Archive for February, 2017
Ah, gift cards. The perfect present when you want to say, “I was too busy to go to the mall and buy you a gift.”
And if you want to say, “In fact, you’re so unimportant, I bought your gift card while I was eating breakfast,” then head to a pancake house.
That’s right. Our local pancake shop is now offering gift cards — and, boy, do they have a great sale! Check this out…
You smell it coming, don’t you? No, not a stack of pancakes! I’m referring to the math question on the other side of that image.
Which is the best deal?
One way to attack this problem is to compare the free amount to the original price. That is, which fraction is greatest: 2/15, 4/25, 7/50, 11/75, or 15/100?
Ack. Too much work.
A better way is to do a piece-wise comparison:
- Which is better, $15 or $25? Clearly the $25. You get twice as much free for only $10 more.
- Which is better, $25 or $50? Well, two $25’s will get you $8 free, but for the same price, you’ll get one $50 card and only $7 free. So, the $25 card wins again.
- Which is better, $25 or $75? Well, three $25’s will get you $12 free, but for the same price, you get one $75 card and only $11 free. Don’t look now, but $25 is on a roll.
- Which is better, $25 or $100? Well, four $25’s will get you $16 free, but for the same price, you get one $100 card and only $15 free. There you have it, $25 is the champ.
Now that that’s out of the way, you can probably anticipate my next question.
Who the hell came up with this pricing scheme?
It’s not typical to get a smaller reward when you spend more money. Usually, the more you spend, the more you get free. Then again, it’s a pancake shop. Maybe they did some significant market analysis, recognized that no one could actually spend $100 on pancakes, and since $25 is a more common breakfast total, that’s the one that gets the biggest reward.
Or, maybe they just goofed up the math.
Sorry, I know no jokes about gift cards. But here are a couple about finance.
Why didn’t the mathematician report his stolen credit card?
The thief was spending less then his wife.
We didn’t exceed the budget. The allocation simply fell short of expenses.
I’m flat broke, so my financial advisor recommended plastic surgery: cut up all my credit cards.
How awesome was Anthony Davis last night? In a word: very. He set a new All-Star Game scoring record with 52 points, adding 10 rebounds and 2 steals.
(Disclosure: I’ve liked A.D. since he was one-and-done at Kentucky. But it wasn’t until last night that I bought an Anthony Davis jersey:
But as much as I like A.D., I couldn’t help thinking that there needs to be an asterisk next to this new All-Star scoring record. If you only look at points, sure, 52 > 42, so Davis scored more points last night than Wilt Chamberlain scored in the 1962 All-Star Game. But that’s only a part of the mathematical story.
First, let’s talk scoring percentage. In 1962, the final score of the game was 150‑130, meaning that Chamberlain accounted for 15.0% of all scoring. The final score of last night’s game was 192‑182, meaning that Davis accounted for 13.9% of all scoring. Chamberlain gets the nod, but only slightly, and I’ll admit it’s not insignificant that Davis only played 31 minutes last night, while Chamberlain played 37 minutes in 1962. So, maybe this is a push.
But let’s consider shooting percentage. Last night, both teams combined for 55.5% shooting, whereas in 1962, they managed just 43.8% shooting. Perhaps the all-stars from 50 years ago just didn’t shoot as well as players today? Actually, that’s somewhat true: The league FG% for 1961‑62 was 42.6%, the league FG% for 2016‑17 (so far) is 45.6%. But the all-stars last night were 9.9% above the league average, whereas the all-stars in 1962 were just 1.2% above their league average, suggesting that the defense in New Orleans was negligible at best. Which brings me to my next point…
Let’s talk defense. Maybe the combined 374 points that were scored last night doesn’t convince you that defense was nonexistent. Then how about this: In the 1962 game, there were 62 personal fouls. Last night, there were only 16. Even more stark, though: In 1962, all-stars shot 95 free throws during the game; last night, they only shot 8. That’s not a typo, and it’s a pretty clear indication that no one was making much effort to contest shots.
Davis played a great game, but it doesn’t feel right that he unseats Chamberlain, given the circumstances. Not to mention, Chamberlain played a more complete game — shooting 73% from the field, grabbing 24 rebounds, and adding 1 assist.
This brings me to my final point, proportions. The teams last night scored 1/3 more points than their 1962 counterparts, and if you take away that extra third from Davis, he’d have ended the night with 39 points. So if an asterisk is good enough for Maris’s 61 and Flo-Jo’s 10.49, then it ought to be just fine for Davis’s 52, too.
But it is what it is. Congratulations, Anthony Davis.
Looking at the math of basketball is something I get to do quite a bit these days. Discovery Education has formed a partnership with the NBA, and we’re creating a collection of “problems worth solving” using NBA stats and highlight videos. Wanna see some of what we’ve done? Check out www.discoveryeducation.com/NBAMath.