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# Baseball futures markets -- live WE

One of my current projects is to understand what potential role prediction markets have in baseball. For those of you who don't know, a prediction market is essentially a binary bet, which is typically run through a betting exchange -- essentially a futures market for baseball.

So how do prediction / futures markets work?

Well, a prediction market operates a series of contracts that have (mostly) two outcomes. This is reflected in a contract that has two values: for example, 100 points if the prediction occurs and 0 points if it doesn't. In a betting market these points will be linked to money (ie, 100 points might equal \$10, or \$100). These extremes set the upper and lower price boundaries. Also a time period may be linked to the contract so that it is forced to expire at some point. In baseball this could either a specific date or the end of a game or a season.

An example contract might be: The Braves will win 75 games by September 1st. If this happens by September 1st (the expiry date) the contract pays \$100 (say), if not it pays nothing. The contract then trades at some point within this range until the prediction comes true or not. Because the scale is 100 point the price represents the probability of the prediction being true. For example, a price of \$50 implies a 50% chance success. As information comes to the market the price of the contract will change as buyers and sellers adjust their price and risk expectations. Taking our example above, if the Braves go on a 15 game winning streak they are more likely to win 75 games by September 1st so the contract will increase in price.

Confusing? Let's walk through another stylized example and perhaps it will become clearer.

Take a game of baseball, say the Angels / Red-Sox match up on 29th July. As the Sox are at home and are a better team they have a higher chance of winning. Indeed, the market opened at \$56, which implies that the Red Sox had a 56% chance of winning before a ball had been pitched. This feels about right (one could use a log5 method to check this probability). In terms of the market this means if you buy the contract for the Red Sox to win at \$56 you scoop the full \$100 if they win, earning a return of \$44. On the other hand, if you believe that the Halos will come through you can sell the contract at \$56 (which is the same as buying the opposite contract for \$44). Hence if the Angels win you rake in \$56.

Basically, the market tracks the win probability of each team and allows you to bet on it. If you are not a bettor it still allows you to get an accurate view as to what the winning probability for each team is given whatever the game situation happens to be.

So, is it accurate? Many studies have shown that markets are the most efficient means of determining the probability of certain events happening. It is well known that the futures markets predicted the outcome of the last two US Presidential elections far more accurately than the usual slew of opinion polls. Provided the market has enough liquidity (those on Tradesports generally do) then the same is true of baseball markets.

For instance, PECOTA's team win-loss predictions have a standard error of about 5 games. This means that a team projected to win 77 games (ie, a skill level of 77) has a 68% chance of winning somewhere between 72 and 82, and a 95% chance of winning somewhere between 67 and 87. For the same predictions, Baseball futures markets are marginally better and have a standard error of 4.5 games (these markets would typically be over/under contracts but could be implemented with futures contracts). So futures beats the most comprehensive, publicly available projections -- that's a good start.

Perhaps a more interesting application of futures markets is during a game. In an efficient market the contract price should reflect the win probability at any time given a range of variables, such as: skill levels of the two teams, line up, home advantage, weather, park factors, inning, number of outs, number of bases etc. Take a look at the market for the aforementioned Angels and Red Sox game.

The red line on the chart represents the win probability for the Red Sox (technically the red line is the price of buying a contract for the Red Sox to win), while the green bars indicate volume of contacts traded (a proxy for liquidity). Without watching the game in real time it is difficult to know the precise situations that led to a change in win probability. However, 2/3 of the way along the x-axis you can see Boston had a win probability of around 10%. This is during the 8th inning when the Red Sox were down by 3. When the Sox tied the game at 6-6 the win probability shot back up to around 60%. Likewise, Oritiz's walk off hit in the bottom of the 11th resulted in the win probability going from 65% to 100%.

Neat. And actually very similar to the WPA charts that are becoming common currency on the Internet. So how does this particular market compare to the WPA chart of the same game?

Hey, fancy that, the WPA chart matches the market pretty closely -- which isn't great news for any arbitrageurs out there. However, WPA is calculated on the basis that both teams are as equally likely to win and only considers the inning and the base / out states when determining win probability. A futures market actually assimilates all of the available information and, provided the market is liquid enough, reflects the *most* accurate win probability. This is evidenced by the starting win probability: WPA tells us that either team is as equally likely to win, but the market predicts the Red Sox have a 56% probability of winning at they are the better team and at home (we know that home teams typically have a 54% win probability, so this feels about right).

This is pretty cool stuff, and the good news is that there is plenty of scope to extend the use of futures markets in baseball. Here are a few ideas, many of which will be subject of future (err ... no pun intended) articles:

1. Assess what impact trades have on current team win expectations

2. Allow us to understand at what point division races are effectively over

3. Understand how regular season performance translates into perceived post season success

4. Assess how likely it is that in-season (or even career) records will be broken

5. Determine the likelihood that Barry Bonds will be indicted (I don't kid)

6. Determine the odds of different teams winning the wild card

7. Allow us to generate live WPA

I could go on as the list is endless. In short you can dream up a market for almost anything, provided you can get enough liquidity.

One thing from that list that is worth a quick look is point 1: The impact that trades have on the probability of a particular team winning its division. One of the most aggressive trades over the last few days was the Rangers' acquisition of Carlos Lee from the Brewers. How many wins does the market expect Lee to add to the Rangers, and are they more likely to make the playoffs? Let's take a look at the contract for Texas to win the AL West:

The Lee trade was finalised early on the 28th July. Early during the day of the 28th you can see that the Rangers gained about 2-3% in additional win probability, which reflects the value that the market put on the Lee deal -- though bear in mind that the market also hears a lot of other information that is reflected in the price. Unfortunately the Rangers got tonked by Kansas that evening and this gain in win probability was erased. After that defeat the market believed that Lee wouldn't make a jot of difference to the Rangers' playoff hopes.

Where this technique could also come in handy is in play-money markets. Studies have shown that play-money prediction markets are as effective as real money. It is possible to set up a variety of play-money markets which could be used to allow GMs and fantasy manager to assess the impact of particular trades in isolation. Currently, such markets are likely to suffer from a lack of liquidity. Something like this may or may not catch on but there are plenty of opportunities abound.

Futures markets are not a new thing, but with the advent and interest in WPA they are becoming more pertinent to analysts. They are also very much in a genesis stage. Analysts don't yet understand how to take full advantage of them, and fans don't really know how to use them. Over the next 10 years that is likely to change.