Measuring Returns

Measuring Returns

Understanding how to measure your performance is a crucial element of being a successful sports bettor. With varying odds and bet allocations, it’s not as simple as just counting your wins and losses. You can win 80% of your wagers, but if those bets were made at poor odds or you had poor bankroll management, you could still have disastrous results.

What you need to measure is your return on investment (“ROI”). In the finance world, ROI is defined as a measurement of the gain or loss generated on investment, relative to the amount of money invested. For example, if you bought Amazon stock at $1,000 per share and it’s currently trading at $1,900 per share, you would say that investment has an ROI of 90% (($1900 - $1,000) / $1,000). Pretty straightforward calculation.

In sports betting, however, there is often confusion regarding how to measure ROI.

Wager ROI

In the 2019 MLB season, we wagered around $1.39 million across approximately 800 games. When it was all said and done, we had made approximately $113 thousand. If you divide $113 thousand by $1.39 million, you get 8.1%. Is this our ROI?

If you ask the average sports bettor, they would say yes. If you ask the average finance professional, they would probably ask you “well, how much money did you start with?”

We’re going to define that 8.1% (Net Win / Wagered Amount) as our Wager ROI. For every dollar that we wagered, we made around 8.1 cents.

Wager ROI = [Net Win / Wagered Amount]

Portfolio ROI

We didn't start the 2019 season with a bankroll of $1.39 million, however.

We started with $130 thousand. And we ended with $243 thousand.

Yes, we wagered significantly more than our bankroll. But we started this endeavor with an investment of $130,000. Thus, by the financial definition of ROI, we had an ROI of approximately 87%. To avoid confusion with Wager ROI (and an unnecessary argument from sports bettors), we will define this as our Portfolio ROI. Calculations as follows:

Portfolio ROI = [Ending Investment / Starting Investment – 1]

Cash Turnover Ratio

So how did we wager $1.39 million when we only started with $130,000? Well one of the beauties of sports betting (besides futures) is that the outcome of a wager is determined quickly (~24hrs for MLB, a week for NFL). When you win a game, your sports betting account is credited, and you can then use those proceeds to bet on something else.

How efficiently we use our bankroll is something we’re going to call Cash Turnover Ratio. The Cash Turnover Ratio is the amount of wagers placed, divided by the average portfolio balance over the measurement period. For simplicity, it’s best to calculate your average portfolio balance as the average between your starting and ending bankroll.

Cash Turnover Ratio = [Wagered Amount / ((Starting Portfolio + Ending Portfolio) / 2)]

Our Cash Turnover Ratio for the 2019 baseball season was 7.4x as calculated below:

7.4x = $1.39 million / [($130k + $243k) / 2]

The Cash Turnover Ratio is a measurement of how efficiently we are using our capital. If we had an average portfolio balance of $10 million and only wagered $1.39 million, that would be a very inefficient use of our capital. The only way to increase our Cash Turnover Ratio is to 1) increase our wager size or 2) place more wagers. Of course, increasing our wager size increases our risk and methods such as at Kelly Criterion give us the framework to optimize our bet allocation.

Performance Objective

So what should be our objective? To maximize our Wager ROI? To maximize our Portfolio ROI? Each person is different, but we prioritize Portfolio ROI over Wager ROI.

There’s always going to be a tradeoff between Wager ROI and the number of wagers you play (and therefore your Cash Turnover Ratio). Let’s say you only bet the most select wagers and are able to hit 60% against -110 lines. You would be sporting a very impressive 14.5% Wager ROI, but you could likely improve your Portfolio ROI by being less selective and betting the games that you may only win at a 55% clip. Your Wager ROI would decrease, but the increased volume would increase your Portfolio ROI.

So maximizing Portfolio ROI is a better strategy than maximizing Wager ROI, but is it our performance objective?

Risk Adjusted Returns

Simply, no. What we haven’t addressed yet is the riskiness of a betting strategy.

For example – Bettor 1 has $10,000 and decides to make five $2,000 wagers at -110 over the course of a week. Bettor 1 wins three and lose two, winning a net $1,455, which is good for a Wager ROI of 14.5% and a Portfolio ROI of 14.5%.

Alternatively – Bettor 2 also has $10,000 and makes 50 wagers of $200 instead, winning 30 and losing 20 over the same one-week period. Bettor 2 also has a Wager ROI of 14.5% and a Portfolio ROI of 14.5%.

Do Bettor 1 and Bettor 2 do have equally strong betting strategies? Absolutely not. Bettor 2 was able to achieve the same returns as Bettor 1 but assumed a lot less risk in the process. We can borrow another concept from the financial realm to assess risk-adjusted performance.

The Sharpe Ratio

I’ll save you the boring history and definition of the Sharpe Ratio, but it is essentially a measurement of investment performance compared to a risk-free asset, after adjusting for risk. The Sharpe Ratio represents the additional return generated for an incremental unit of risk. Risk is generally measured as the standard deviation of returns.

For our purposes, we will assume the risk-free asset to have a return of 0.0% given that these bets are short-term securities (and Treasuries are yielding next to nothing).

We can use the Sharpe Ratio to assess the performance of each Bettor. In the table below, we’ve compared Bettor 1 with Bettor 2.

The big difference between the two bettors is that Bettor 1 assumed a lot more risk with 1) larger bets and therefore a higher standard deviation. As a result, Bettor 2 has a much higher Sharpe ratio than Bettor 1.

You can download a workbook with the above calculations along with a more realistic example of differing betting strategies. Simply replace the shaded cells with your own data to calculate your own Sharpe Ratio. Get the workbook here.

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