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
Julia
<lang julia>function 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 vector of pairs of horse to pair of weight adjusted rating and whether colt (1 == yes, 0 == no)
m = ["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]
# sort in descending order of rating sort!(m, lt = (x, y) -> first(last(x)) > first(last(y)))
# show expected result of race
println("Race 4\n")
println("Pos Horse Weight Dist Sex")
pos = ""
for x in eachindex(m)
wt = last(last(m[x])) == 0 ? "8.11" : "9.00"
dist = x == 1 ? 0.0 : (first(last(m[x - 1])) - first(last(m[x]))) * 0.5
if x == 1 || dist > 0.0
pos = "$x"
elseif !occursin("=", pos)
pos = "$(x - 1)="
end
sx = last(last(m[x])) == 0 ? "filly" : "colt"
println(rpad(pos, 4), rpad(first(m[x]), 7), rpad(wt, 8), rpad(round(dist, digits=1), 6), sx)
end
# expected time of winner (relative to A's weight adjusted time rating in first race)
t = 96.0 - (first(last(first(m))) - 100) / 10
min, sec = divrem(t, 60.0)
println("\nTime $min minutes and ", round(sec, digits=1), " seconds.")
end
main()
</lang>
- Output:
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 1.0 minutes and 35.4 seconds.
Nim
<lang Nim>import algorithm, math, strformat, strutils
- Ratings on past form, assuming a rating of 100 for horse A.
var
a = 100.0 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 var j = a - 3 + 10 * 0.2
- Filly's allowance to give weight adjusted weighting.
b += 3 d += 3 i += 3 j += 3
- Create table mapping horse to its weight adjusted rating and whether colt.
type Pair = tuple[key: char; value: tuple[rating: float; colt: bool]] let list: array[10, Pair] = {'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)}
- Sort in descending order of rating.
let slist = list.sortedByIt(-it.value.rating)
- Show expected result of race.
echo "Race 4\n" echo "Pos Horse Weight Dist Sex" var pos = "" for i, (key, value) in slist:
let wt = if value.colt: "9.00" else: "8.11"
var dist = 0.0
if i > 0: dist = (slist[i-1].value.rating - value.rating) * 0.5
pos = if i == 0 or dist > 0: $(i + 1)
elif not pos.endsWith("="): $i & '='
else: pos
let sx = if value.colt: "colt" else: "filly"
echo &"{pos:<2} {key} {wt} {dist:3.1f} {sx}"
- Weight adjusted rating of winner.
let wr = slist[0].value.rating
- Expected time of winner (relative to A's time in Race 1).
let t = 96 - (wr - 100) / 10 var min = int(t / 60) var sec = t mod 60 echo &"\nTime {min} minute {sec:.1f} 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
Phix
Disclaimer: I know nothing about horse racing, all calculations were reverse-engineered from those in the Go entry.
Made table-based so you can plug in different races and adjustments, but any horse appearing in more than one race input would too in the output.
with javascript_semantics requires ("1.0.1") // [else sort_columns() needs a deep_copy()] enum Colt, Filly constant cf = {"colt","filly"} enum Runners, Time constant races = { // (with F adjusted, plus the prediction) {{{"A", 9,00, 0.0, Colt}, {"B", 8,06, 2.0, Filly}, {"C", 9,04, 1.5, Colt}},"1min 36s"}, {{{"D", 8,10, 0.0, Filly}, {"E", 9,03, 1.0, Colt}, {"F", 9,07, 3.0-2, Colt}},"1min 36.4s"}, {{{"G", 8,04, 0.0, Colt}, {"H", 8,10, 1.5, Colt}, {"I", 9,05, 0.5, Filly}},"1min 35.8s"}, {{{"J", 8,11, 0.0, Filly}},"1min 35.8s"}} constant adjusts = columnize({{"B",+4}, {"C",-4}, {"H",+3}}) function str2time(string t) sequence r = scanf(t,"%dmin %fs")[1] return r[1]*60+r[2] end function sequence horses = {} string name, pos = "" integer stone, pounds, sex atom wt, dist, rating for i=1 to length(races) do sequence runners = races[i][Runners] atom s = str2time(races[i][Time]), distt = 0 for j=1 to length(runners) do {name, stone, pounds, dist, sex} = runners[j] distt += dist pounds += stone*14 rating = pounds+934-10*s-distt*2 -- (make "A" a nominal 100) integer k = find(name,adjusts[1]) if k then rating += adjusts[2][k] end if if sex=Filly then rating += 3 end if horses = append(horses,{name,sex,rating}) end for end for horses = sort_columns(horses,{-3}) printf(1,"Race 4\n\nPos Horse Weight Dist Sex\n") for i=1 to length(horses) do {name,sex,rating} = horses[i] wt = iff(sex=Colt?9.00:8.11) dist = iff(i=1?0:(horses[i-1][3]-rating)*0.5) if i=1 or dist>0 then pos = sprintf("%d",i) elsif not find('=',pos) then pos &= '=' end if printf(1,"%-2s %s %.2f %3.1f %s\n", {pos, name, wt, dist, cf[sex]}) end for // weight adjusted rating of winner rating = horses[1][3] // expected time of winner (relative to A's time in Race 1) atom t = str2time(races[1][Time]) - (rating-100)/10 string m = elapsed(floor(t/60)*60), s = elapsed(remainder(t,60)) printf(1,"\nTime %s %s\n", {m,s})
- 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 35.4s
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