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#41




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Hi woof43, Time is continuous, whereas sporting scores are discrete. The former can use a normal distribution (with 'real life' provisos, such as you state), but the latter needs to take the actual distribution of scores into account. Back in post #20 in this thread I attached a bar chart of NRL scores from the past howevermany years, it shows:  only whole number scores occur  no negative scores can occur  due to the points awarded for certain feats, some scores occur more than others  a maximum score is approached, which is limited by the set duration of games and nearguaranteed quality of opposition (in the NRL, at least) I can also produce a similar graph for each of "team A's" scores. For example: 18 is a very common score overall, but not nearly as common for Team B, if Team A has also scored 18. (During the Monte Carlo simulation I let each team have turns at being A or B). I randomly select (weighted according to historic frequency) from these distributions so that a modelled game will never have a score that has not occurred before. It avoids the "track record" scores at the narrow tails and it also avoids the "nonsense" scores like 113, which are able to occur but pretty much never would given how the sport is played (i.e. somewhat sensibly). I'm making an assumption that I have enough historic matches to give a fair representation of the likelihood of final scores. Quote:
I first played around with Stdev and Monte Carlo sims with horse racing but didn't think to look for barrier bias in that way... I could definitely see how it would be useful for cricket, for example, given that the grounds aren't uniform in size: larger scores are likelier in Hobart than at the MCG, I'd think. I suppose you could use it just about any way you put your mind to (scoreundercoach stdev, score after 5day turnaround stdev, night footy score stdev, scores at games played within a certain temperature range stdev, rainfall stdev). It's just as well I don't have any of that information; it was starting to sound complicated! ...and if I did, I'm not totally sure how I would wrap it all up into one figure. Do you use Pooled Standard Deviation? http://en.wikipedia.org/wiki/Pooled_variance How I was coming up with my standard deviation was bothering me, and I think that may solve it somewhat. For a match A vs B, I was solely looking at the standard deviation in scoring error of Team A (attackA), but I should also account for the standard deviation in scoring error of Team B's past opponents (defenseB). Quote:
I'm also applying a time degradation factor to the errors in score prediction (that determine the stdev), so I'm not sure I can use that approach. ...but then, I'm also unsure about how best to determine a time degradation factor, without trial and error.... 
#42




NRL Round 6 Review
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Tips this week 4/8. Season total of: 29/56 (51.8%). Thinking of tipping comp strategy, the presumption may be made that other people will be following the betting market (or vice versa) so it could be advantageous to be tipping these value bets instead of the straightout picks.... It's more valuable to be right when more people are wrong. Quote:
The subselection method for Value Bet + Tipped to Win (after I forgot about it last week) is now 8/13, as it drifts towards irrelevancy. The subselection method for Value Bet + Price < $2.95 is now 8/10. Bets were at $25.60 This Week Out: $102.40 In: $132.35 29%POT Overall Out: $637.34 In: $948.78 48.9%POT New Bank: $1311.44 (stakes for next round: $26.20) Line S/R: 2/2 (100%) H2H S/R: 14/27 (51.9%) The overachieving goes on... ..and keeps on keeping on: Quote:
Odds for the Parramatta Eels shortened, but the Sharks were out to value bet territory of $2.45 around lunchtime today; with the weather and captain Paul Gallen's withdrawal I imagine they would've gotten even longer. So there was another $37.12 profit there, but I've chosen not to include it in the results as I haven't been monitoring betting fluctuations for other matches. If anyone's putting money on my selections ( are you crazy?!?!? ) then I hope you picked up on this one. Quote:
So in this instance, had I applied a teambased home grown advantage figure, I would've got an additional game correct with my tipping (and 9/14 for Value Bet + Tipped To Win). The "advantage" figure was in the order of 0.11 though, so I consider it a rounding "feature" rather than evidence that a change in my strategy is required. Quote:
Probably not a coincidence that the bets with the lowest Expected Growth of Bankroll were the ones that Lost. Reviewing the results over the weekend, I found success appeared to be more closely aligned with the Percentage of Bank to Bet figure (as determined by Kelly Strategy). Though combined with Expected Growth, once it hit around 0.55%, the imaginary bank balance was supercharged. The highest % I was indicated to bet was 30% on Canberra +12.5. I would've been very nervous when the Tigers led 220... The highest Expected Growth of Bankroll (by far) was Canberra H2H at 7.67% (I had them as a $2 shot; they were out to $3.70 by the time I ran my Monte Carlo simulation). I was interested in how I might bet in a reallife situation so I gave it a go  on paper, sadly. Firstly, many of the qualifying bets were Pick Your Own Line duplicates. Rather than betting on every line, I chose the most advantageous; using a little human intelligence (i.e. a balance between growth/stake/risk). I also used the more conservative Half Kelly Staking. Preanalysis of the weekend's results, I was simply looking at bets where I believed I had at least a 15% pricing advantage. To follow Kelly correctly, one should take into account simultaneous bets. Games aren't necessarily played concurrently, but you're likely to have more than one bet on each match. In this instance the bank should be considered to be down the stake/s for each preceding bet/s. I wasn't sure how to order my bets though  most confident first?  so instead I just pretended my imaginary bank of $100 remained constant for every bet, through every match. Here's how the weekend would've gone: Bulldogs vs Manly: $62.67 out, $90.50 in Dragons vs Broncos: $7.70 out, $0 in Titans vs Panthers: $20.58 out, $0 in Cowboys vs Warriors: $16.73 out, $24.37 in Melbourne vs Roosters: $13.93 out, $15.69 in Tigers vs Raiders: $74.78 out, $214.81 in Knights vs Eels: $23.37 out, $46.33 in Sharks vs Rabbitohs: $17.10 out, $18.25 in I probably made some arithmetic errors along the way  and I changed how I determined standard deviation of scores midway through the weekend  so the figures shouldn't be taken as gospel. But encouraging results. 
#43




