Posted by Johnnymac 9:40 AM
A sort of bad beat story

Champ Canonico and I have played fantasy football together for the past 6 years and every year we end up in a very competitive league on ESPN. We also tend to game the schedule in such a way that we end up playing against each other only once a year and this year our head-to-head matchup happened to occur late enough in the season to be quite relevant to the playoff chase in our league - going into this past weekend, we were both hanging on the cusp of qualifying for the playoffs and needed a win to stay alive.

Chris started strong with Marvin Harrison's big game on Thanksgiving day, and he stayed strong with a couple of huge games from both of the Cincinnati Johnsons, Rudi and Chad. I got strong performances from Donovan McNabb and Willis McGahee on Sunday (I DRAFTED McGahee back in August, btw) and was able to keep it close and the whole thing came down to last night's MNF game and my last remaining player, Isaac Bruce. Going into the game last night, Chris had me by 20 points, which, according to our FFL rules, is the equivalent of 140 yards and a touchdown, or 80 yards and two touchdowns, both of which would be slightly better than any game Bruce had played this year, but not necessarily an impossible outcome to expect.

If you watched the game you know that Ike had his best game of the year - 170 yards and a touchdown - 23 pts! (17 + 6) Unfortunately, he had a fumble earlier in the game and a second fumble with less than a minute to go, and even more unfortunately, our league deducts 2 points apiece for turnovers. Voila, my 23 points turned to 19 points and Chris defeated me by one point. I went to bed before the end of the game last night and I was rather disappointed when I saw the results this morning. I was eliminated from playoff contention, and, thanks to tiebreakers, Chris was also eliminated, even in victory.

That's the bad beat narrative of this post, but the more interesting part is that in the resulting trash talk this morning, Chris and I got into an argument over who was more "lucky", and that's what I want to share here. Specifically, while the underlying stats themselves don't mean anything to this discussion, our respective point totals of 125 and 124 were both significantly above our weekly averages this season, and as my weekly average was 10 points higher than Chris going into this weekend, my position is that Chris was the lucky one, and in fact, when I applied all of this to a "normal"* distribution, this is what I got:




*(I couldn't use a normal distribution because my sample size of 12 weeks isn't large enough, therefore I had to use the less accurate t-distribution)

The meaning of all of this is that, based on my team's performance throughout this football season, I can expect to score 124 (or more) points only 15.2% of the time, and accordingly, Chris can expect to score 125 (or more) points, 9.6% of the time. Based on these results, it would appear that we were both quite lucky this week because we were both significantly higher than our respective weekly averages, but Chris was slightly more lucky because his weekly mean was lower to begin with. The really interesting part of all of this is that the odds of us both doing as well as we did was only 1.5%! (.152 x .096)

Well, I pointed this out to Chris and he made a keen observation - that perhaps the statistical significance of our teams is not as important as the statistical significance of the individual players - specifically, he was quick to point out that Willis McGahee was the top rated running back on Sunday and that his performance had been "lucky". I retorted that Rudi Johnson was the 2nd best back and that his performance compared to previous weeks was much more lucky than McGahee's, and so we were back to the statistical analysis.

One of the few points We agreed that 4 players were significantly better than their average performance and thus affected the results of the FFL game: Rudi Johnson (Chris), Chad Johnson (Chris), Willis McGahee (JohnnyMac) and Ike Bruce (Johnny Mac).

And this is what we got:




Hmmm... Who got luckier?

Chris, whose running back was a 97% longshot to score as many points as he did, or me? Similarly, was Chris not "lucky" in that the Browns gave up 58 points and thus gave up enough points that two players on the same team had multi-touchdown games? Which, incidentally, in my opinion, is a violation of an unwritten FFL rule of starting a WR and RB from the same team and is thus analogous to taking insurance in Blackjack?

Now, I will admit that the stats above for McGahee only count from weeks 6 onward, because he wasn't the full-time starter until Oct 17 against Miami, and, when I showed these data to Chris, his first remark was, "Willis McGahee's average is too high," so the grounds for dissent are sown. That said, I went back and calculated these results using McGahee's stats for the full season, and while they certainly push his t-stat back in the direction of Rudi Johnson, McGahee is still better and I will repeat that Johnson has been starting all year and McGahee was having to share time in September and October with Travis Henry... so OF COURSE his averages should be lower. So even with a bigger sample size and a better team, Rudi's performance was STILL more unusual than Willis's.

I think we know who got lucky, and it wasn't me.

But then again, just like poker, the winner is all that matters in the end.



Also - in the interest of full disclosure, this link will take you to a page that has links to all of the relevant data discussed here. If someone can do a better job of this analysis, or if you find an error in mine, please send me an email and I'll be happy to post your comments. I am not at all a statistical guru and freely admit it.

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