Horse racing
- Background
In three recent races at Rosetta Park, the results have been:
Race 1
| Pos | Horse | Weight | Dist | Sex |
|---|---|---|---|---|
| 1 | A | 9.00 | 0.0 | Colt |
| 2 | B | 8.06 | 2.0 | Filly |
| 3 | C | 9.04 | 1.5 | Colt |
Time 1 minute 36.0 seconds
Race 2
| Pos | Horse | Weight | Dist | Sex |
|---|---|---|---|---|
| 1 | D | 8.10 | 0.0 | Filly |
| 2 | E | 9.03 | 1.0 | Colt |
| 3 | F | 9.07 | 3.0 | Colt |
(F was slowly away and lost 2 lengths at the finish as a result)
Time 1 minute 36.4 seconds
Race 3
| Pos | Horse | Weight | Dist | Sex |
|---|---|---|---|---|
| 1 | G | 8.04 | 0.0 | Colt |
| 2 | H | 8.10 | 1.5 | Colt |
| 3 | I | 9.05 | 0.5 | Filly |
Time 1 minute 35.8 seconds
It is assumed that:
1. Weights carried are expressed in stones and pounds (traditional in US and UK racing) where 1 stone equals 14 pounds.
2. The distances are the actual distances between horses at the finish of the race.
3. All races are run at 1 mile in similar going and weather conditions and the time shown is the time taken by the winner to run the race.
4. 2 pounds slows a horse down by 1 length at the finish.
5. 1 second is equivalent to 5 lengths at the finish.
- Task
All 9 of these horses, plus a further horse J, are due to compete against each other in Race 4 at Rosetta Park again over 1 mile and in similar conditions to the earlier races. Colts will carry 9.00 and fillies 8.11.
Suppose that:
1. Horse B has been moving well on the galops and her trainer thinks she has improved 4 pounds since her last outing.
2. Horse C has had a setback in training and his trainer expects him to perform 4 pounds below his best.
3. Horse H is being ridden by the champion jockey which is expected to improve his performance by 3 pounds compared to what it would otherwise have been.
4. Horse J, a filly, has never run before but her performance on the galops suggests she can run 1 mile in 1 minute 35.8 seconds when carrying 8.11.
Other things being equal (which they seldom are in actual horse racing!) what would you expect the full result of Race 4 to be including the time of the winner?
Go
<lang go>package main
import (
"fmt" "sort" "strings"
)
func main() {
// ratings on past form, assuming a rating of 100 for horse A a := 100 b := a - 8 - 2*2 // carried 8 lbs less, finished 2 lengths behind c := a + 4 - 2*3.5 d := a - 4 - 10*0.4 // based on relative weight and time e := d + 7 - 2*1 f := d + 11 - 2*(4-2) g := a - 10 + 10*0.2 h := g + 6 - 2*1.5 i := g + 15 - 2*2
// adjustments to ratings for current race b += 4 c -= 4 h += 3 j := a - 3 + 10*0.2
// filly's allowance to give weight adjusted weighting b += 3 d += 3 i += 3 j += 3
// create map of horse to its weight adjusted rating and whether colt (1 == yes, 0 == no)
m := map[string][2]int{
"A": {a, 1},
"B": {b, 0},
"C": {c, 1},
"D": {d, 0},
"E": {e, 1},
"F": {f, 1},
"G": {g, 1},
"H": {h, 1},
"I": {i, 0},
"J": {j, 0},
}
type kv struct {
key string
value [2]int
}
// convert to slice of kv
l := make([]kv, len(m))
x := 0
for k, v := range m {
l[x] = kv{k, v}
x++
}
