betting the same amount on each game) defines the edge as immaterial, and embraces randomness and humility.  With either style of managing bankroll, allowing one to stick around long enough to hit a long shot is eminently assumed, in my opinion of course.

Again, Kelly essentially finds the optimal wager for an event that maximizes E(G), from above.  Given an edge, however measured, the “Kelly Stake” can now be calculated as a percentage of bankroll (of course if there is no edge there is no wager).

Conveniently at even odds the stake is equal to the edge.  One thing to keep in mind, Kelly intended each particular stake to relate to each particular moment of current bankroll.  Meaning a $1 winner with a bankroll of $100 now increases the bankroll to $101 and therefore changes the value of the next wager given similar parameters of the wager previous.

Kelly is very aggressive, there is no doubting that, which is why fractional Kelly is more common, in my experience anyways.  I don’t use the Kelly criterion because there is seldom a time where a calculated edge has any actual meaning, and I’m not arrogant enough to think I am smarter than Vegas.  Therefore I bet frivolously and arbitrarily.

The simulator is below, and uses “static” Kelly Criterion, if you will, to compare to flat unit stakes.  Enter numbers in the blue boxes then click simulate.   Its a zip file.  Two excel macro files inside, 0ne is a side by side comparison, the other just allows for the simulation of the specified methodology.

FlatvKelly_Sim

Doesn’t look like either side has any immediate value. Personally I like the Rangers but what do I know.

The players in bold appear to have over 1% market value.  Conveniently they play for different teams in different capacities.  If the Cardinals do win I find it hard to believe they out hit the Rangers, and conversely the Rangers are built around a tremendous lineup and a deep bullpen.  A bet both on Carpenter and Hamilton brings together the winning attributes of their respective teams.

It appears Texas has slight World Series market value of a little over 1%, and considerable ALCS value at 3%.  They have an interesting draw in the first round against the Rays.  Tampa has decided to start the highly touted Matt Moore, who in 9.1 IP this year has 15 K , 3 BB, and a 1.286 WHIP.  Moore is a bit of an enigma, a term that can just be thrown around to any player who lacks a sufficient sample size.  But the Rays expect tremendous things from Moore.  He held his opponents to an OPS under .500 in 52.2 IP while playing for AAA Durham of the International League this year.

The game one line is set at Texas -172 (Wilson) with a total (8 -118/108) right in line with Wilson’s season average.  Wilson will pitch again, if necessary, in game four versus David Price, unless Tampa decides to pitch Price in game three.  The decision to start Matt Moore means either Niemann or Hellickson (or both) will be moved to the bullpen, at least for this series.

I haven’t found an offshore book that currently has MVP odds posted, unfortunately.  The odds above depend on the total number of players receiving votes, so if I limit the odds to only those in the top 10:

Once again, I decided to make an arbitrary formula for pitchers since the distribution of voting points is wildly inconsistent from year to year for pitchers that earned voting points (largely due to the relatively low correlation between voting points and WPA, voting points and ERA or WHIP).  In contrast to the NL, where only five pitchers have even been considered for the award since 2000, 51 pitchers in the AL have received voting points over the last eleven years.  Unfortunately this does little to satisfy voting trends for pitchers, due to the aforementioned inconsistencies.  Because of this, I used the ’99 and ’00 seasons from Pedro Martinez as models for what pitchers have to do relative to offensive players being considered for the MVP award, to finish in the top five.  Essentially a 10 WAR pitcher with a WPA around 7 or greater for a playoff team and an ERA+ of about 200 has a legitimate shot to win the MVP in any given season.  Justin Verlander falls short of these arbitrary values , and the table above shows where he ranks in the top 15.

We can actually assess how many wins above average Verlander is worth that may offer more clarity.  The Tigers score 4.73 runs per game and are 25-9 when Verlander starts.  For simplicity, let’s make the assumption that psychological factors do not come into play, and 4.73 r/g is solely contingent on the listed starter of the opposition.  When Verlander doesn’t start, the Tigers allow 4.87 r/g.  Using Pythagenpat, and an average pitcher resolving Verlander’s 34 starts in the same run environment, the Tigers would win 16-17 of those 34 starts.  This would place Verlander at between 8-9 wins above average for his team, and the Tigers would still win the division rather comfortably.

Miguel Cabrera has made a vicious surge in September, with a ridiculous 1.291 OPS and an impressive 2.484 WPA, all this amidst a jaw-dropping .443 BABIP.  For the season his BABIP is .363, not outlandish when you consider for his career his hit/contact rate approaches 35%.

Is he the MVP?  He’s third in the AL in WAR, and again the table above merely reflects a voting trend for hitters since 2000.  But this isn’t 2000.  Sabermetrics is an unstoppable force for which there appears to be no barrier.  If we rank the contenders solely by WAR, there is still a major flaw.  WAR for pitchers and WAR for hitters are founded on different units.  Can we convert performance metrics to one robust measure for both pitchers and hitters?  Well one can measure runs allowed or runs produced per inning, but hitters account for three or four times as many innings as a typical starting pitcher.

One possible way would be to calculate how many runs the Tigers need to score to maintain that 25-9 record if an average pitcher pitched in place of Verlander.  I’m going to use base runs to ensure the units are consistent, and the Tigers allow 4.79 BsR/g when Verlander doesn’t start.  The quick way to find the runs needed to maintain a 69% winning percentage over 34 games is to use solver in Microsoft Excel, and the answer is 7.16 BsR/g, which equates to .27 BsR/out.  For Cabrera use the BsR formula for offensive players to find an approximate estimation of total run production, and divide by the number of outs (AB – H).  The result is .32 r/out.  An extremely crude way to compare hitters and pitchers but intuitively Cabrera being worth about .05 more r/out than Verlander is reasonable.

