Although it is entirely too early to glean too much information about how the 2018 MLB season will shake out, that’s never stopped Vegas from issuing odds as soon as the day after the last fall classic ended. While most of the public views this as a novelty, simply a way for odds makers to get their names into the news, Economists generally think of these odds as pricing information. The idea goes like this; a bet is like a stock with binary outcomes, the company makes a profit, in which case you make money, or the company fails, in which case the value of the stock goes to 0 and you lose your initial investment. The “stock” is priced based on the probability of either that success or failure.
In statistics this makes for a simple expected value equation; let’s set the betting odds at 10 to 1, for say the chances that a team wins the World Series; for your $10 bet, you net $100 if you win and -$10 if you lose. If the probability p is equal to the probability of you winning, and thus 1-p is the probability of you losing; bookies want to set the line such that your expected value of winning is zero. Setting the expected value to zero means that taking the same line on a bet over and over again, you would neither profit nor lose money, ignoring any fees. This is so that you cannot gain an advantage by betting one side or another, otherwise the bookie is losing money. Based on this assumption, we can find the probability of you winning:
p*($100)+(1-p)(-$10) = $0
$100*p-$10+$10*p = $0
$110*p = $10
p = .09
Based on these odds, the chances of winning this bet are 9% and therefore the chances of losing the bet are 91%. Now let’s say that you have inside information that the team you were betting on has a couple of young players who are going to break out, have incredible seasons, and improve your team’s chances of a World series from 9% to 25%. The expected value problem changes to this:
(.25)($100)+(.75)(-$10) = $17.5
This is a bet you would take all day, since the expected value, or return on the bet, is greater than zero, meaning you will profit on that bet if you play it several times. In fact you would likely bet a lot more than $10 and you might even tell your friends to place big bets and so on. The bookie would see this influx of cash betting on your team and thus he would change the odds accordingly;
.25/.75= 1/3 => new odds are 3 to 1.
To check these new odds work out, we can plug them back into the expected value equation with the new 3 to 1 line, and see that the answer to the new equation is 0.
What is intriguing about this idea is that the information you had about a change probability of your team winning the World Series was conferred to the bookie, through the “price”, or odds of the bet, rather than having to be explicitly stated. In the world of finance this happens all the time, when new information about a company’s profit or loss last quarter is released, the market immediately responds by either raising or lowering the price of the respective stock. Economists call this the Efficient Market Hypothesis (EMH). The essence of the EMH is that markets have all available information already priced into an asset. If there is new information that changes the probability that a company will have a successful year, markets arbitrage away any “free money” such that the expected value equation equals 0. This information doesn’t necessarily have to be something as certain as “the firm will have a good quarter” either; an investor could also be a consumer who really likes the product that the company is selling or they could just have a gut feeling; in any case this is still valuable information. Specifically with betting, the “price” is just the odds of the bet. Although it is a somewhat controversial topic in Financial Economics, for our purposes we will assume that the EMH holds in the betting realm, and thus the most current betting odds reflect all available information regarding the strength of teams.
I used the most recent Bovida odds for teams to win the 2018 World Series. To make the numbers a bit easier to work with and a bit more intuitive to me, I subtracted the actual line form the average line, and then divided by 100. So a team with an above average chance of winning the World Series has a positive rating and teams with a worse than average chance have a negative rating.
After finding inspiration in a 12 year old Pro Football Refrence article, I modified the idea a bit to fit the realities of baseball and set up a system of equations to solve to team’s relative strength of schedule. The system goes like this; a team’s rating is a function of their betting line rating, plus the rating of the teams they’re slated to play, weighted by the number of times they play them. Take as an example the rating of the Pirates (we note them as r_PIT for “rating_Pittsburgh”);
r_PIT=bet_rating_PIT+ 7*r_ARI+ 6*r_ATL+ 19*r_CHC+ 19*r_CIN+ 4*r_CWS+ 3*r_CLE+ 6*r_COL+ 6*r_DET+ 3*KCR+ 6*r_LAD+ 6*r_MIA+ 19*r_MIL+ 4*r_MIN+ 7*r_NYM+ 7*r_PHI+ 7*r_SDP+ 7*r_SFG+ 19*r_STL+ 7*r_WSN
All the coefficients on the other team’s ratings are just the number of times they play the Pirates in 2018.
Then repeat the same process for the other 29 teams in the league. This results in a system of 30 equations with 30 unknowns. You likely learned how to solve a 2 or even 3 equation system in a high school algebra class, the theory is to solve a 30 equation system is the exact same. Like much of what you learned in that algebra class, however, a computer can now solve in a matter of seconds what might have taken hours to do in class.
The resulting Power Ranking goes like this:
This Power Ranking gives a good overall estimate of teams “absolute” value, rather than relative to just who they’re playing. This ranking is good for playing a theoretical “plug-and-play” game; if you take a team like Boston, who is playing in the toughest division in baseball, and plug them into the weakest division, the NL East, suddenly they’d be the favorite to win the division, rather than being 2nd to the Yankees. Also interestingly, in light of the MLBPA’s complaint against the Pirates and Rays not spending money, whether or not they’ve been spending money doesn’t seem to have affected either team’s competitiveness, with both teams relatively close to the 0 mark of an average team.
You might notice that better teams tend to have negative Strength of Schedule (S.O.S.) rankings, signifying an easier schedule, and by and large that is true, as a result of those better teams not having to play themselves. Vice versa goes for bad teams.
In terms of information this provides, this process doesn’t add anything. In fact the whole point of this method is to strip away the information about a team’s schedule and their strength relative to their opponents, as that information that is already priced into the odds. This provides a more objective measure about team strength of a team, which therefore is a more robust “Power Ranking”. Rather than just using the subjective opinion of a given writer to rank teams, this measure is based on what people who have actually put their money where their mouths are think, or know, about the teams at hand.
By taking the average of each team’s power ranking within a division, we can power rank the divisions, and even the leagues.
None of these are particularly surprising. The AL East is stacked, Yankees and Red Sox are loaded for 2018, the Blue Jays, Rays, and Orioles all seem like decent teams, but will have to scratch and claw to get anywhere in the division. The NL West is equally as stacked; the Dodgers are the odds on favorite to win the World Series, and rightfully so; the Rockies and Diamondbacks were playoff teams last season and are bringing back most of their team, and the Giants look to be much healthier in 2018 and have added veteran weapons Evan Longoria and Andrew McCutchen.
The NL East is largely dragged down as a result of the Marlins having extraordinarily long odds, although the Braves are also in the bottom 5 which doesn’t help. What this means is that the Nationals and Mets get a big boost in the betting arena since both teams should have something like 15-19 free wins against them; these are mostly meaningless games in terms of the Power Ranking because they’re not “quality wins” against strong competition.
These Power Rankings should change a few times prior to Opening Day as free agents are signed, rosters are solidified, and any injuries are accounted for in the betting odds. As such, look back closer to March 29th for a pre-Opening Day odds based power ranking.