// sort in descending order of rating
sort.Slice(l, func(i, j int) bool { return l[i].value[0] > l[j].value[0] })
// show expected result of race
fmt.Println("Race 4\n")
fmt.Println("Pos Horse Weight Dist Sex")
pos := ""
for x := 0; x < len(l); x++ {
wt := "9.00"
if l[x].value[1] == 0 {
wt = "8.11"
}
dist := 0.0
if x > 0 {
dist = float64(l[x-1].value[0]-l[x].value[0]) * 0.5
}
if x == 0 || dist > 0.0 {
pos = fmt.Sprintf("%d", x+1)
} else if !strings.HasSuffix(pos, "=") {
pos = fmt.Sprintf("%d=", x)
}
sx := "colt"
if l[x].value[1] == 0 {
sx = "filly"
}
fmt.Printf("%-2s %s %s %3.1f %s\n", pos, l[x].key, wt, dist, sx)
}
// weight adjusted rating of winner wr := float64(l[0].value[0])
// expected time of winner (relative to A's time in Race 1)
t := 96.0 - (wr-100)/10
min := int(t / 60)
sec := t - float64(min)*60
fmt.Printf("\nTime %d minute %3.1f seconds\n", min, sec)
}</lang>
- Output:
Race 4 Pos Horse Weight Dist Sex 1 I 8.11 0.0 filly 2 J 8.11 2.0 filly 3 A 9.00 1.0 colt 4 F 9.00 0.5 colt 5 H 9.00 0.5 colt 6 E 9.00 0.5 colt 7 D 8.11 1.0 filly 7= B 8.11 0.0 filly 9 C 9.00 1.0 colt 10 G 9.00 0.5 colt Time 1 minute 35.4 seconds
Wren
<lang ecmascript>import "/fmt" for Fmt
// ratings on past form, assuming a rating of 100 for horse A var a = 100 var b = a - 8 - 2 * 2 // carried 8 lbs less, finished 2 lengths behind var c = a + 4 - 2 * 3.5 var d = a - 4 - 10 * 0.4 // based on relative weight and time var e = d + 7 - 2 * 1 var f = d + 11 - 2 * (4 - 2) var g = a - 10 + 10 * 0.2 var h = g + 6 - 2 * 1.5 var i = g + 15 - 2 * 2
// adjustments to ratings for current race b = b + 4 c = c - 4 h = h + 3 var j = a - 3 + 10 * 0.2
// filly's allowance to give weight adjusted weighting b = b + 3 d = d + 3 i = i + 3 j = j + 3
// create map of horse to its weight adjusted rating and whether colt var m = {
"A": [a, true], "B": [b, false], "C": [c, true], "D": [d, false], "E": [e, true], "F": [f, true], "G": [g, true], "H": [h, true], "I": [i, false], "J": [j, false]
} // convert to list of {key, value} map entries var l = m.toList
// sort in descending order of rating l.sort{ |i, j| i.value[0] >= j.value[0] }
// show expected result of race System.print("Race 4\n") System.print("Pos Horse Weight Dist Sex") var pos = "" for (x in 0...l.count) {
var wt = l[x].value[1] ? "9.00" : "8.11"
var dist = 0
if (x > 0) dist = (l[x-1].value[0] - l[x].value[0]) * 0.5
pos = (x == 0 || dist > 0) ? (x+1).toString : (!pos.endsWith("=") ? x.toString + "=" : pos)
var sx = l[x].value[1] ? "colt" : "filly"
Fmt.print("$-2s $s $s $3.1f $s", pos, l[x].key, wt, dist, sx)
}
// weight adjusted rating of winner var wr = l[0].value[0]
// expected time of winner (relative to A's time in Race 1) var t = 96 - (wr - 100) / 10 var min = (t/60).floor var sec = t % 60 System.print("\nTime %(min) minute %(sec) seconds")</lang>
- Output:
Race 4 Pos Horse Weight Dist Sex 1 I 8.11 0.0 filly 2 J 8.11 2.0 filly 3 A 9.00 1.0 colt 4 F 9.00 0.5 colt 5 H 9.00 0.5 colt 6 E 9.00 0.5 colt 7 B 8.11 1.0 filly 7= D 8.11 0.0 filly 9 C 9.00 1.0 colt 10 G 9.00 0.5 colt Time 1 minute 35.4 seconds