# Underdogs and Inefficiencies

## Ford Bohrmann

Odds makers tend to do a fairly good job in sports-- While they may not be perfect, it tends to be tough to find any consistent exploitable inefficiencies. In other words, it is rare that the odds of "Liverpool winning at home", or some other event like that, are consistently over or underestimated. You may think that the odds in an individual game may be incorrect, but in the long run inefficiencies like that rarely persist. Why? Because bookies would lose money on them. If they realize they are starting to lose money, the odds are going to be adjusted to better reflect the probability of each result occuring.

While I am not really interested in betting on soccer myself, odds do provide an interesting estimate of the probability of an outcome occuring. For example, take Arsenal's home game against Chelsea this past year. Bet365 put the odds of an Arsenal victory at 2.38. These decimal odds imply that they expect the probability of an Arsenal victory to be about 42%. Taking in to account that the odds makers usually lower the payouts so that they make money, the adjusted probability of an Arsenal victory is just over 41.1%.

This is all pretty standard stuff. The odds for relatively evenly matched games like the one above are probably pretty accurate, or at least more accurate than your average person. But what about significant underdogs? What about City against Cardiff? These are a little more difficult to assess. It's clear that Cardiff is an underdog in this game, but how much of an underdog? And do odds makers do a good job of assigning implied probabilities to these lopsided games?

To look in to this, I defined games with a significant underdog to be games where one outcome has an implied probability of occurring under 15%. This could be either a home win, an away win, or a draw. If the odds makers are effective at predicting underdog outcomes, we should see underdog outcomes (as I define them) occuring under 15% of the time, since the implied probability could be anywhere from just above 0% to 15%.

I used data from Football-Data.co.uk and took the Bet365 odds for the past 5 seasons of the Premiership. After limiting the data to signficant underdogs as defined above, I ended up with 643 games with a significant underdog. Of those, 110 were games with a home team underdog, 441 were games with an away team underdog, and 92 were games with a draw underdog. These splits make sense, because clearly away teams are underdogs more often than home teams due to home field advantage.

Next I calculated what percentage of underdog games resulted in the underdog outcome actually occuring. As mentioned above, these percentages should be under 15% if the odds makers are doing a good job. Below is a graph showing these percentages over the past 5 years, split in to home, away, and draw underdogs.

The red dashed line is the 15% cutoff. For draw and away underdogs, we see about what we would expect: the percentage of underdog outcomes occuring fluctuates, but it remains under the 15% line. For home underdogs though, there is a different story. For each year besides 2012, home underdogs actually won more than 15% of the time, in some cases significantly more so. This seems to indicate that odds makers are underestimating home field advantage when weaker teams play stronger teams.

This evidence seems to indicate that there is an inefficiency present, specifically in the odds of underdog home teams. However, there are still a few caveats that should be mentioned. First, there were a smaller number of home underdog games in the past 5 years, which may be influencing the results somewhat. Second, odds are made so that they somewhat lessen the payoffs so that the odds makers can make money. This means that if you find an inefficiency like the one above, it has to be large enough so that you can overcome the advantage that odds makers have when they make the odds. For the first 3 years, this does not seem to be the case for home underdogs.

Overall though, it seems like there could be something here. But don't blame me if this betting strategy doesn't work. Who knows if it will persist in to the future or not.