Examining the performance of the Monte Carlo Simulations over this past round. 1031 betting markets were considered. The estimates/probabilities were grouped into 5% bands. Attached are two graphs. One shows the number of estimates that were in each band.
The line graph shows actual (i.e. whether the bet won or not) vs expected (i.e. how often the bet should win given the implied probability). It looks VERY impressive in the middle and a little sketchy at the ends. The rightmost end of the line shows unlikely occurences. Why does it go sketchy here? As I noted earlier, I'm probably not running enough simulations (10,000) to correctly measure unlikely occurences. It's also interesting that the dip below the line at 2025% corresponds to a dip above the line at 7580%: often there are two sides to a market (under/over, H2H, etc) so, for this particular week, perhaps the likelier events occurred and in subsequent weeks it'll be the reverse, with results returning to the mean. My model also does not take into account the weather. Given how wild it's been in and around Sydney, it may have affected game outcomes in a way I was unable to forecast. Lastly, I'm using a range that I'm 95% confident (1.96*standard deviation) will contain the actual scores. To model at 99% I would have to use 2.58*standard deviation. The leftmost end of the line shows occurences that my model considers very likely to occur. Why does it go sketchy here? Firstly, there are few markets about which I can be exceedingly confident; only 19 estimated at greater than 95% probability. With so few under consideration, any failures will cause that line to wander off course greater than if they were to occur in the bottom 5% (66 markets). Looking at the unexpected failures and unexpected successes it was all pretty much due to ONE GAME! Panthers vs Titans. Panthers +18.5 and above failed. Titans 25.5 and above succeeded. Titans ended up winning 326 but the margin wasn't indicative. 2 Panthers players were injured and didn't return for the 2nd half and a further one was subsequently sinbinned for 10 minutes. It wasn't until there were 10 minutes left in the match that the Titans rolled them  likely due to fatigue; 'til then the Panthers were only a try or two away from the lead. The circumstances don't seem like a regular occurence and precisely those which one could expect would have to occur to knock off a sureish thing. Last edited by walkermac : 21st April 2015 at 08:27 PM. Reason: Titans 25.5 was the correct figure, not 19.5 
#44




Quote:
I run 40,000 sims per race, but I'm also blending a few factors into the fold, you might find a wet weather factor might be beneficial. When I test factors such as that, I will remove all that data and provide random generated data in it's place. Have you looked at sorting the games by the Favoured teams standard deviation or a combination of both and see that provides some answers. It does have an effect in racing especially a Favourite with a wide stdev 
#45




