Kelly, comparing full Kelly versus 50% Kelly

There is some disagreement amoung the posters on the topic of “Kelly Re-Visited” in the “Handicapper Think Tank” forum on sportsbookreview.com about the issue of betting the fully Kelly percentage versus a partial Kelly percentage. The basic issue is variability of Kelly bets. Some argue that full Kelly leads to substantial variation, while betting a smaller percentage tends to stabilize the results. I’ve modified my simulator to look at replacing full Kelly wagers with one using 50% of Kelly. Following is a table of the results.

Treating Seasons Individually	Kelly	50% Kelly	Flat
Best Using Ret/$	39.4%	50.6%
Average Ret/$ Per Season	$1.036	$1.051	$1.051
All Seasons Totals	Kelly	Kelly	Flat
Average Kelly Pct	5.50%	2.74%
Average Bet Size	$65.69	$30.06	$100.00
Average Net Per Bet	$4.27	$1.98	$5.09
Total Ret/$ All Seasons	$1.065	$1.066	$1.051
Maximum Season Gain	$5,610.41	$1,680.21	$2,988.00
Maximum Season Loss	-$827.79	-$564.75	-$2,169.00

It should be pointed out that the 1^st column, the full Kelly, varies slightly from the table in a previous blog post. That’s because, as mentioned in my last post, I moved from generating a random edge to a rotating one. The slight change in values is due to the additional randomness in the previous post.

Again, the metric used is “Ret/$” (Ret/$ = (Bet + Net) / Bet). Using this ratio removes the impact of bet size. The full Kelly was better than flat betting in only 39.4% of the seasons, while using 50% Kelly made this Kelly approach slightly better than flat betting (50.6% of the seasons). When looking at the “Ret/$” average per season, 50% Kelly and flat betting were identical and both better than full Kelly.

If you add all the seasons together, full Kelly and 50% Kelly were essentially the same and better than flat betting. Naturally, the maximum gains and losses were more extreme with full Kelly over the other two.

So, what does this mean? I’m going to give this some thought before summarizing my view of the pros and cons of Kelly over flat betting.  I’ll tweet on Twitter, @ole44bill, when I’m ready to share these.