I’m not finished yet.  In proportion one can create a scenario where Verlander’s hypothetical offensive output mirrors his pitching output by removing hitters of similar value after a certain number of innings pitched to express innings pitched per start.  This scenario was reconciled by the calculations on Verlander in the previous paragraph, but much of the variance can at times be explained by how well the bullpen performs.  The goal is for the offense to score 7.16 BsR/g to achieve 25 wins in 34 games.  If Verlander averages 7 IP/GS, then after 7 IP his hypothetical offensive performers will be removed  from the lineup accordingly, though in this case his equivalent worth will continue on through the 9th inning.  The Tigers currently average 4.86 BsR/g during Verlander’s starts, or 1.08 BsR every two innings, which means the Tigers with an offensive player of Verlander’s value inserted into the lineup every inning would score .29 r/out, increasing his runs per out by .02 runs.  This explanation at least accounts for a pitcher’s ability to pitch late in games.

To find the voting points, the formula basically resembles something similar to:

Where the coefficients a, b, and c are found by regressing voting points onto a number of different variables  (doesn’t have to be just three) which appear to be statistically significant.  This is based on the preference of the user, but whatever combination resolves the most variance in voting points is desirable.  In this case R² = .59. The typical MVP winner earns around 250-300 voting points.

To find the probability, take each individual player whose voting points registers as positive and divide it by half the total number of voting points for all players.  Obviously if a player receives over 50% of the voting points then they will win the MVP 100% of the time.  Expressed in mathematical form:

Historical voting trends may soon be rendered insignificant as the new generation of sabermetrics becomes the prevailing form of player assessment.  Yet to make such an assumption would not only be a general statement on my unlikely ability to gauge future voter temperament, but would also be devastating to my entire MVP Predictor. And I would assume such self-mutilating reflections are unknown to standard issue practices of bloggers, therefore lets assume these assumptions were never assumed.

Like I said before, the regression excluded pitchers, so I developed an arbitrary formula of which the goal was to align the calculation of voting points with a reasonable MVP ranking after one makes a brief survey of the tabulation.  I came up with this:

“Playoffs” is a binary variable, and the points added is either 30 or 0.

The formula appears to work.

NL MVP Top 15:

I think it safe to say either Braun or Kemp will win the MVP. And if the eventual NL Cy Young winner has any influence on the MVP, then Ryan Braun is going to be your probable winner. I find it hard to believe a third place team will have both the Cy Young award winner the MVP winner on the same team. The joint probability of a mediocre team having also the two best players in the league is probably very low. This way of thinking perhaps might not be justifiable, if Kemp and Kershaw are the most deserving of the respective awards, why should any other factors come into play? Again the table above merely displays an eleven year voting trend and nothing more.

Factors contributing to the variance of previous MVP awards were more contingent on team success, judging by the significance placed on the playoff variable (For hitters the coefficient is 78.3). But in the “MoneyBall” era, where many teams are more concerned with actually buying wins as opposed to getting stars, such a concept may spill over to the MVP voting process. If it does, than “valuable” simply means value to your team, regardless of how good the team is, and “valuable” as well as “the best” has been simplified into one all-encompassing stat, WAR. Fittingly, both leagues have a “most valuable” player on a mediocre team, if value is decided by WAR, and without that player (Kemp in NL, Bautista in AL), their respective teams would “lose” more wins. Does that make them the most “valuable?”

The Cy Young is much easier to digest than the ambiguities that embody the MVP award.  The best pitcher in the league wins the Cy Young, and justifying the eventual winner can be analytically reduced to any metric that would warrant “best pitcher” status.  That could be wins, winning percentage, ERA, or sabermetrics.  Out of the top four candidates, I don’t think anybody would be surprised if any one of the four win the Cy Young.  And the voting trends since 2000 incidentally align with considerations implied by the “FanGraphs generation.”  The top four in WAR for National League pitchers also rate in the top four in the probability of winning the Cy Young.  Again this is because factors that go into evaluating pitching using advanced metrics will inevitably lead to results aligning closely with what the “Triple Crown stats” show, and unlike WAR for position players, there is no random dummy variable (UZR, TZR) deciding a player’s performance rating.

With that in mind, at what point did sportsbooks catch on to the type of season Ian Kennedy is having.  A brief survey of his projections before the season, and nowhere do I see 20-4 and an ERA+ of 137 (ZiPS made a valiant effort however, 8-5 125+, and MARCEL had 7-9 106+).

Below I made a graph charting each individual line with his moving average, expressed as a probability, p.

From his first start to about June 5th, his 12th start of the season against Jason Marquis (-160), we saw a steady increase.  Obviously this could be more an expression of the Diamondbacks performance rather than Kennedy’s market value.  But Kennedy’s line compared to his team line is only 1.9% higher.  Here are a few notable lines over his last few starts.

Thus it appears the sportsbooks do not think too highly of neither Kennedy nor the Diamondbacks.  He currently ranks 37th out of 277 pitchers who have been listed on a Vegas card, though when adjusted for home/road start discrepancy and his opponents’ line that ranking moves up six spots to 31st, four spots behind his teammate Daniel Hudson, who has the same average opponent’s line.  The lack of respect for Kennedy explains his monetary intake from a bettors perspective.  The top 10 in units earned on the season for starting pitchers.

*From Statfox