NRL Round 8
Selections continue to be made using the "old" method. Dollarvalue estimates are from a 40,000 rep Monte Carlo Simulation using a 95% confidence interval of the standard deviation. Teams are as per Tuesday team lists, standard deviation is a pooled one; taking into account each team's "attack" timeweighted stdev and their opponent's "defence" timeweighted stdev. (I tried it with a 99% confidence interval but it appeared to flatten out the midresults too much  and that's where H2H and Line Bets odds generally lie. 95% (1.96) vs 99% (2.58) is a difference of 816 points, in practical terms, to the range of scores a team can get. With this greater overlap between the two team's possible scores, it seems to cancel out the midprobabilities. It's not the case at the top and bottom 15% of probability though. Last week, at least, it was spot on there. In fact I reran the actual vs expected results from last round and the findings were reversed: the 95% graph in my last post showed that actual vs expected results were great in the centre and a little sketchy at each end; the 99% graph opposite.) Tips CanterburyBankstown Bulldogs ($1.97) New Zealand Warriors ($1.80) North Queensland Cowboys ($2.02) Sydney Roosters ($1.65) Melbourne Storm ($1.27) Brisbane Broncos ($1.76) Penrith Panthers ($1.90) South Sydney Rabbitohs ($1.95) Only the Panthers differ from the current market favourite, at present. Value Bets (Bets at $26.20) Gold Coast Titans @ $3.30 ($2.28) Newcastle Knights @ $2.40 ($2.01) ManlyWarringah Sea Eagles @ $3.65 ($4.94) Parramatta Eels @ $3.25 ($2.37) Canberra Raiders @ $3.65 ($2.09) Obviously, the Sea Eagles don't look like a sensible "value" bet after the Monte Carlo Simulation. If you're looking for an upset result in your work tipping comp though, all bar the Eagles may be worth your consideration. If the Panthers get out any more than their current price of $2.15, they become a value bet (though the MCSim has them at $1.90  not a huge difference). Similarly, if the Dragons get to $2.90 (my price: $2.60). Neither of these will count in my statistics, as I won't be monitoring price changes. 
#46




NRL Round 8 Review
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The subselection method for Value Bet + Tipped to Win remains at 8/13. The subselection method for Value Bet + Price < $2.95 is now 8/11. Bets were at $26.20 This Week Out: $131 In: $277.72 112%POT Overall Out: $768.34 In: $1226.50 59.6%POT New Bank: $1458.16 (stakes for next round: $29.15) Line S/R: 2/2 (100%) H2H S/R: 17/32 (53.1%) Quote:
Just for interest's sake, Dragons were at $3.30 an hour or two before they played, so this would've been a (successful) value bet. Panthers had shortened to $1.91 when I last checked. Odds usually appeared more favourable the closer it was to the match. Presumably as the selections are never the favourite team and bookmakers are endeavouring to attract interest in the outsider to balance their ledger (?). Titans were out to $3.55, Knights were steady, Manly got to $4, Eels $3.35. It was only the Raiders who came in a little to $3.40. These later figures would've added an extra 6% return to the weekly profit. Anyway, it's been going far better than I think it should so, while the going's good, here's a coollooking graph: 
#47




walkermac,
It really is incredible how your hitting these value bets over $2 odds at such a high rate. You'd have to think you'll have a bad week sooner or later but congrats on riding the wave for now. That POT level for value bets is fantastic will be interesting to reflect on these selections by seasons end. Almost tempted to jump onboard myself each week haha. Hopefully you received my email and had a read as well? Cheers 
#48




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Yeah, I don't believe it's sustainable. Thought I'd enjoy a graph while I had the chance Quote:
People jumping on will assuredly bring the good run to an end! Yep, thanks for the email. Good stuff, but yet to apply. As for the performance of the Monte Carlo simulation, 2 graphs are attached. One for this round, one for the past two rounds (though I found a couple of cutandpaste errors which made around half a dozen of my estimates for each game wrong, this week  so there's a few wronguns in with last round's estimates). A long scroll down (don't know why, but it's formatted neatly, at least) is a table for markets where I thought I had an edge PLUS reasonable confidence in the result (the "bet at least 8.5% of bank" marker that I mentioned in an earlier post).

#49




Just missed the editing window....
I meant to add that of those 12 FAILs above, 7 of them only failed courtesy of a 78th minute try in the WarriorsTitans game and a 77th minute try in the BroncosEels game (NRL Games are 80 minutes long). So they didn't seem unreasonable wagers to be confident about. 2 further wagers were also above the $3.50 ceiling that I'd previously noted. 
#50




walkermac, ran my eye over those results and noticed a few things.
If you only bet once per market (i.e. not taking all different pick your own lines for the same game) it remains profitable and I worked it out to be: +7.44 units 8 wins, 7 losses If you only bet where the expected growth is >2.00% : +62.71 units 31 wins, 2 losses If you only bet where the expected growth is >3.00% : +32.35 units 12 wins, 0 losses Whatever your doing its working and i'd be very interested as to if/how it could be applied to the AFL as well. Maybe something we can discuss via email if you don't wish to bog down this thread. I'm sure there are many ways you could filter these selections to be profitable but certainly seems your on the right path thats for sure. 
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